Home

Chapter 1 - Biblioteca CIO

1. Lastly a software user friendly platform is being developed which will enable the user not only to visualize the results in real time but also to control specific features of the system such as mechanical rotation start pause and stop measurement create a datalog for various successive measurements and specify the number of measurements for the system to make automatically without any needed intervention from the user V STOW Analysis Strengths Opportunities Weaknesses Threats Mexico and the rest of Latin America might prefer Continuous system Significantly lower upgrade for other System still under cost compared to similar systems acquiring this system for its lower cost shipping and customs expenses development instruments in the market Works in both transmission and reflection No similar system manufactured within the country Lacking mechanical and electrical design of mount Worldwide renown manufacturers as main competitors Development of system not over costly Food and pharmaceutics industry relatively strong in the Country Lacking funding for equipment acquisition i e CCD Camera People might prefer a much more costly system manufactured in the US or Europe Mechanical mount for different types of samples and functioning modes Medical instrumentation is getting stronger in the country among universities and hospitals Dependence on another
2. 1p F capacitor 7 5 pF capacitor 100 nF capacitor Power Source 15 V Metallic encasing for the circuit in order to minimize noise Acquisition and transmission card currently under development This card is to be designed and manufactured by the research team with two objectives in mind first to reduce the cost of the entire product and second to make the system as independent from other companies as possible Additionally this card will be designed specifically for the system that is to say it will be made to meet the particular needs of the instrument including sampling rate required signal outputs and inputs and voltage specifications This card will be controlled via the instrument s software which is also under current development The list of components that will be used for the card is shown in the table below Element System Quantity PIC18F4553 MASTER PROG SOCKET QUARTZ CRYSTAL USB CONNECTOR USB CABLE BREADBOARD CABLE mtr N l Currently the photodiode model 13 DSH 005 from Melles Griot is being used 99 CONNECTORS 15 RED LEDS 2 GREEN LEDS 2 Micro switch 4 FENOLIC PLATES 3 PNP BLUE SHEETS 3 NE555 3 IC AD823AN 6 DIODES 6 DIODE BRIDGE 1 TRANSF 1 MC7912 1 MC7812 1 ZENER DIODE 2 FERRIC CLORIDE 1 CP DE 100UF 5 CP DE 4
3. 38 Fig 3 3 Ideal output of system for a retardance of a half a wave A x and b 1 5 waves A 3z Using a commercial photoreciever New Focus Model 1801 the above signals can be obtained using the experimental setup shown in figure 3 2 Fig 3 4 Output signals obtained using a New Focus photodetector with a retardance of a half a wave A and b 1 5 waves A 31 Detector Since the instrument ought to be independent from commercial equipment besides the modulators a photodetector system was to be developed in order to detect the signal The design was based on the performance characteristics from the commercial one The photodetecting system consists in itself on different stages which shall now be analysed separately the better to describe its overall operation As stated in the previous chapter a silicon PIN photodiode was selected for this system due to its spectral response more specifically to its high sensitivity to red light Considering the operating frequency of both photoelastic modulators 45 KHz and 47 KHz respectively it is advisable that the response speed of the detector be several times these frequencies Since the response of PIN photodiodes is 39 fast enough for this case and for simplicity purposes it was decided to use this type of diode in the project Two different photodiode models were tested whose characteristics are shown on Table 3 2 Let it be note
4. 0 7 1 00E 00 5 54E 01 3 91E 02 8 31E 01 0 6 1 00E 00 6 50E 01 3 14E 02 7 60E 01 0 5 1 00E 00 7 66E 01 1 35E 02 6 42E 01 0 4 1 00E 00 9 87E 01 7 69E 04 1 62E 01 0 3 1 00E 00 9 93E 01 4 40E 03 1 17E 01 0 2 1 00E 00 9 96E 01 5 93E 03 8 95E 02 0 1 1 00E 00 1 00E 00 1 18E 02 2 25E 02 0 0 1 00E 00 1 00E 00 2 05E 02 1 22E 02 0 1 1 00E 00 9 99E 01 3 24E 02 1 93E 02 0 2 1 00E 00 9 71E 01 4 79E 02 2 33E 01 0 3 1 00E 00 9 30E 01 5 64E 02 3 64E 01 0 4 1 00E 00 8 88E 01 5 08E 02 4 56E 01 0 5 1 00E 00 7 89E 01 4 67E 02 6 13E 01 0 6 1 00E 00 6 84E 01 4 18E 02 7 29E 01 0 7 1 00E 00 5 44E 01 3 73E 02 8 38E 01 0 8 1 00E 00 4 01E 01 3 23E 02 9 15E 01 0 9 1 00E 00 2 65E 01 2 76E 02 9 64E 01 1 0 1 00E 00 1 43E 01 2 14E 01 9 66E 01 Table 4 4 Stokes vectors for each of the generated ellipticities at 90 It must be noted that these results were taken after various adjustments had been made to the system which is the reason why the normalised Stokes parameters are much closer to the ideal values than was the case for the linear polarisation results These same results are graphed in figure 4 7 1 50E 00 1 00E 00 5 00E 01 0 00E 00 5 00E 01 4 S1 AH S2 4 S3 1 00E 00 1 50E 00 Figure 4 7 Curves representing the last three Stokes vectors for each of the elliptical polarisations oriented a 90 and ellipticities varying from 1 to 1
5. 0136 9638 606 0 1768 PTA 4 6 ml ders o21m onee 02332 o 0054 0 1464 0 0498 0 9718 If we compare the above matrices to the ideal ones it is clear that the obtained results differ from the expected ones though a tendency to either 0 or 1 is apparent in each case none of the values with the exception of those in the first row actually reaches O or 1 This suggests as stated above a certain amount of inaccuracy both in the optical elements used for the analysis and the instrument itself 4 2 2 Repeatability and Precision Using the same three media as in the previous section i e air quarter wave plate retarder and half waveplate retarder a series of 5 measurements for each of them was performed in order to test the repeatability and precision of the system The graphed results for the three cases are shown on figures 8 10 73 Mueller matrix elements average for HWP fo 5 w 15 20 05 1 5 Figure 4 8 The sixteen Mueller Matrix elements averaged throughout five different measurements along with their respective error in black for a 1 2 retarder Mueller Elements Average for QWP 1 5 1 0 5 0 a a aa San ef E 1 2 3 4 5 6 3 g 9 10 11 12 13 14 15 16 0 5 A s 1 5 Figure 4 9 The sixteen Mueller Matrix elements averaged throughout five different measurements along with their respective error
6. 71 Although the above curves do not display an ideal pattern the behaviour and trend do match the expected results thus ensuring that the system is indeed functioning adequately 4 2 1 Results for different media and comparison to ideal response Listed below are the Mueller Matrices for three different common media air quarter waveplate retarder and halfwave plate retarder These media were selected to perform a series of test using the completed instrument in order to characterise the system and locate sources for inaccuracies and errors 1000 0100 M 4 1 R 10010 oY 0001 100 0 010 0 Mowe 712 5 SE ee 4 2 001 0 10 0 0 01 0 0 M 7 4 3 mE lo 1 9 4 3 00 0 i Let us bear in mind however that these three matrices represent the ideal elements Nevertheless in reality as we know no optical element is one hundred percent ideal Along with this the system is still bound to have a certain amount of error It is for these two reasons that the obtained results we present although approximate to what was expected are not necessarily the best possible ones After a series of measurements the averages of the obtained results are as follows 72 1 0 0 0 0028 996 0 08175 0 007 M ap 4 4 0 0445 0 0033 92675 0 0775 0 027 0 04375 0 0698 9385 1 0 0 0 Mog 212 0 007 9824 0 193 0 3046 4 5 JT one 0 0234 0 089 0 0192 9486 0 0052 0 0354 9886 0 0052 1 0 0 0
7. Given that the polarisation state generator PSG is one of the two main stages in the project it is of vital importance to ensure that its constituting elements are functioning correctly for the generated states to be as precise as possible This is why before attempting to make the PSG it was necessary to analyse both LCVRs responses and compare them Given that both LCVRs are the same brand and model in this case the manufactures being ARCoptix it is to be expected that both their responses are the same or at least very similar The selected procedure for these characterisations is simple though the process might be lengthy Using a Helium Neon laser whose wavelength is approximately 633 nm and a commercial polarimeter from Thorlabs this characterisation was possible First off the necessary electrical connections to control each LCVR were made For this particular model the retarder has two banana type connectors with independent voltage polarisation i e it is irrelevant which terminal is connected to ground and which to positive voltage The LCVR ought to be oriented with its fast axis at a 45 angle with respect to the incoming laser beam polarisation Thus the incoming beam was oriented at 45 whereas the LCVR remained horizontal Using a data acquisition card from National Instruments NI DAQ USB 6229 a Labview program was developed in order to inject the LCVR with a square 1 KHz signal at a specific voltag
8. respectively Both LCVRs are controlled by means of a 1KHZ square wave signal of variable amplitude generated by a function generator and controlled via software Depending on the amplitudes of both signals the LCVRs induce a retardation in the light and hence a change in polarisation Specific amplitude values are to be sent to the retarders in order to induce a known polarisation state By applying a series of square signals at different amplitudes and combinations between both LCVRs the required voltage values for achieving the six main polarisation states from an incident linearly polarised beam oriented at 0 were determined The set of voltages fed to the LCVRs and the generated polarisation state in the probe beam are shown on Table 3 1 Polarisation Voltage ee State LCVR 0 V V Linear 0 4 9 0 98 Linear 90 1 599 2 873 Right Circular 2 92 2 245 Left Circular 1 457 4 68 45 5 25 2 227 45 5 4 4 75 Table 3 1 Applied voltages to both LCVRs required to obtain all six main polarisation states 37 Photoelastic Modulators Initial tests were carried out using only one of the modulators evaluating the correct performance of both modulator and detector against the computer generated curves The set up to examine the functionality of the elements consists on pair of linear polarisers oriented perpendicularly with respect from one another null system and a PEM fast axis orie
9. manufacturer regarding the modulators The system is still years away from being launched into the market by which time there may well be a similar yet affordable system already for sale Customers in Mexico wouldn t need to pay import taxes and the shipping would cost considerably less VI Similar Products already on the Market J A Woollam Co Inc 97 Ellipsometry Solutions VASE According to the catalogue information this ellipsometer can be used on materials research such as semiconductors metals and polymers It has a spectral range of 193 to 2500 nm which is achieved using a monochromator Among the mentioned measurement capabilities there are reflection and transmission ellipsometry depolarization and scatterometry Furthermore the device provides an acquisition rate of 0 1 to 3 seconds per wavelength depending on reflectivity of sample though for high accuracy measurements in may take up to 20 seconds per wavelength J A Woollam Co Inc Ellipsometry Solutions M 2000 According to the information provided by the manufacturer this device is a spectroscopic ellipsometer mainly used for thin film characterization It encompasses CCD detection for the entire spectrum i e it is able to measure hundreds of wavelengths simultaneously and offers different configurations One of the most attractive features of this device is its mechanical flexibility The device s mount allows
10. state of light that interacts with them This is due to intrinsic qualities and properties of said materials such as optical activity chirality and reflectivity Applications for Dual PEM Systems range from the medical to the military Depending on the wavelength and other parameters the system enables analysis and characterisation of different materials most of them organic in nature but also certain reflecting materials Such materials are used in medical analysis holography food processing and pharmaceutics among others Dual PEM polarimeters are used in astronomy to study light polarisation from nearby stars and sunspots Another useful application of this system is in optical fibres When a fibre is bent it generates mechanical stress which in turn causes the polarisation state of the light travelling through the fibre to change Light polarisation may also vary depending on the environment the fibre is in Polarimeters are hence used to monitor the polarisation state of light coming out of the fibre Hinds Instrument 2005 Intrinsic qualities of materials have an effect on the way light interacts with them Properties and characteristics such as stress defects reflectivity and polarisation loss may be determined with the instrument by measuring the polarisation state of light after passing through a material Other applications include thin film characterisation as well as laser test and measurement 2 5 Detection Devic
11. 0 0 00 0 05 10 05 0 00 0 ug m o 00 0 0 00 0 05 0 1 05 0 00 0 uc ms o 00 0 0 00 0 0 00 0 05 0 0 05 vol Imo o 00 0o 0 00 OF 0 00 0 05 0 0 05l vg ms 000 0 0 00 0 0 00 0 05 1 0 05 Ve m lo 00 0 0 00 0 0 00 0 05 0 1 05S Ve ms 8 21 Hence one last program was implemented onto the main one which merely gathers the data and calculates the Mueller Matrix of the material under analysis figure 21 displaying the results for the user s perusal figure 22 and sending it as well to a datalog should the user wish to import the results to a spreadsheet later on 61 Mueller Matrix 0 1540 0 01738 0 0303 0 0366 0 02125 0 02042 0 02654 0 00970 Figure 3 21 Subvi which calculates the Mueller matrix from a given set of four Stokes vectors wets od tr trois Sequen Voltage Results Results A mo A pa Meta Be Tete Cd thee Oe a lt n mm gt mn 5 are sor TE a D eee ge CTE AA aA A Ue Y aaiue Ler CATE HOME ODO A E RCE a E ET E N EE EA OT T RT IGE EA N SA OO Ml E Y MOT DIO CE E E IFR IT 7 VI ATI TION SIR Y MD Y 41 00 ASIA OF 1 ADS TT IO E A Y EA Y 1 10 A on Measuring data Moeller Matrix Manned tuua orm uun aan isas ams Figure 3 22 Automatic measurement user panel displaying the Mueller matrix of the sample under study 62 Chapter 4 Results 4 1 Characterisation of elements and system 4 1 1 LCVR characterisation
12. 90 e 7 1 933 3 96 0 90 e 8 1 929 4 17 0 90 e 9 1 925 4 364 0 90 e 10 2 92 2 245 O 0 e 0 4 9 0 98 O 45 e 0 5 25 2 227 O 45 e 0 5 4 4 75 Table 4 2 Applied voltages for generating various polarisation states used for the complete system characterisation Note O stands for orientation and e for ellipticity With these voltages established and the second stage e the polarisation state analyser PSA completed it was possible to verify the correct performance of both stages It must be stated however that the PSA was previously tested using other means to generate known polarisation states such a linear polarisers and waveplate retarders Once more the ThorLabs Polarimeter was used as reference for such measurements A picture of the optical setup for the PSA is shown in figure 4 5 67 Analyser at 22 5 Sample Chopper PEM1 Figure 4 5 Experimental setup for the polarisation state analyser based on two photoelastic modulators 4 2 Characterisation of the system With both stages working and by measuring a series of different states of polarisation both linear and elliptical it was possible to characterise the system Firstly a linear polarisation was generated using the two LCVRs After each measurement the polarisation was rotated by 10 degrees going from 0 to 180 The necessary calculations for determining the 4 Stokes parameters along with ellipticity an
13. acquired data thus simplifying the mathematical analysis Whenever more than one element is rotating they must both do so at the same frequency Azzam 1977 The mathematical analysis for these type of system usually encompasses Fourier analysis of the recorded signal Goldstein 2003 though a weighted least square best fit has also been proven efficient Giudicotti Brombin 2007 Finally it must be stated that when these systems are used as ellipsometers they are of no real use for samples undergoing rapid changes Rotation Fig 2 2 Two mechanical rotation setups suitable for rotation of elements in a polarimeter 2 2 2 Oscillating element polarimeters These systems rotate the polarisation of light using an electro or magneto optical device such as a Faraday cell Goldstein 2003 If the plane of polarisation is 19 rotated in the cell the effect would be the same as mechanically rotating the elements in a rotating element polariser by a proportional angle As stated in last chapter these cells may be driven by a periodic voltage signal thus forcibly requiring a signal generator The most widely used devices are the liquid crystal variable retarders LCVRs For the specific case of LCVRs two of them are required to measure all four Stokes parameters Meadowlark optics 2005 These systems provide for a significantly faster response than those previously described thus proving far more efficient wnen used w
14. from the z axis the electric field representing vector has a constant magnitude but its orientation changes over time in such a way that the vector s head describes a circular route over time Thus the vector in the z 0 plane seems to draw a circle clockwise when seen from the z side in front of the origin Hence this polarisation is called left circularly polarised light 1 2 3 Elliptically Polarised Light Elliptically polarised light may be considered as the general case of polarisation Again if the phases are separated 90 from each other but the component E 0 and E lt Ex then the light will be elliptically polarised with the major axis of the ellipse directed along the x axis If on the other hand E 0 and E lt Ey the major axis of the ellipse will be along the y axis Hence the ellipticity and orientation of the polarisation ellipse will depend on the relative values of E and Ey and on their respective relative phases Similarly to circularly polarised light the electric field vector of elliptically polarised light forms an ellipse through time as seen from the z axis It would appear like a flattened spiral wnen seen from the xy plane figure 3 a b Figure 1 3 Representation of elliptically polarised light represented by the arrows a isometric view b frontal view Another possible way of obtaining elliptically polarised light is with different phases of 0 90 180 and 270 despi
15. have been carried out in their natural habitat These insects often forage wide desertic areas in search of food with no landmarks to guide them back to their nest If for instance the entire sky is to be obscured by a cardboard box the ants pathway becomes erratic rendering the insects unable to find their way back In other experiments the sunlight was shielded from the ants and in its stead a reflection of the sun was projected toward the insects The result was a direction reversal of their course It is not only insects that can see polarisation and use it in their daily lives Research with molluscs has also been carried out with results suggesting they are also able to detect it Exactly what use polarisation is to them is as yet unknown but scientists have theorised it may be used to their advantage in spotting food Some small fishes they feed on have reflecting scales imitating the reflections of light in water rendering them nearly invisible to most predators However these reflections in the fishes scales do not match in terms of polarisation to the scattering produced by incident light on water thus enabling the octopus to distinguish its prey with relative ease Finally a crustacean species commonly known as Peacock Mantis Shrimp has been reported to be able to detect circularly polarised light better in fact than any man made optical device currently in existence Matson 2009 1 5 3 Polarisation in Med
16. high cost of each modulator 20 These systems though popular as a dual PEM system are used in different physical setups involving axis orientation 2 3 The Mueller Matrix Consider the Stokes vector from equation 2 1 with its four parameters represented by o N Nh ha an 3 which together represent the polarisation properties of a given light beam Let us now assume that the beam interacts with a polarising medium whose characteristics are at present unknown The emerging beam will then be represented by a new Stokes vector which we shall represent by So Si Sa e If we represent each of the S where i 0 1 2 3 parameters as a linear combination of the original S parameters we may obtain the following relations Goldstein 2003 So Moso EMS MoS My 2 3a Si Moso m S m S m 38 2 3b S MS m S m S m 83 2 3c S Mso MS MS M338 2 3d In matrix form 2 3 can also be expressed as So Moo Mo My My So sr 2 Mo Mm Mm m S 2 4 S May My M My S Sy Mo M3 Mz MS 3 21 or S MS 2 5 Where S and S are the Stokes vectors and M is the 4 x 4 matrix known as the Mueller Matrix Whenever an optical beam interacts with matter whatever the media its polarisation state nearly always suffer changes Depending on specific properties of the material the polarisation state of the incident beam varies accordingly Some of these variations in polarisations s
17. inducidos en cada una Por otra parte el PSA esta formado por un sistema dual de moduladores fotoel sticos PEM que permiten la medici n de los cuatro par metros de Stokes sin modificar el arreglo experimental La medici n de los 16 elementos de la matriz de Mueller asociados a un medio ptico transparente se lleva a cabo utilizando una sola longitud de onda 4 632 8nm El procedimiento consiste en propagar un haz de luz con cuatro estados de polarizaci n diferentes generados por el PSG a trav s de la muestra y medir los estados de polarizaci n en el haz transmitido empleando el PSA Lo anterior proporciona un sistema de ecuaciones que llevar a la obtenci n de todas las anisotrop as lineales de la muestra bajo estudio birrefringencia lineal circular diatenuaci n lineal circular El sistema utiliza como dispositivo de detecci n un fotodiodo de silicio con etapa de preamplificaci n y un amplificador de amarre de fase para el an lisis de la se al El sistema es controlado por medio de una computadora y una tarjeta de adquisici n de datos de National Instruments El programa de control desarrollado en la plataforma Labview permite al usuario tomar las mediciones de manera manual paso a paso o con una secuencia autom tica Las aplicaciones en donde las bondades de este instrumento de medici n son de gran utilidad incluyen el estudio de materiales para el desarrollo de dispositivos pticos la caracterizaci n de teji
18. is desirable to minimise the effects of light intensity fluctuation and normalise the total light intensity of the incoming beam For this purpose a mechanical chopper was added to the system whose rotation takes place at a regular frequency F of 500 Hz in this case and 44 locking the chopped intensity signal at this frequency using the lock in amplifier once again Guo 2007 The optical chopper model SR540 from Stanford Research Systems can provide a chopping frequency from 4Hz to 3 7 KHz The chopper consists of a disc with a series of equidistant apertures The disc is divided in two sets of apertures the inner series which is closes to the disc s centre chops the beam with one specific frequency fi while the outer series farther from the centre chops at a different frequency fo A self explanatory diagram of these divisions is shown below S02 Figure 3 9 Diagram of slot blade disc used for the chopper unscaled Outer slot blade Frecuency f Inner slot blade Frecuency f The controller for the chopper besides sending the signal to the motor also has two analog outputs in which different reference signals may be read including the square signal that matches the chopping frequency twice the frequency and the sum and difference of the inner and outer frequencies 3 2 2 Full Stokes polarimeter Mathematical Analysis and Interpretation Consider the following optical setup 0 0
19. oL PEM1 PEM2 A Detector Figure 3 10 Schematic of the dual photoelastic based full Stokes polarimeter 45 In which A represents a linear polariser and 6 0 and 6 represent the orientation angle of the PEM1 PEM2 and A respectively and the incident monochromatic beam is polarised with a specific orientation and ellipticity Then the transmitted beam has a Stokes vector Q U V given by IL L 0 P OP ODL 3 6 where P 0 RO PR 4 P 0 R 0 P R 0 L 0 R 0 LR 0 and 1100 1 1 100 La 210 0 0 0 00 0 0 10 0 0 0 1 0 0 P 00 amp Sa 0 0 S Ca 1 0 0 0 R 0 0 Cw E Sag A O FS Cy 0 0 0 0 1 i 1 2 R is the Mueller rotation matrix is the retardance induced by the i th photoelastic modulator and S and C represent the sin x and cos x respectively 46 The signal collected by the photoreceiver D is proportional to the light intensity which is given by the first row of lo 1 1 5 Ayl 40 AU AV 3 7 where A 1 7 2 A C Cna Cao Ca S29 820 0917 54595295200 5 Cog Cra 2000 C4S20520 2050 ay 2 A Es L 829 C20 0 Cp Cr0 5206 0 Sg Sg C29820 0 So S20 Cx 20 0 Ca C20 8 210 20 0 L 9 2 A CS Sa0 0 tSp C4 5200 0 545 692 6 20 0 It can be seen from equation 3 7 that each term is proportional to one Stokes parameter at the input The phase retardation values 4 and 2 induced by
20. of different polarisation states both linear and elliptical were generated using the 2 LVCRs The setup for these retarders was fairly simple merely requiring the first LCVR to be oriented at 45 and the second one to remain horizontal Through trial and error a series of input signals were fed to each LCVR ranging from 0 to 8 volts While fixing one of the input voltages to a specific value the second voltage would be varied gradually until the desired voltages were obtained These voltages were to vary in ellipticity while the orientation remained constant These values were then to be applied to the retarders in order to characterise the finished instrument Furthermore obtaining linear polarisations ellipticity 0 at different orientations was desirable as well for the same reasons Thus the following values were obtained for each of the described state of polarisation 66 ue Voltage Voltage Silvas for LCVR for LCVR 45 V 0 V O 90 e 1 1 457 4 68 0 90 e 9 1 451 4 448 O 90 e 8 1 453 4 193 O 90 e 7 1 455 3 979 0 90 e 6 1 458 3 832 0 90 e 5 1 461 3 639 O 90 e 4 1 467 3 43 O 90 e 3 1 476 3 248 O 90 e 2 1 485 3 143 0 90 e 1 1 55 2 935 0 90 e 0 1 599 2 873 0 90 e 1 2 299 2 855 0 90 e 2 2 31 0 90 e 3 1 985 3 245 O 90 e 4 1 96 3 36 0 90 e 5 1 946 3 57 O 90 e 6 1 939 3 75 O
21. on photoelastic modulators P y P2 A is a linear polariser analyzer and D is a photoreceptor Il Applications Whether in transmission or reflection certain materials can affect the polarisation state of light that interacts with them This is due to intrinsic qualities and properties of said materials such as optical activity chirality and reflectivity Applications for Dual PEM Systems range from the medical to the military Depending on the wavelength and other parameters the system enables analysis and characterization of different materials most of them organic in nature but also certain reflecting materials Such materials are used in medical analysis holography food processing and pharmaceutics among others Properties and characteristics such as stress defects reflectivity polarisation loss and polarisation mode of dispersion may be determined with the instrument Other applications include thin film characterization and laser test and measurement Ill Overview of the Device The device is mainly composed out of two blocks The polarisation generator block and the polarisation analysis block see figure III 1 94 The former is constituted by a linear polarizer P1 with its transmission axis at 0 followed by two liquid crystal retarders LCVR1 and LCVR2 oriented at 45 and 0 respectively Both LCVRs are controlled by means of a 2KHZ square wave signal of variable amplitude generated by a function
22. quantify the optical properties of photosensitive materials to a single wavelength Such a system is able to measure the changes different polarisation states in a beam of light experiment while propagating through a material sample by means of the optical anisotropies it possesses A comparison between experimentally obtained signals and ideal ones is presented Furthermore an approximate of the ideal curved using Bessel functions is also compared in order to establish differences between all three curves Finally a statistical analysis of 16 experimental curves was carried out in each case randomly varying various factors that may influence the quality of the measurements so as to determine the degree of impact of each one of them and thus enhance the system s performance THEORY Suppose that a beam of polarised light S S o Si1 Si2 Si is cast upon a polarimetric system constituted by two photoelastic modulators P4 and P2 with their optical axes oriented at 0 0 y amp 45 respectively followed by a polariser i e analyser A oriented at 9 0 and a photoreceiver The retardance values for P4 and P2 are designated as and respectively whilst the modulating frequencies are and z Thus the outcoming beam may be obtained from the product S AR 0 P R 0 P S 1 84 where 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 A P i 2 0 0 0 0 0 0 cos sin t sino sin r 0 0 0 0 0 0 sin
23. remaining factors as was to be expected it is best to keep the mechanical noise to a bare minimum to have a metallic encasing for the circuitry and use the calcite analyser Curiously the corresponding result for input voltage Vin was 88 somewhat unexpected resulting in a low level voltage which is that of 12 volts as opposed to 15V which it must be said was the value recommended by the manufacturer In the following table a summary of the results is presented Recommended Factor Level Ambient Light High Distance between L Ow modulators Mechanical noise Low Metallic Encasing High Input Voltage Low Analyser Type High Table 2 Recommended values for each of the studied factors Now based on the graph on figure 3 it is necessary to determine which of the factors will be maintained at the recommended level and which are not significant to the measurements thus allowing us to select which level to use not necessarily because it is recommended but because it is more economical From figure 3 it is clear that the effect of both ambient light and distance between modulators is negligent Therefore it is possible to choose either level for these factors without significantly affecting the final result It was then decided to encase the whole system thus blocking the ambient light and simplifying the mechanical design for the system The distance between modulators will also b
24. sin w t cos o sin o t and R x is the rotation matrix The light intensity registered by the photoreceiver p is given by the first row of Ss That is Tp S 9 ZS Zoso sin t IS sin sin t sin o sin w 1 S 2 zlo sin t cos p sin w 1 S In Mueller polarimetry equation 2 is usually expressed in Bessel function terms as 1 1 In S 0 zu gt Vo 9 23 9 cos 20 1 1S 1 E 5PM sinfo 2 5 sin w 1 s 3 sl 9 sin o t Jo o2 24 6 Jeos 2 1 S where J x is the first degree polynomial i This approximation is useful when choosing f1 and f2 and optimising the system for obtaining the Stokes vector from the incident light 0 45 22 5 PEM1 PEM2 A Detector Fig 1 Polarimetric system based on photoelastic modulators PEM and PEM2 85 A is a linear polariser and D a photoreceiver EXPERIMENTAL SETUP One of the modulator s optical axes is oriented at 45 while the second one is set horizontally The retardance value is considered as one of the values under study by comparing the ideal experimental and mathematically estimated curves The detected signal is sent to a computer for processing by means of LabView software The device that is being developed aims to obtain the transmission Mueller matrix of different materials with optical applications thus providing information on various of its properties The obtained results present a root mean square error a
25. surmised UV light being shorter in wavelength than blue is scattered even more strongly and although the human eye cannot see it several other animals are able to detect near UV light and use it for different survival purposes 1 5 2 Seeing Polarisation Besides UV light certain animals mostly insects are also able to detect polarisation Fifty years ago Karl von Frisch studied the bees navigation abilities He discovered that bees used the orientation from the sun to tell their kin the location of food sources When an explorer bee leaves the hive in search of food it locates the position of the sun and can travel relatively large distances up to nearly 4 hours away from the hive before heading straight back Nevertheless the Sun s position will obviously change throughout that period of time In addition Frisch also noted that bees are able to navigate accurately even when the Sun is covered by a cloud or mountain thus realising the Sun s position isn t the bees true compass but rather the polarisation pattern in the sky determined in turn by the Sun itself Through experimentation with Polaroid film Frisch was able to prove his theory and proposed that each segment in the eight segmented bee eye is more sensitive to one specific direction of polarisation thus enabling the bees to detect different orientations 14 Ants are also able to discriminate polarisation in sunlight Pye 2001 Experiments on desert ants
26. th EE ener deae Easier Ot 25 Figure 2 7 Typical spectral response of a silicon photodiode 28 Figure 2 8 Photodiode operating MOdES cecceeceeceeeeeeeeeeeeeeeeeeeeeeeeneeaaaaas 29 Fig 2 9 Lock In Amplifier Functional Block Diagram cececeeeeeeeeeeeeeeees 31 Figure 2 10 Graphical representation of two sinusoidal signals with a phase difference of 90 and the resulting multiplication 32 Fig 3 1 Full Mueller polarimeter 20 scccceccceeeeeeeeeeeeeenesedeesenneceeeeeeeeeeees 37 Fig 3 2 Experimental setup used for the characterisation of the photoelastic modulator oasis iss ere cna See hinds wa ss A 38 Fig 3 3 Ideal output of system for a retardance of half a wave IV WAV SS sls fan cd es A A Gori ead A da eet ks 39 Fig 3 4 Output signals obtained using a New Focus photodetector with a retardance of half a wave and 1 5 WAVES ceseeeeeeeeeeeeeeeeeeeeeeeeeeeneees 39 Fig 3 5 Basic current to voltage Comvertel 6ccccceeeeeeeeeeeeeeeeeeseesseeeces 40 vi Fig 3 6 Current to voltage converter with a bandwidth of BW 1 65 MHz and dark current COMPENSALION ia orcas 42 Fig 3 7 Signals obtained with the developed detector and the commercial A ns ia Dada ce Lod hails 43 Figure 3 8 NI DAQ USB 6229 Data acquisition card from National lnStiumentS os a O 43 Figure 3 9 Diagram of slot blade disc
27. the accuracy of the experimental system previously shown in figure 3 2 The following images were taken using an oscilloscope connected to the two photodetectors The results for both the commercial and the developed detectors are presented 42 Fig 3 7 Signals obtained with the developed detector upper curves and the commercial one lower curves for a retardance of a 0 54 and b 1 54 If we compare the above curves to the ideal ones in figure 3 3 it is possible to conclude that the developed photoreceiver functions correctly and that its performance and bandwidth are suitable for the application at hand NI Data Acquisition Card The bidirectional communication between the system and the computer is controlled via a National Instruments Data Acquisition Card model NI DAQ USB 6229 Figure 3 8 NI DAQ USB 6229 Data acquisition card from National Instruments The technical characteristics for this card are stated in the following table NI DAQ USB 6229 Analog Inputs 32 Analog Outputs 4 Analog Resolution bits 16 Digital I O 48 Digital Resolution bits 32 Input Max Rate S s 250 K Output Max Rate S s 833 K Range V 10 Table 3 4 Technical specifications for National Instruments data acquisition card 43 Commercial Lock in Amplifier Characteristics The lock in amplifier from Stanford Research Systems model SR830 was used for measuring the diff
28. the incidence angle to be modified either manually or automatically It also includes an automated focusing camera feature for more accurate exploration of the sample Teledyne Judson Technologies Policam II Polarimetric Imaging Camera Although still under development this camera is already being promoted among the science community Some of the main features this camera offers are CCD sensors VGA or Megapixel sensor resolution complete Stokes parameter measurement and a spectral bandwidth of 450 670 nm The device will use a Firewire interface VII Required resources and elements As stated in the sections above there are various elements constituting the whole device In this section we shall state both the main and complementary elements required for the system assembly and functioning as well as experts and engineers to put the whole thing together and ensure its correct overall functioning Optical and electro optical elements Light Source white spectrum must include from UV to IR Monochromator Dual System PEM modulators 1 98 Dual System PEM modulators 2 2 linear polarizers select type Photodiode wavelength response from UV to IR high speed response CCD Camera wavelength response from UV to IR Electronic Elements Photodiode pre amplifier not purchased but designed and manufactured by the research team IC AD823AN 2 Identical Photodiodes 3 33 2 Kw resistors 2 100 Kw resistor
29. the propagation through P1 and P2 respectively may be expressed as 6 sin t i 1 2 3 8 where is the phase retardation amplitude and is the modulation angular frequency Using equation 3 8 equation 3 7 is often rewritten by means of the Fourier expansion in terms of the first class Bessel functions sin sin 1 2 J _ 6 sink Dat 3 9 k l and cos sin t J 6 25 J 6 cos 2ka t 3 10 k l In practice the angles 01 92 01 the retardation amplitudes 51 62 and the index order k of the Bessel function expansion are chosen conveniently to simplify the analysis of lo 47 Special Case Circular Polarisation Sensitivity Full Stokes polarimeters may be classified in accordance to their sensitivity to either linear or circular polarisation In this project we shall focus on the latter One set of conditions to be met for obtaining circular polarisation sensitivity in the system are as follow 9 74 0 0 0 7 J 6 3 6 0 and k 1 These settings correspond to an already commercially available dual PEM polarimeter After using equations 3 9 and 3 10 equation 3 7 can be further simplified as ene ee 2 6 cos 2 t J 8 cos t cos t Q FRO cos 2 t U y 9 sin ot J J O sin 2 t sin 2 t PvV 3 11 where 6 0 0 From equation 3 11 it is possible to obtain an approximate value lap for li b
30. the readings to a data log either creating the file or writing in an already existing one Finally the control window also includes a set of buttons for controlling the switching device through the DAQ card and hence the reference signals for the system Write the file path in which you want to create the datalog or create new file TXT or ASCIl File Path 4 C Documents and Settings Administrador Escritorio LIA txt MN Controls Sequence Results Results Il READINGS Theta RM CONTROLS ION Unlocked Overload 0123 4 5 6 7 8 9 WO 11 12 13 14 15 16 17 18 19 Sensitivity fo SWITCHES wi 241 gt gt Ground SYNC filter 0 2 4 6 8 WM 42 14 15 18 2 22 24 2 Notch filt 2we2 Chopper Autoreserve Autophase bi sl 2 gt P a e gt Se 1 in PE A E Reference Signal Autogain o 4 gt eS ca Ex Int Figure 3 18 Control panel for manual operation of system The automatic option of the program enables the user to specify how many measurements to take and performs a sequence for the specified number of times switching among the four different signal references reading each of the amplitudes from the lock in and calling upon the different calculation programmes to obtain the polarisation state of the incident beam Note that after each measurement the program pauses and displays a message to the user asking him or her to realign the elements for the next measurement The program waits u
31. used for the ChoOpper ooccccccccccicnnnncnnnoo 45 Figure 3 10 Schematic of the dual photoelastic based full Stokes polarimetera dia 45 Figure 3 11 Fourier spectrum of the modulated intensity signal using the circular polarisation sensitive configuration for three different states of polarisation linearly polarised light and right circularly PolaniSea lts a aeeoe eaat e aieeaa 50 Figure 3 12 Difference between calculated and incident Stokes parameters while varying a the ellipticity and b the orientation of the incident IgRtDS AO ANA ienirt 51 Figure 3 13 Control program for dual LCVR SySteM cooooccccccccccccconcnanncnnnnnnnnnos 52 Figure 3 14 Digital switch used to control the input of the reference signal for the lock in AMplifier 2 2 2 ccccccceceeeeeseeeeeeeeeessececeneeecteneeeeeeeeeeeeeeeeteessens 54 Figure 3 15 Software simulation for the switching device 54 Figure 3 16 Connection diagram for the SYSteM cc eessesteeeeeeeeeeeeeeeeeeeeeeees 55 Figure 3 17 Control window for Basic Serial Write and Read vVi 08 56 Figure 3 18 Control panel for manual operation of systeM ccseeeeeeeeeeees 57 Figure 3 19 User interface for automatic measurement sequence 58 Figure 3 20 Implementation and control panel of the voltage sequence OM LEMA a 59 Figure 3 21 Subvi which calculates the Mueller matrix from a given set Of four Stoke
32. varying stress in a normally isotropic material An isotropic material will become anisotropic when stressed and will thus induce the same kind of birefringence as an anisotropic crystal like calcite The construction of a photoelastic modulator is shown in figure 1 1 A piezoelectric transducer is a block of crystalline quartz cut at a specific orientation 18 Xcut A metal electrode is deposited on each of two sides and the transducer is cut in such a way that it resonates at a specified frequency f The resonance is uniaxial and is directed along the long axis of the crystal A block of fused quartz is cemented to the end of the transducer The length of the fused quartz is such that it also has f as the fundamental longitudinal resonance When both elements are cemented together resonance of the transducer causes a periodic strain in the fused quartz Signal Input Figure 1 1 The components of a photoelastic modulator Dual PEM Systems in Polarimetry 93 A dual Photoelastic modulator system can obtain all four Stokes vectors simultaneously The typical configuration for such an ellipsometer would be tuning the first PEM P1 at frequency F1 and orientation of 0 and the second PEM P2 tuned at frequency F2 where F2 is slightly different from F1 Furthermore P2 must have an orientation of 45 P2 is then followed by a linear polariser at 0 as shown in figure 1 2 P1 P2 D Fig 1 2 Polarimetric system based
33. 17 Furthermore from these parameters it is possible to obtain the degree of polarisation ellipticity and orientation of the analysed beam Besides there being different measuring systems there are also different components and configurations used in them Aspnes 1976 These mainly include modulating elements detection devices and data processing systems All of them with both advantages and disadvantages An analysis of the most commonly used systems and elements is presented Note that only the systems that are able to measure all four Stokes components will be mentioned Furthermore besides the polarimetry system itself an appropriate data processing system ought to be implemented in order to interpret the results correctly calculate the Mueller Matrix and finally obtain the polarisation state and properties from the sample under study 2 2 Polarimeters that enable measurement of the 4 Stokes Parameters 2 2 1 Rotating element polarimeters The elements that constitute these systems are all linear retarders and polarisers V U Rotating retarder R and rotating analyser A Detector Fig 2 1 Example of a rotating element polarimeter These elements are usually rotated by mechanical or electromechanical means Measurements need to be forcibly taken periodically with a rotation at a continuous speed or making pauses at periodic intervals to take each measure The former method is undeniably the most accurate and fastes
34. 17 17 78 78 79 79 79 79 80 81 84 92 List of Figures Figure 1 1 Representation of linearly polarised light at 45 ee 6 Figure 1 2 Representation of circularly polarised light ccccceeeeeeeeeeeeeeeeeees 7 Figure 1 3 Representation of elliptically polarised light oooonnnccnnnnnnnnnn 8 Figure 1 4 Glan ThomMpsSON PriSmM cccccccccceeeseeeeeeeeeeeeeeeeeeeeceeeeeeeeeaaeeeseseeeeess 9 Figure 1 5 A quarter waveplate retardel c cccceeeeeeeeeeeeeeeeeaeeeeeeneeeeeeeeeees 10 Figure 1 6 Principle of operation of an LOVR ccccccseeseeeeeeeeeeeeeeeeeeeeeeeeeees 11 Figure 1 7 The components of a photoelastic modulator ccceeees 12 Figure 1 8 Polarimetric system based on photoelastic modulator s 13 Fig 2 1 Example of a rotating element polarimeter ceecceeeeeeeeeeeeeeeees 18 Fig 2 2 Two mechanical rotation setups suitable for rotation of elements LFV AL POP ATIF SUC jc ate II A A 19 Fig 2 3 Dual PEM Stokes polarimeter cccececceeceeeeeeeeeeeeeeeeeeeeeeeeeeeaaaeeeees 20 Fig 2 4 Rotating element Mueller polarimeter ceeeeeeeeeeeeeeeeeeeeeeeeees 24 Fig 2 5 Complete Mueller polarimeter based on photoelastic modulators 24 Fig 2 6 Complete Mueller polarimeter based on liquid crystal variable r tarders UC VR A sven bdenSuennzbuxeve
35. 30 08 Photoelastic Modulators Dual Syst 209 070 87 2 418 141 74 Data Acquisition Card Manufactured 3 000 00 1 3 000 00 CCD Camera Edmund Optics 47 812 82 1 Note Prices are in Mexican Pesos 47 812 82 Q Q Q 40 104
36. 7 UF 5 CAP DE 1NF 6 CAP 2200 UF A 25 2 VOLTS CAP 33 PF 10 CAP 47 NF 10 CAP 10NF 10 CAP 470 PF 10 CAP 22 PF 10 CAP 470 PF 10 CAP 27 Pf 2 CAP 100mF 8 CAP 1mF 6 R 4 7K 4 R 470 OHMS 10 R1K 10 R 22k OHMS 10 R 27k OHMS 10 R 15k OHMS 5 R 100k OHMS 5 R 33k OHMS 10 100 Software resources As previously mentioned the system is to be controlled via a computer and its own software From among the different platforms that could enable the creation of this software LabVIEW from National Insttuments was chosen because of the ease of use versatility and tools it offers Furthermore an acquisition card also from National Instruments is currently being used for testing while the system s own card is completed VIII Manufacturing process Mechanical Mount The design and implementation of the mount must go through various stages in order for it to function The mount will have to modes of operation Manual and Automatic This requirement encompasses the need for both a mechanical and an electrical design Requirements for the subsystem are yet to be defined but it will definitely be controlled via the same software generated in LabView and make use of one or more stepper motors for automatic movement Data Acquisition and Transmission Card This card will have essentially two constituent elements the electronical and he programming The control of the data I O will be controlled using a progra
37. ATES 16 00 3 48 00 10x15cm PNP BLUE SHEETS 64 00 3 192 00 For printing circuit boards NE555 7 00 3 21 00 Linear signal generator IC AD823AN 180 00 6 1 080 00 AD823AN DIODES 2 00 6 12 00 1N4004 DIODE BRIDGE 10 00 1 10 00 TRANSF 130 00 1 130 00 12 VOL 1 2 AMP MC7912 10 00 1 10 00 VOLTAGE REGULATOR MC7812 10 00 1 10 00 VOLTAGE REGULATOR ZENER DIODE 6 00 2 12 00 ZENER DIODE 2 WATT FERRIC CLORIDE 71 00 1 71 00 930 ML CP DE 100UF 3 00 5 15 00 ceramic 60 V CP DE 4 7 UF 3 00 5 15 00 ceramic 60 V CAP DE 1NF 3 00 6 18 00 ceramic 60 V CAP 2200 UF A 25 f VOLTS 3 00 2 6 00 ceramic 60 V CAP 33 PF 3 00 10 30 00 ceramic 60 V CAP 47 NF 3 00 10 30 00 ceramic 60 V CAP 10NF 3 00 10 30 00 ceramic 60 V CAP 470 PF 3 00 10 30 00 ceramic 60 V 102 CAP 22 PF 3 00 10 30 00 ceramic 60 V CAP 470 PF 3 00 10 30 00 ceramic 60 V CAP 27 Pf 3 00 2 6 00 ceramic 60 V CAP 100mF 3 00 8 24 00 25 VOLTS MIN CAP 1mF 3 00 6 18 00 25 VOLTS MIN R 47K 1 00 4 4 00 1 2 Watt R_470 OHMS 1 00 10 10 00 1 2 Watt R 1K 1 00 10 10 00 1 2 Watt R 22k OHMS 1 00 10 10 00 1 2 Watt R 27k OHMS 1 00 10 10 00 1 2 Watt R 15k OHMS 1 00 5 5 00 1 2 Watt R 100k OHMS 1 00 5 5 00 1 2 Watt R 33k OHMS 1 00 10 10 00 1 2 Watt Total Cost 6 084 33 Note Prices are in Mexican Pesos The system will include its own funct
38. Centro de Investigaciones en Optica A C CENTRO DE INVESTIGACIONES EN OPTICA A C TESIS POLARIMETRO DE MUELLER COMPLETO BASADO EN RETARDADORES DE CRISTAL LIQUIDO Y MODULADORES FOTOELASTICOS QUE PARA OBTENER EL GRADO DE MAESTRO EN OPTOMECATRONICA PRESENTA Ing Alicia Fernanda Torales Rivera LEON GUANAJUATO ABRIL 2010 A MIS PADRES 11 AGRADECIMIENTOS A mi madre por siempre creer en mi y alentarme a seguir adelante A mi padre por todo el apoyo que siempre me ha dado durante mi vida y particularmente a lo largo de mis estudios de postgrado A mi hermana Ceci por toda la paciencia y cari o que siempre me ha tenido A mis asesores el Dr Geminiano Mart nez Ponce y la Dra Cristina Solano Sosa por todo lo que me ense aron su infinita paciencia y muy especialmente por haberme apoyado y cre do en m desde el principio A mis sinodales el Dr Daniel Malacara Hern ndez y Dr Juan Manuel L pez Ram rez por muy amablemente haber consentido a revisar y evaluar este trabajo Al Dr Sergio Calixto por haberme proporcionado un lugar de trabajo cerca de mis asesores y laboratorio y por todo su apoyo Al Consejo Nacional de Ciencia y Tecnolog a CONACYT y el Consejo de Ciencia y Tecnolog a del Estado de Guanajuato CONCYTEG por las becas que me fueron otorgadas durante mis estudios 111 Summary English sara al ROS 1 Res menm Espa ol tonal ii a did 2 Chapter 1 Introduction 1 1 On
39. Physics London Rashid M 1999 Circuitos Microelectronicos Mexico Thomson Editores p 297 Refr gi r P 2007 Intrinsic Coherence A New Concept in Polarization and Coherence Theory Optics and Physics News Optical Society of America Signal Recovery 2005 The Incredible Story of Dr D P Freeze Technical Note TN 1007 Signal Recovery 2008 The Analog Lock In Amplifier Technical Note TN 1002 Stanford Research Systems 2004 About Lock In Amplifiers Application Note 3 Tuchin V V Wang L V Zimnyakov D A 2006 Optical Polarization in Biomedical Applications Germany Springer Tuchin V V 2009 Handbook of Optical Sensing of Glucose in biological Fluids and Tissues CRC Press Taylor amp Francis Group Urbena R 2006 New Polarisation generator analyzer for imaging Stokes and Mueller polarimetry The international Society for Optical Engineering SPIE W G Jung 2002 Op Amp Applications United States of America Analog Devices Inc Wang B 2005 Dual PEM Systems Polarimetry Applications Hinds Instruments Application Note 83 Appendix A ANALYSIS FOR TRANSMITTED LIGHT INTENSITY FOR A DUAL PHOTOELASTIC MODULATOR SYSTEM A Torales Rivera G Martinez Ponce C Solano Centro de Investigaciones Optica Apdo Postal 1 948 37000 Le n Guanajuato M xico alitorales cio mx INTRODUCTION The construction of a photoelastic modulator based polarimeter has been motivated by the necessity to
40. Polarisation and its importance in Science ooooooonnccciciciniciconocinoconincnnnnnos 3 1 2 Polarisation and CONSTE aia 3 1 2 1 IMG Ar POlaTIS all occas tice alee eters 4 1 2 2 Circular Polarised Lightx 222 ets nt ied dale 6 1 2 3 Elliptically Polarised Light cece seeeeeeeeeeeeeeeeeeeeeeeeeeeeteeeeeeeeeeeee 7 1 3 Polarising Elmer nas 8 Lo 1 Linear PolaiserS oi 8 1 3 2 Glan Thompson PS WM irc a cia 8 1 3 3 Dichroic Sheet PolariSer ooooccnnnnnccccnnncnnncccccoccoooonnnnncnnnnnnnnnnnnnnnos 9 TRE RetardersS ic 9 1 3 5 Birefringent Plate Retarders 2 ccesecesseeeeeeeseecceeetecteeeceeneeeeteeeees 10 1 3 6 Liquid Crystal Variable Retarder LCVR ccccecceeeeeeeeeeeeees 11 1 3 7 Photoelastic Modulator PEM ooooocccccccccccccccccncncncnnnannnnnncnnnnnnnnnns 12 1 4 Dual PEM Systems in PolariMmetry oooociooococconncicorcorcnrenranannnnncnnnannncccaninas 12 1 4 1 Applications of a Dual Modulator System ceeeeeeeeeeeeees 13 1 5 Polarisation in Nature iuiiacionitaaai ricino data 14 1 5 1 Why is the sky blue inci cial ta di da iii 14 1 5 2 Seeing Polaris ON its o 14 1 5 3 Polarisation MEDICOS Aia 15 Chapter 2 Review of Literature 2 A o Sancta gna dione salen e e e eei cpa o wa tiene ee Oraa ERa 17 2 2 Polarimeters that enable measurement of the 4 Stokes Paramelerss cities iacdehe vinceetssedizabnuavatasavicas di 18 2 2 1 Rotating element polarimeters ccccee
41. S3 which ought to be close to zero are in turn smaller than S1 Although further adjustments were still required at this point the graph of these data shows that the behaviour of the results at least was the expected one Stokes Vectors for different orientations 2 50E 01 2 00E 01 1 50E 01 1 00E 01 5 00E 02 0 00E 00 5 00E 02 1 15 17 19 1 00E 01 1 50E 01 2 00E 01 2 50E 01 Figure 4 6 Curves representing the last three stokes vectors for each of the linear polarisations with varying orientation from 0 to 180 The amplitude is given in millivolts 69 As we can see in figure 4 6 S3 remains relatively constant its value nearing zero as ought to be the case for all linear polarisations thus indicating that the input beam had a linear polarisations regardless of the orientation The parameter SO was not included in the graph since it always amounts to one once all four parameters have been normalised As for the elliptical polarisations as stated above the orientation was fixed at a specific angle in this case 90 while the ellipticity was varied from 1 to 1 by 1 each time The results are shown in the table below 70 Ellipticity SO S1 S2 3 1 0 1 00E 00 1 08E 01 1 81E 01 9 78E 01 0 9 1 00E 00 2 38E 01 9 63E 02 9 66E 01 0 8 1 00E 00 4 11E 01 6 30E 02 9 09E 01
42. a aoiatoer aie ouse ainda eens Ge aaa a 74 Figure 4 9 The sixteen Mueller Matrix elements averaged throughout five different measurements along with their respective error for a A 4 AS A A o ys 74 Figure 4 10 The sixteen Mueller Matrix elements averaged throughout five different measurements along with their respective error for Alr 74 Figure 4 11 Elements for the Mueller matrix corresponding to a quarter waveplate retarder throughout a series of measurements with various ht IMtensilOs un E AA 75 List of Tables Table 3 1 Applied voltages to both LCVRs required to obtain all six main Polaris uo States iia 37 Table 3 2 Technical specifications for silicon photodiodes ccccccccccccc 40 Table 3 3 Technical specifications for the AD823 OpaMP ooooooocccocccacccancncncnnnnnos 41 Table 3 4 Technical specifications for National Instruments data acquisition o A A O A A A A A a 43 Table 3 5 Sample list of ASCII commands for the Lock in amplifier 44 Table 4 1 Results for LOVR characteriSation cccccceeeeeeeeeeeeeeeeeeeeeteeeeeeeeeees 64 viii Table 4 2 Applied voltages for generating various polarisation states used for the complete system characterisation cccccceeeeeeeeeeeeeeeeeeeeeeeeteeeeeeeees 67 Table 4 3 Stokes vectors for each of the generated orientations for the linear polarisations in the SyStemM 0 ccccccccc
43. ample Polarimeters also enable the study and analysis of parameters such as the complex refractive index and thickness of thin films The term Polarimetry describes the polarisation properties of light Hence a polarimeter measures and analyses such properties from a beam of light In its simplest form a polarimeter is composed of a polarisation state generator and a polarisation state analyser Together they constitute a closed loop system in which control and feedback is provided to and from the system For this project we will use the terms polarimeter and ellipsometer as equivalent In addition polarimeters may also be classified as Stokes Polarimeters and Mueller Matrix Polarimeters The former merely describes the polarisation state of light through the Stokes Parameters whereas the latter enables the description of the polarisation properties of a material in reflection or transmission The Stokes vector is a set of four parameters which together define the polarisation state of a given beam of light The vector is defined as follows o 2 1 2 Ann na 3 Where So represents the total light intensity of the beam regardless of the polarisation state S4 refers to the linearly polarised components either vertically or horizontally oriented Sz also refers to the linearly polarised components but with 45 of orientation and finally S3 represents the right and left circularly polarised components
44. ansference function and necessary equations to determine the minimum and 40 maximum frequencies the circuit could handle were obtained In the circuit in figure 3 4 C4 denotes the net capacitance Conotodiode Copamp and fy is the Unitiy Gain Bandwidth product GBW which determines the frequency at which the unity gain occurs Analysing the circuit the following equations may be obtained 1 f IRG 3 1 1 ETTA 3 2 O fo f fy f 3 3 Z 3 4 an ar 3 4 5 2n Ro fy Combining equations 3 1 and 3 2 A 3 5 fo 27 Ro C Thus knowing the characteristics for both the photodiode and the operational amplifier it is possible to determine the bandwidth of the circuit From equation 3 5 it may be established that in order to maximise f2 the opamp must have a high fu as well as a low Cin Thus the relationship f Cin allows for an adequate selection of an operational amplifier With this in mind and after having evaluated different models the AD823 IC whose main characteristics are shown in Table Ill was selected AD823 wri Capacitance Cin ey KOR pF pF 16 18 8 9 Table 3 3 Technical specifications for the AD823 Opamp The obtainable bandwidth using the AD823 IC and the Melles Griot diode can be calculated using equations 3 1 to 3 5 Thus the resulting bandwidth is 1 65 MHz with a maximum frequency of 1 868 MHz Since the diode will be inversely polaris
45. arisation of incident light this system would not be adequate by itself 34 Yet another configuration proposed by Hinds Instruments Wang 2005 involves one of the modulators oriented at 45 and the second one horizontally followed by an analyser oriented at 22 5 35 Chapter 3 Methods 3 1 Introduction The full Mueller Matrix polarimeter described here is based on both dual Liquid Crystal Variable Retarders LCVR and Photoelastic Modulator PEM systems The instrument is constituted by two stages a polarisation state generator PSG and a polarisation state analyser PSA The first controls and feedbacks the polarisation state of an incoming red beam at a wavelength of 1 632 8 nm while the second is a full Stokes polarimeter As above mentioned the polarisation state of a beam emitted by a continuous wave He Ne laser is controlled by means of a set of two LCVRs each driven by a periodic voltage signal These signals are computer generated and fed to the phase modulating elements through a Data Acquisition Card The voltage amplitudes are combined according to the desired polarisation state thus providing full knowledge of the initial polarisation state of the light beam before entering the sample under study On the other hand the full Stokes polarimeter measures the four parameters describing the polarisation state of the outgoing beam once it has gone through the sample being analysed The PSA is based on two PEMs an
46. careful selection of the constituting elements as well as an in depth analysis of the overall circuit must be carried out in order to meet the system requirements and obtain usable and reliable data out of the measurements The main characteristic to bear in mind for this kind of application is bandwidth Which means one must be sure to select an appropriate photodiode with a high enough response speed and low junction capacitance As for the operational amplifier to be used it must also provide the necessary bandwidth one requires for the application at hand This opamp is usually selected with the highest unity gain 29 bandwidth product to input capacitance as possible Graeme 1995 The unity gain bandwidth refers to the frequency at which unity gain occurs Neiswander 1975 A more detailed description of analysis and design of the preamplifier stage will be presented later on It has also been proposed Neiswander 1975 Fjarlie 1977 that under harsh environmental conditions such as airborne or space borne monitoring it might be advisable to cool the entire circuit diode and preamplifier stage included up to 200K It has been reported that by doing this dark current and other noise sources may be actively suppressed 2 6 Data Processing System A Lock in Amplifier LIA is a filtering system designed to acquire a particular AC signal buried in noise or other signals and extract it from the rest providing its amplitude a
47. ceeeeeeee cent eens eeeeeeeeees 18 2 2 2 Oscillating element polarimeters cee cece sees eeeeeeeteeeeeeeeeeeeeees 19 2 2 3 Phase modulation polarimeters cceeeeeeeeeeeeeeeeeeeeeaeeeaes 20 2 3 The Mueller Malu id DA 21 2 4 Mueller matrix polarimeter cceceeeeeeeeeeeceeeeceeeeaeesessseesseeeeeeees 23 2 4 1 Rotating element polarimeter coocoonnnncnnininoncoooncccccoteneennnnns 24 2 4 2 Phase modulating polarimeter c eceeeeeeeeeeeeeeeeeeeeeeeeeeeeee 24 2 4 3 Oscillating element polarimeter cceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 25 2 4 4 Applications of a Mueller polarimeter e eeeeeeeeeeeeeeees 26 2 5 Detection Devices Different types of photon detector oooocccccoconnccnnncccnnoo 26 2 5 1 TRe pPRhotomultlplisrtUDe susi di ess 26 PASA pie A O A A 27 2 6 Data processing SYSteM oooococcccccccccccononanononononnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 30 2 6 1 Lock in Amplifier Principle of Operation eeeeeeeeeees 30 2 0 2 Basic TOC Vicio ae RGR ORS 32 2 6 3 Why design and implement a LIA when there are commercial ones available 2 7 Analysis of Different System Configurations based on PEM deVICES cccceeceececceececeeseseees Chapter 3 Methods 3 1 INTO UICN AAA A A 3 2 Optical measurement system description 3 2 1 Constituting elementS ooonnnicnnnnnn ccco 3 2 2 Fu
48. certain degree of consistency their behaviour is not as constant as that of the elements that represent the value of 1 Finally the element maz which for this case should be close to the value of 1 deviates from the ideal value by a significant amount except for the second measurement Yet again apart from the second value the curve s behaviour is relatively constant 76 Chapter 5 Conclusions 5 1 System performance As the results from the previous section have shown there is still work to be done in regard to the system s accuracy In order to make a more robust instrument further adjustments and modifications ought to be implemented Nevertheless the system proved to be working up to a certain point The obtained Mueller matrices for different media do coincide with the predefined ones albeit with limited accuracy The basic functions of the instrument however have been successfully implemented as were both stages the polarisation state generator PSG and the polarisation analyser Endeavouring to make a fully autonomous instrument a photoreceiver was designed and implemented specifically design for the system and the frequency and amplitude of the signals to be read Also a switching system that would enable to automatically read all reference signals by turns to be fed to the lock in system was made and encompassed with digital commands controlled via the PC enabled the measurement process to be automated As
49. cident polarisation states are 1 i lin E 1 1 1 Al a Nole al 0 Tas 1 Tro 0 3 E 3 18 0 0 1 0 and the polarisation states after having exited the medium lin Lis Tic ly a ee sie 3 19 U U4 U rc Uy Vin Vas Vac Viv The 16 elements are obtained by solving the linear equations system 1 1 0 0 0 O 0 0O 0 0O O0 O O O O Olalla 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 Olm be 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 O m Te 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 m i 0 0 0 O 1 1 0 0 0 0 O 0 O 0 0 Offm Q 0 0 0 0 1 O 1 0 0 0 0 0 0 0 0 Olmi OS 0 0 0 0 1 0 O 1 0 0 0 0 0 0 0 0I m Q 07 0 0 O 1 1 O0 0 0O 0O O O O O O Olm Q 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 m U 0 0 0 0 00 0 0 1 O 1 0 0 0 0 Olm Us o 0 0 0 0 0 0 O 1 0 O 1 0 0 0 Diag Ug 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 Offm U 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0Im a 0 0 0 0 0 0 0 0 0 0 0 O 1 O 1 Olm Vie 0 0 0 00 0 0 0 0 0 0 0 1 0 0 1 4fm Ve 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 Offm V5 3 20 The solution for the elements of M is 60 o5 00 05 0 00 0 0 00 O 0 00 Wl mo o5 0 0 05 0 00 0o 0 00 0O 0 00 0 Z m 0 5 10 05 0 00 0 0 00 0 0 00 0 Wire m 0 5 01 05 0 00 0 0 00 0 0 00 0 7 ma o 00 0 0500 05 0 00 0 0 00 o0 llos lm o 00 0 05 00 05 0 00 0 0 00 0 llo m 0 00 0 05 10 05 0 00 0 0 00 0 llo m 0 00 0 0501 05 0 00 0 0 00 0 lo ms o 00 0o 0o 00 0 05 00 05 0 00 o0 e Imo o 00 0 0 00 0 05 00 05 0 00 0 lus m o 00
50. cneeeeeeseeeeedeeencecceeeeeeeeeeeeteeeeereeee 69 Table 4 4 Stokes vectors for each of the generated ellipticities at 90 71 1X Thesis Title COMPLETE MUELLER POLARIMETER BASED ON LIQUID CRYSTAL VARIABLE RETARDERS AND PHOTOELASTIC MODULATORS Candidate Eng Alicia Fernanda Torales Rivera Chairsperson Dr Geminiano Martinez Ponce Dra Cristina Solano Program Masters in Optomechatronics The implemented Mueller polarimeter works in transmission and is constituted by two modules a polarisation state generator PSG and a polarisation state analyser PSA The PSG is based on a dual system of liquid crystal variable retarders LCVR set up in accordance to generate any state of polarisation by combining the induced retardance in each ON the other hand the PSA is constituted by a dual Photoelastic Modulator PEM system which in turn allows for the measurement of the four Stokes parameters without the need to modify the experimental setup The measurement for the 16 element Mueller matrix associated to a transparent optical medium is achieved by using a single wavelength 4 632 8nm The procedure consists on propagating a beam of light with four different polarisation states generated by the PSG through the sample and to measure the polarisation state in the outcoming beam with the PSA The aforementioned provides a system of equations which will in turn lead to details on all the sample s linear anisotropies s
51. d an analyser followed by a photoreceiver that in turn send the information to a Data Analysis system in order to determine the beam s state of polarisation After collecting a number of measurements they are sent to the computer in order to be analysed so as to determine the full Mueller Matrix of the sample and hence useful information on the material s optical properties This chapter will thus focus on the methodology and tools used to control and enable correct performance of the overall system 3 2 Optical Measurement System Description In Fig 3 1 the overall measurement system is presented schematically The device will enable the calculation of the 16 coefficients from the Mueller matrix and hence different optical properties of the material under analysis LCVRs are 1 diameter scientific grade elements from Arcoptix On the other hand PEMs are made of fused silica IISF42 and IISF47 and provided by Hinds Instruments 36 PSG PSA oat oo 0 0 a A g ae Source P PEM1 PEM2 Sample PEM3 PEM4 detector Fig 3 1 Full Mueller polarimeter P and A denote polarledr and analyzer respectively PEM 1 2 3 and 4 are photoelastic modulators 3 2 1 Constituting elements Liquid Crystal Variable Retarders The polarisation state generator is constituted by a linear polariser P1 with its transmission axis at 0 followed by two liquid crystal retarders LCVR1 and LCVR2 oriented at 45 and 0
52. d budget limitations the commercial one was used as a temporary measure postponing the plans for the other one 5 3 2 Data acquisition card Another piece of equipment that must be replaced for the system to become autonomous is the data acquisition card Now that the required number of signals to generate and acquire the frequency and sampling requirements and voltage range have all been established it is possible to design and implement an acquisition card solely dedicated to meeting this instrument s needs Another important detail is that since the control program was developed in Labview it might be advisable to develop a user interface in the same platform so as to simplify the communication among all the elements in the system 5 3 3 PEM based PSG Two liquid crystal variable retarders LCVR are being currently used for the polarisation state generator However two photoelastic modulators PEM will replace these LCVRs in order to achieve a faster response 5 3 4 Mechanical system As stated in the previous section the optical elements ought to be fixed down so that alignment problems do not ensue Nevertheless although the LCVRs retarders polarisers and PEMs can be fixed in a certain position a mount for all of these elements and the sample must be properly designed This however can only be done once the definite constituting elements are acquired Another aspect to consider is that the ellipsometer is expected to perfo
53. d orientation were performed by the labview program and logged into a text file The obtained results are shown in the table below 68 Orientation Ellipticity SO S1 S2 S3 0 8 50E 04 1 00E 00 2 14E 01 3 03E 02 1 70E 03 10 8 40E 04 1 00E 00 2 15E 01 2 37E 02 1 68E 03 20 7 69E 04 1 00E 00 2 03E 01 7 47E 02 1 54E 03 30 5 33E 04 1 00E 00 1 72E 01 1 30E 01 1 07E 03 40 1 33E 04 1 00E 00 1 10E 01 1 86E 01 2 65E 04 50 6 89E 04 1 00E 00 1 27E 02 2 16E 01 1 38E 03 60 1 64E 03 1 00E 00 4 40E 02 2 11E 01 3 28E 03 70 2 71E 03 1 00E 00 9 13E 02 1 96E 01 5 42E 03 80 3 97E 03 1 00E 00 1 54E 01 1 52E 01 7 94E 03 90 5 19E 03 1 00E 00 2 03E 01 7 32E 02 1 04E 02 100 5 77E 03 1 00E 00 2 10E 01 4 70E 02 1 15E 02 110 4 43E 03 1 00E 00 1 60E 01 1 45E 01 8 86E 03 120 2 95E 03 1 00E 00 1 03E 01 1 89E 01 5 90E 03 130 1 82E 03 1 00E 00 5 43E 02 2 09E 01 3 63E 03 140 8 26E 04 1 00E 00 8 43E 03 2 16E 01 1 65E 03 150 4 42E 05 1 00E 00 8 63E 02 1 98E 01 8 83E 05 160 1 02E 03 1 00E 00 1 99E 01 8 43E 02 2 04E 03 170 1 11E 03 1 00E 00 2 14E 01 3 02E 02 2 22E 03 180 1 10E 03 1 00E 00 2 14E 01 3 04E 02 2 19E 03 Table 4 3 Stokes vectors for each of the generated orientations for the linear polarisations in the system As we can see from table 3 the S1 parameter which in the first row ought to be approximately 1 is significantly smaller than SO Nevertheless S2 and
54. d that the response time of both diodes while different is brief enough for the application at hand Nevertheless the Melles Griot diode is not only faster but its junction capacitance and thus the active area is significantly smaller providing a greater bandwidth Manufacturer Advanced Photonix Melles Griot 13 DSH Model Number SD 445 11 21 305 005 Junction Capacitance C 10V 350pf 5 5pf Dark Current 30nA 0 25nA 350 Spectral Range 350 1100nm 1100nm Active Area 107 2mm2 1 57mm2 Response Time 10V 13ns 2 5ns Table 3 2 Technical specifications for silicon photodiodes Once the photodiode had been selected tests with different electronic designs for the preamplifier stage were made as well as with different models of operational amplifiers Opamps available on the market Naturally integrated circuits specifically designed for instrumentation applications were selected which provide for a more efficient design together with less noise susceptibility For the initial tests an instrumentation amplifier model AD624AD was used along with a basic design involving a current to voltage converter as that shown in figure 3 5 However the bandwidth this model offers proved to be insufficient for this application making it necessary to test other options iia L c2 Fig 3 5 Basic current to voltage converter Starting from the same design of a current to voltage converter the tr
55. ding to the graph silicon photodiodes provide a fairly good responsivity along the red part of the spectrum making them suitable for the application at hand 27 1 4 1 0 0 9 08 100 Quantum aE Efficiency 0 7 gt E 0 6 5 0 5 5 0 4 e 0 3 0 2 0 1 00 a 3 0 2 04 06 08 10 12 14 16 18 20 22 24 26 Wavelength um Figure 2 7 Typical spectral response of a silicon photodiode Dark Current It is a small current that flows when a reverse voltage is applied to a photodiode i e when the diode is used in photoconductive mode even when no illumination is incident on the diode This current adds noise to the overall signal and must therefore be minimised as much as possible Active Area Physically the active area refers to the amount of surface in the photodiode that detects illumination It is directly related to yet another characteristic which is the junction capacitance cj The smaller the active area is the smaller the junction capacitance which in turn provides for a greater frequency bandwidth Graeme 1995 Mode of Operation Any photodiode may be used in one of two different operating modes the photovoltaic and the photoconductive In the former one the photodiode functions as a current source simply changing light to an electric signal On the other hand the photoconductive mode requires an inverse voltage to be applied to the diode This mode provides a great
56. do biol gico la detecci n de contaminantes el control de calidad de f rmacos entre otros muchos Chapter 1 Introduction 1 10On Polarisation and its importance in Science Light polarisation is widely acknowledged to be one of the most important properties of light Collet 2005 being broadly used in several applications in a wide variety of fields including Medicine Holography Biology Pharmaceutics and Food Processing This property has led to numerous discoveries and technological breakthroughs all the way back to the 1600s Goldstein 2003 According to Maxwell s theory light as an electromagnetic wave presents both an oscillating electric field and an oscillating magnetic field The former oscillating at the same frequency than the latter but with a perpendicular orientation Only the electrical field is considered when determining the polarisation state of light 1 2 Polarisation and Coherence In 2005 Nobel Laureate R J Glauber proposes that the coherence condition is fulfilled only if the light is totally polarised R fr gier 2007 Additionally Emil Wolf Pye 2001 stated that there is an intimate relationship between polarisation properties of a random electromagnetic beam and its coherence properties Assuming that monochromatic light travels in sinusoidal waves the amplitude and phase of such waves can only be maintained constant throughout certain amount of time Afterwards the amplitude is bound to va
57. e which the user was to vary from 0 to 10 volts In the following figure a screenshot of said program is presented 63 oe Maa Dag srd a eee ee ee DA irm e hat H lt S Figure 4 1 Labview program for controlling the input square signal used to characterise the LCVR Two sets of measurements were performed one for each of the two retarders to analyse The results for the measurement are listed on the following table LCVR2 LCVR1 2nd measurement Amplitude Orientation Ellipticity Amplitude Orientation Ellipticity 0 00 47 35 0 3 0 0000 44 52 0 33 0 5 47 35 0 29 0 5000 44 55 0 33 1 00 47 4 0 00 10 000 45 75 0 04 1 5 142 16 0 2 15 000 152 89 0 28 2 00 48 22 0 17 20 000 45 03 0 26 2 50 141 04 0 52 25 000 152 67 0 38 3 00 141 86 0 04 30 000 151 73 0 11 3 50 143 84 0 35 35 000 154 37 0 39 4 00 147 1 0 57 40 000 160 49 0 6 4 5 154 73 0 76 45 000 174 4 0 74 5 00 178 49 0 87 50 000 15 53 0 76 5 5 26 3 0 82 55 000 28 99 0 7 6 00 35 45 0 73 60 000 35 08 0 63 6 5 39 03 0 66 65 000 38 2 0 57 7 00 40 85 0 6 70 000 40 03 0 52 7 5 41 96 0 54 75 000 41 15 0 47 8 00 42 6 0 5 80 000 41 99 0 44 8 5 43 04 0 46 85 000 42 35 0 41 9 00 43 5 0 43 90 000 43 0 38 9 5 43 71 0 4 95 000 43 15 0 35 10 00 43 91 0 38 100 000 43 44 0 33 Table 4 1 Results for LCVR characterisation 64 Figure 4 2
58. e kept at a low level since one of the purposes for the project is to keep the instrument as compact as possible Before validating any of these conclusions though the data variance must be verified ensuring that it is constant and the factors are independent First off the term residual must be approached A residual is defined as the difference between the observed value in a test and the response that was initially predicted by the model for such test Guti rrez 2008 In order to verify that the variance condition is met the residuals versus the predicted values must be graphed Figure 5 presents the resulting graph 89 Residual Graph for RMS Error 0 08 F 7 r i 5 0 04 L al Residuals o T E 0 04 L J 0 08 t f fis 0 14 0 17 0 2 0 23 0 26 0 29 Predicted Figure 5 Residual Graph for the experiments regarding the polarimeter s performance From the previous graph one can see that the data points do not follow a specific pattern that is the ay appear to fall randomly which enables us to conclude that the variance is indeed constant and thus the conclusions gathered from the analysis are valid In order to verify the independence the residuals for each of the tests are graphed in the same order in which they were obtained Thus Residual Graph for RMS Error Residuals o T fi 0 04 L J 1 1 1 1 1 0 4 8 12 16 Test Number Fig
59. e main program As each of the four states is generated the resulting Stokes vector is measured resulting in a series of four measurements 58 C Documents and Settings Administrador Escritorio LIA txt y Controls Sequence Voltage Results Results Il LC R 0 LCYR 45 m tnearor Ban E Al s 25 Linear 45 Bal 2 227 a 2 92 Right Circular ha 2 245 bal 1 599 Linear 90 E 2 873 OFF ME Figure 3 20 Implementation and control panel of the voltage sequence for the LCVRs Finally the sample to be analysed was added to the experimental setup Since the incident light upon the material under study has a known polarisation state due to the LCVRs system the sole unknown information is the polarisation state of the outcoming state which is in turn measured by the dual PEM system and detector All in all the system constitutes a closed loop given that the input is controlled by the PC and the output is fed onto it Finally with the required information from both the system s input and output it is possible to calculate the Mueller Matrix of the sample The calculation of the Mueller Matrix by the labview program is as follows Suppose that a medium can be represented by the Mueller matrix 3 17 59 On way of finding the 16 constituting elements is propagating a light beam with four different known states of polarisation and by analysing the changes the beam suffers upon exiting the sample Thus the in
60. e structure and birefringence of its components may be obtained by measuring the degree of depolarisation of initially polarised light passing through a tissue sample However it is not only from these polarisation properties that useful information can be obtained Several tissues retina and tooth enamel among them present properties such as linear birefringence and optical activity due to their composition and nature Collagen keratin or glucose being present in them Considering all the aforementioned it is safe to say that biological tissues and fluids are in most cases polarising materials to some extent These properties are expected to enhance the improvement of the current techniques in medical tomography and other diagnostic methods Tuchin 2006 Other important medical applications which use polarisation include glucose and bacteria sensing This work will not delve on the history of polarisation studies but rather in the nature of the phenomenon and its applications 16 Chapter 2 Review of Literature 2 1 Introduction Several instruments for measuring polarisation of light i e polarimeters and ellipsometers have been proposed throughout the years Guo 2007 Wang 2005 Oakberg 2005 Giudicotti 2007 Aspnes 1976 Azzam 1977 Ord 1977 This kind of systems in which this work will focus enable measurement of light polarisation properties before and after light has gone through or has been reflected by a s
61. e the most convenient for the system at hand In contrast when a lock in is developed specifically for an application in mind it is possible to consider the available and most suitable resources for interfacing and to effectively establish communication with the computer or any third party equipment that is needed by the instrument thus allowing for the engineer to choose the hardware and software to use at least to some extent Needless to say this significantly simplifies the overall implementation of the complete system 2 7 Analysis of Different System Configurations based on PEM devices The appropriate orientation of the PEMs varies depending on the application at hand In imaging applications specifically while using a spectropolarimetric camera a dual system with both PEM retardance axes aligned and the modulators used in tandem proved successful the experimental setup being as follows One setup involves a quarter waveplate retarder with its fast axis oriented at 45 followed by both PEMS oriented horizontally and finally a second quarter waveplate retarder oriented at 45 This setup provided for a circular retarder that modulates the Q and U parameters Since measurement of the parameter V circular polarisation was not required for the specific application it sufficed for satisfactory measurement of only 3 of the 4 Stokes parameters Q and U Diner 2007 Nevertheless if it were required to fully measure the degree of pol
62. ect signals within a significantly wide spectral band and the avalanche photodiode which has a faster response Graeme 1995 Nevertheless controlling the second type presents a somewhat greater challenge The photodiode to be used must be carefully selected in accordance to the signal characteristics such as amplitude and frequency Not all photodiodes will be able to detect a signal at a high frequency nor will they be equally sensitive to all wavelengths Also operation conditions should be taken into account so as to minimise possible electrical noise and temperature variations during measurements The main properties to keep in mind while choosing a suitable photodiode are junction capacitance Cj dark current spectral range active area and response time Graeme 1995 Spectral Response The current generated by a given level of incident light varies with wavelength The relation between photoelectric sensitivity and wavelength is referred to as the spectral response of the photodiode The operating wavelength for this stage of the project is that of 632 8nm which corresponds to the red color Bearing this in mind a silicon photodiode was chosen due to its high sensitivity to red light In the following figure a typical spectral response curve of photodiodes made of different materials is presented Johnson 2004 in which the diode s sensitivity along a specific range of the spectrum may be seen Notice that accor
63. ectrical signal that is driving the photoelastic modulators as the reference for the lock in A block diagram of the main stages of a lock in amplifier is presented in figure 1 9 ie Noise Notch Filte Signal rom amples A filtering H a Y Out Reference Phase Locked n Loop X Out Fig 2 9 Lock In Amplifier Functional Block Diagram Phase sensitive detectors shown in the above figure measure the phase difference between two signals of the same frequency lt does so by multiplying 31 both signals and thus obtaining a DC signal proportional to the phase difference between the signals For two square signals at a low frequency an XOR gate will suffice to achieve this Nevertheless for higher frequencies in sinusoidal waveforms a more specialised circuit is required The IC AD633 is an analog multiplier designed for this purpose i y T to B Cos X A Sin X y B Cos X V A SIN X A Figure 2 10 Graphical representation of two sinusoidal signals with a phase difference of 90 left and the resulting multiplication right 2 6 2 Basic Theory Mathematically speaking if we express the desired signal as V si SINO t Opg 2 9 Where Vsig is the amplitude of the signal And the reference signal as V Sin t 8 2 10 By multiplying both signals we get Vosp V y V Sinlo 1 0p Sin t 8 sig sig 2 11 V_Cos o 0 1t 0 O sig s
64. ed some amount of dark current and hence a certain amount of noise is unavoidable Adding a second photodiode D2 to the circuit can reduce the error this generates It must be noted that D2 ought to have the same characteristics as the first diode D1 inversely polarised with the same 41 voltage as D1 so that it conducts a dark current of approximately the same magnitude through a 100 KA resistor thus suppressing the effects of D1 s dark current The following figure shows a diagram of the circuit C2 Ik 1pF R2 100KOhm MN NVV MN 33 2kKQ 33 2kKQ 33 2kQ 4 vec 15V y c cea ot 121 AD823AN li 100kQ oad Fig 3 6 Current to voltage converter with a bandwidth of BW 1 65 MHz and dark current compensation In order to minimise the undesirable effects of electrical noise the circuit was encased in a metal box The complete element list constituting the preamplifier is as follows IC AD823AN 2 Identical Photodiodes 3 33 2 Kw resistors 2 100 Kw resistor 1pF capacitor 7 5 pF capacitor 100 nF capacitor Power Source 15 V Metallic encasing for the circuit in order to minimize noise With the photodetector finished several tests for performance and accuracy were carried out For comparison purposes a commercial detector was initially used New Focus Model 1801 and its response was then verified by the computer generated simulation henceforth ensuring
65. ence minimise the error whilst striving to obtain the most reliable instrument possible 87 In figure 3 a graph illustrating the impact of all the factors is presented As it may be surmised the two factors whose impact is the strongest are metallic encasing and analyser quality It must be noted that the calcite polarisers have better quality and thus are more costly than those of glass Bar graph for RMS Error o metencasng II rans MS C Mech Noise E Vin A Ambient Light E B Modulator Dist 0 0 005 0 01 0 015 0 02 0 025 0 03 Effect Figure 3 Bar graph illustrating the amount of impact each factor has on the system obtained from the results of the 16 first tests According to figure 4 which depicts the correlation between the most significant effects it is possible to determine the optimal values for each of the factors so as to minimise the RMS error Main Effects of RMS Error 0 2 F qT 0 195 4 o49 4 F D gise e 4 7 E J 0 18 4 0 175 4 0 17 E w w g S s S f f FF E gt ESPE SA ig Figure 4 Effect of both levels for each of the analysed factors on the other factors From the above figure it can be seen that for the case of ambient light the ideal value to minimise the RMS error is high i e with the lights on The distance between modulators ought to be the low one which in this case is 6 cm Similarly for the
66. enoted as Ey and the S polarisation component denoted as E As a wave light propagates sinusoidally throughout space at an angular frequency o If we represent the maximum amplitudes of the two components as Eox and Eoy and the phases as q and by a beam of light can be represented by the following equations E z t Eox cos t kz ox Ey z t Eoy cos at kz dy Where k 27 A which is the wave number magnitude In the case in which the components have identical phases one can obtain linearly polarised light in several directions It is possible to combine the orthogonal components of linearly polarised light so as to produce other types of polarised light Another case worth noting is when the components phases are 90 out of phase with each other whereas the amplitudes are exactly the same This results in circularly polarised light If neither of the conditions described above is met then the light will present an elliptical polarisation which is considered to be the most general case In order to analitically visualise the above description we shall briefly develop some theory 1 2 1 Linear Polarisation Considering light as an electric field whose magnitude oscillates through time and which is oriented along the polarisation axis the polarisation is linear Thus for light propagating along the z axis it is possible to describe linearly polarised light along the x axis as Ex Eox Sin ot kz o
67. enuation 45 CD Circular Diattenuation CB Circular Birefringence LBo Linear Birefringence 0 or 90 LB4s Linear Birefringence 45 However not all materials alter polarisation in the same way or indeed in the same degree When it is required to analyse the polarising properties of a specific material a Mueller Matrix polarimeter is then used which enables the measurement of the different elements that constitute the Mueller Matrix that represents said material thus providing useful information on properties and characteristics of the sample under study 2 4 Mueller Matrix Polarimeters Mueller Polarimeters aim to measure the elements from the 4x4 Mueller Matrix of a given sample either in reflection or transmission A polarimeter is said to be 23 complete if it measures all 16 elements from the matrix whereas an incomplete polarimeter merely measures a part of the matrix Given that different elements from the Mueller Matrix represent different properties of the material under study it is sometimes unnecessary to measure all 16 elements and thus an incomplete polarimeter may be used for such cases In order to have a complete measuring system the instrument must encompass two stages both functioning in strict synchronicity The first stage consists of a complete polarisation state analyser PSA and the second a complete polarisation state generator PSG The reason for both stages is clear it is necessar
68. er linearity and frequency response but is more susceptible to noise and dark current Jung 2002 By applying and inverse polarisation to the photodiode the junction capacitance is reduced which in turn 28 will improve the diode s response time Rashid 1999 This mode is generally used for applications requiring a fast response Furthermore the photoconductive mode usually requires a preamplifier which encompasses a current to voltage converter Thus the linearity is lost after the conversion Photovoltaic Photoconductive Zero bias Reverse bias No Dark Current Has Dark Current Linear Nonlinear with preamplifier Low Noise Higher Noise Precision Applications High Speed Applications Figure 2 8 Photodiode operating modes In the photoconductive mode it is possible to read either a voltage or current signal However the generated electrical current is a linear function of the light intensity as opposed to the voltage response Since most devices are designed to reading voltage rather than current in most cases a preamplifier stage in order to obtain suitable readings in volts The preamplifier stage as the name indicates encompasses an operational amplifier used as a current to voltage converter which basically takes the generated current from the photodiode and converts it to voltage This stage also functions as a filter which aims to minimise the noise effects of the dark current generated by the diode A
69. erent components of the output signal read and sent by the photodetector The LIA can communicate bidirectionally with the computer via the serial port rs232 and a series of commands in ASCII characters The SR830 has a 256 input character buffer and different commands may be sent in quick succession so that the buffer lines them up and the device performs them in the order they were received FIFO Some examples of the main instructions used for these particular applications are presented on table V These commands are either for an action to be performed by the amplifier or for monitoring the LIA s status such as locked and overloaded states in order to prevent any measurement errors All commands must end with a carriage return in order that the device knows the instruction line is over Command Description IDN Queries the device identification PHAS x Sets the phase to the value of x where x is expressed in degrees IGND 1 Specifies the input shield grounding to the Ground state OFLT i Sets the time constant to the value of i where ranges from 10us to 30 Ks APHS Performs the autophase function OUTP 1 Reads the current value of X Table 3 5 Sample list of ASCII commands for the Lock in amplifier Optical Chopper In order to accurately measure the dc signal with synchronous detection using a lock in amplifier in an analogous way as the ac signals are measured it
70. es Different Types of Photon Detectors 2 5 1 The Photomultiplier Tube A typical photomultiplier tube consists of a vacuum tube containing a photosensitive cathode followed by a series of electrodes known as dynodes that collect and multiply the photocurrent generated in the cathode Jonasz 2009 A voltage of the order of hundreds of volts is distributed between the electrodes of the multiplier by a voltage divider network A photon that strikes the photocathode ejects an electron with the quantum efficiency of less than one fourth Such electron is then accelerated by the potential differences between the cathode and the following electrode The impact with said electrode results in the ejection of several next generation electrons This electron multiplication continues for each of the following dynodes ending up in the anode where the electrons are collected The overall process hence provides for an approximate of 10 electron gain 26 2 5 2 Photodiodes Sensing devices for polarisation measuring systems require a high speed low noise response Since the system presented in this work is to measure a single light beam we will focus on photodiodes as the preferred means of measuring light intensity Photodiodes generate a small electrical current which is proportional to the level of the illumination incident on its surface There are two types of photodiode available for this kind of application the PIN photodiode which can det
71. es Polarimeter Applications http www hindspem com DUALPEMStokesPolarimeter default aspx Hinds Instruments 2007 PEM 100 Photoelastic Modulator User Manual Hinds Instruments Inc J G Graeme 1995 Photodiode Amplifiers United States of America McGraw Hill Jellison G E Modine F A 2005 Polarization modulation ellipsometry in Handbook of ellipsometry New York Springer Johnson M 2004 Photodetection and Measurement McGraw Hill Ch 1 Jonasz M 2009 Handbook of measuring system design Light Sources and Detectors T 3 Ch 91 Wiley Ed Jung W G 2002 Op Amp Applications Analog Devices Inc Kim Myeonghee 1987 Differential Polarization Imaging Il Symmetry Properties and Calculations Biophysical journal Vol 52 Kromer P Pc Based Lock In Detection of Small Signals in the Presence of Noise Department of Physics University of Texas Austin Meadowlark 2009 Polarization Control with Liquid Crystals Neiswander R 1975 Low noise extended frequency response with cooled silicon photodiodes Applied Optics Vol 14 No 11 Oakberg T 2005 Magneto Optic Kerr Effect Hinds Instruments Application Note Ord J 1977 Self Nulling Ellipsometer Design SPIE Optical Polarimetry Vol 112 Perkin Elmer Instruments 2000 Specifying Lock in Amplifiers Technical Notes TN 1001 Perkin Elmer Instruments 82 Pye D 2001 Polarised Light in Science and Nature United Kingdom Institute of
72. f analysing the impact each of the modulator s retardance value on the system the experiment was carried out using a specific combination of retardance amplitudes for the modulators The tests were made with retardance values of 1 2 radians for the first PEM and x for the second one The resulting curves in each case were compared to the computer generated curve A total of 62 values in each of the tests was obtained and a cubic interpolation was performed using a mathematical software in this case Matlab Next the RMS error for each of the results was computed having considered this the output variable in the experiment in order to analyse the variables and thus optimise the system based on the result from the corresponding statistical analysis In figure 2 one of the graphs light intensity vs time is presented The data for this graph was obtained from the experimental tests The blue curve represents the ideal computer generated response whereas the red curve represents the experimentally obtained data Normalised Intensity Time 5 Figure 2 Comparison between the experimental curves red and the computer generated ones by means of a mathematical software blue From the obtained RMS error values a statistical analysis was carried out with the aid of the statistical software Statgraphics with the purpose of establishing up to which point does each of the studied factors influence the performance of the system and h
73. for the software a program that allows the user to request a measurement or manually control the measurement process that for both cases logs and displays the obtained results was developed and is functioning correctly Finally it must be noted that the system may be used either as a laser transmission ellipsometer or a standard polarimeter which determines the state of polarisation ellipticity orientation and stokes vector of an incident light beam 5 2 System limitations From the system s characterisation it remains clear that the system s accuracy and repeatability need to be improved Also the system s susceptibility to ambient factors must be minimised for it to be considered robust First off all noise needs to be minimised Although the photoreceiver was enclosed in a metal case which indeed proved effective the rest of the system remains in the open In order to reduce the instrument s susceptibility to light changes as well as other sources of noise it might be advisable to enclose the whole system blocking as much ambient light as possible Another source for inaccuracy as with all optical systems is a faulty alignment Try as one might to realign the constituting elements for each set of measurements differences however slight in alignment are inevitable Thus T11 the retarders modulators polarisers and the rest of the elements should be fixed in a specific position so as to guarantee a proper al
74. generator and controlled via software Depending on the amplitudes of both signals the LCVRs induce a retardation in the light and hence a change in polarization Specific amplitude values are to be sent to the retarders in order to induce a known polarisation state Polarization Generator Polarization Analysis A illl Linear He Ne Laser otarizer LCVR1 LCVR2 Sample PEM1 PEM2 bese A Dotertar analizer Figure Ill 1 Element diagram of the device The second block of polarisation analysis is formed by two photoelastic modulators PEM1 and PEM2 the first one being oriented at 0 and the second at 45 followed by a second linear polarizer at 0 and a photodetector Both modulators resonate at slightly different frequencies and allow the incoming light to be modulated thus sending a characteristic signal to the detector depending on the polarisation state of said light figure III 2 Eventually this pair of liquid cristal retarders will be replaced by a pair of photoelastic modulators thus providing the system with a significantly greater speed response 95 a JA ASAS ES PN V V AA AR 0 A fhe j Wet Nai VW a ve Yoy erg gt 11 Ch 1 1 Volt 5 us 2 Ch 2 1 Volt 5 us Figure IIl 2 Sample signals obtained with two different detectors outcoming from a dual modulator system The signal from the detector is then sent to a PC via an acquisition board for analysis Using a Lock In A
75. i 1 1 And along the y axis as Ey Ey sin ot kz oy j 1 2 Where Eoxoy gt Amplitude electric field magnitude i gt Unit vector along the x axis j gt Unit vector along the y axis 2nv v wave frequency k 2n X A wavelength do absolute phase Hence the electric field of linearly polarised light may be described as the vector sum of E and Ey E E E Eox i Eoy j sin ot kz do 1 3 This configuration may be better visualised in the following figure in which the two orthogonal components are represented in blue and the resulting polarisation in red a b f A m Pa a aa ji 7 W7 MI AY HS UA peo Figure 1 1 Representation of linearly polarised light at 45 a isometric view b frontal view 1 2 2 Circular Polarised Light Consider the case in which both components are equal in magnitude but 90 7 2 rad apart from each other in phase Ercp Eofsin ot kz do i sin ot kz bo 1 2 j Esfsin ot kz do i Cos t kz do j 1 4a Eip Eofsin ot kz do i sin ot kz o 1 2 j E sin at kz o i cos ot kz do j 1 4b This configuration results in circularly polarised light which can be better visualised in the following figure a sot gee Pro Figure 1 2 Representation of circularly polarised light represented by the arrows a isometric view b frontal view As seen
76. icine Applications in tissue studies Biological media comprise two large categories in which the different tissues and fluids may be divided Tuchin 2006 The first one known as Weakly Scattering Media which transparent tissues and fluids such as cornea vitreous humour and crystalline lens The second one the Strongly Scattering Media includes opaque or turbid tissues and fluids like the skin brain blood and lymph Biological tissues are rendered transparent in the near infrared NIR region of the spectrum due to the absence of absorbing chromophores in this spectral range A chromophore is a chemical and part of a molecule that absorbs light with a characteristic spectral pattern Tuchin 2006 hence being responsible for the molecule s color However biological tissues produce rather strong scattering in this spectral region making it difficult to obtain clear images of inhomogeneties within the sample making them hard to localise Due to this classic imaging is virtually useless for studying this kind of media and specialised techniques need to be used when analysing biological tissues 15 In certain tissues for example the degree of polarisation of transmitted or reflected light is measurable regardless of the tissue s thickness whereas in other media reflected or transmitted light depolarises much too fast for obtaining useful information out of it degree of polarisation Still information about th
77. ig 1 1 ri V Cos lo lt Oi Oar e The output is then passed through a low pass filter to remove all AC components keeping solely the DC one which is proportional to that of the signal Thus 32 1 Vsp 5 V 2 sig V LCOS Oig m 0 2 1 2 Assuming that Osig Oret then Osig Ore O and COS Bsig Oret 1 Resulting in 1 Vosp gt V 2 sig V L 2 13 If on the other hand Osig Orer 90 the output would be zero In short a lock in with just one PSD renders an output of VsigCos Since we are looking for the value of Vsig the phase dependency needs to be eliminated This can be achieved by adding a second PSD and using the same reference signal but shifted 90 with respect to the previous one Thus after low pass filtering the second output 1 Vospo Y SintO sig O V Sin 0 2 14 Conventionally this last expression is referred to as Y or in phase component whereas the expression VsigCos is called X or quadrature component Having both X and Y it is now possible to obtain both the amplitude R and the phase 0 of the signal by R x y gt v 2 15 and 0 tan 2 16 Thus obtaining the required information from the signal 1 2 It must be noted that LIA s output is given in RMS so a factor of 2 must be considered during calculations Also in order to minimise ambient noise and light intensity fluctua
78. ignment during all measurements Another possible source for inaccuracies is the integration time constant that is being used Although a time constant of 1ms was used which according to an ideal system s response ought to provide a minimum error in the lock in s readings it is possible that another value proves to be more effective Thus further tests should be performed while trying other time constants comparing the response in each case Finally the system s speed must be addressed The lock in amplifier s response needs to be faster and the communication between amplifier and PC can be enhanced by changing the communication interface The amplifier had an already developed communication interface via the serial port RS232 However by using the USB port instead the communication speed could be increased and thus the entire measurement process sped up Another way of enhancing the system s response would be optimising the control program An in depth analysis of the code and functions must be done which when properly done might lead to locating bottlenecks in the processing and finding more efficient and faster ways of carrying out certain functions 5 3 Future work Besides the proposed adjustments and enhancements necessary for the system further work is required for a feasable marketable instrument to be obtained 5 3 1 Lock In amplifier Although the commercial amplifier was able to take the appropriate measuremen
79. imeters based on Modulated Optical Rotation SPIE Optical Polarimetry Vol 112 Carey R 1996 Programmable liquid crystal waveplates in ellipsometric measurements IOP Publishing Ltd Chabay 1975 Infrared Circular Dichroism and Linear Dichroism Spectrophotometer Applied Optics Vol 14 No 2 Collins R W Chen An C 2005 Rotating polarizer and analyzer ellipsometry in Handbook of ellipsometry New York Springer Corn R 1996 Rapid scan Polarization modulated Fourier transform Infra red Reflection Absorption Spectroscopy Hinds Instruments Inc De Martino A 2003 Optimized Mueller polarimeter with liquid crystals Optics Letters Vol 28 No 8 Optical Society of America Diner J D 2007 Dual photoelastic modulator based polarimetric imaging concept for aerosol remote sensing Applied Optics Vol 46 No 35 Fjarlie E 1977 Photodiode preamplifier systems low noise positive feedback Applied Optics Vol 16 No 2 Giudicotti L 2007 Data analysis for a rotating quarter wave far infrared Stokes polarimeter Applied Optics Vol 46 No 14 Goldstein D 2003 Polarized light 2nd ed United States of America Marcel Dekker Graeme J G 1995 Photodiode Amplifiers United States of America McGraw Hill Ch 4 Guo X 2007 Stokes polarimetry in multiply scattering chiral media effects of experimental geometry Applied Optics Vol 46 No 20 81 Hinds Instrument 2005 Dual PEM Stok
80. in amplifier The program is called as a subvi from different parts of the main programs 55 E Basic Serial Write and Read vi Front Panel File Edit Operate Tools Browse Window Help E In rn Aeptcaten Fort e Eo Select the serial resource and the operations Read Write or both to be performed If both are selected the YI will write the data First read data and then close the VISA session that is opened to the port This YI will wait until the specified number of bytes is received at the port Only the number of bytes specified will be read For additional information select File gt gt VI Properties gt gt Documentation write string to write mre zt Pann comi xl t baud rate pn l Effizoo data bits Je parity Hrone stop bits 1 0 J ON flow control PJRTSICTS read read string delay before read ms bytes read 1000 lO 10 Figure 3 17 Control window for Basic Serial Write and Read vi Calculations and Ellipse Simulation programs The calculations from the Analysis section from this chapter were implemented in a Labview program Basically the program receives the data measured by the lock in amplifier and sent via the serial port This information includes amplitude and phase for the different components of the output signal The calculations provide the full Stokes vector as well as polarisation state orientation ellipticity and degree of polarisation The Eli
81. in black for a 1 4 retarder Mueller Matrix Elements Average for Air 1 2 1 uu E E 0 8 0 6 0 4 0 2 0 it JE m E l 0 2 1 2 3 4 5 6 7 8 9 10 11 1 13 14 E 16 0 4 0 6 Figure 4 10 The sixteen Mueller Matrix elements averaged throughout five different measurements along with their respective error in black for Air 74 From figures 8 10 it is evident that the repeatability for the three different measurement sets is not constant For the case of the Half Waveplate figure 6 the standard deviation represented by a black line in all 16 points remains the smallest of the three sets whereas the measurements for air present a far greater deviation particularly among the zero elements The latter case might be due to variations in ambient factors among the different measurements noting that they were performed on different days as opposed to other two cases Nevertheless it is also the half wave plate retarder measurement that presented a greater inaccuracy in all 16 elements landing farther from either 0 or 1 depending on the element than was the case for the other two media This may be caused by the superior thickness in this media when compared to the other two The highest accuracy was obtained for the quarter waveplate retarder whose values were far more proximate to 0 or 1 though a fairly decent accuracy was also achieved when measuring air 4 2 3 Ana
82. ion generator power supply and some other necessary equipment for the instrument to function properly However for comparison purposes only we consider the cost of the equipment should it be acquired separately as will be the case of some of the following components Cost per Element System unit Qty Total Details Power Supply 15 6 497 12 1 6 497 12 3 Amperes Function Generator 8 816 55 3 26 449 64 Monochromator 29 596 47 1 29 596 47 White light from UV to Light source 23 424 89 1 23 424 89 NIR Polarizer Glan Thompson 5 886 74 2 11 773 48 Beam Splitter 3 730 08 1 3 730 08 Photoelastic Modulators Dual Syst 209 070 87 2 418 141 74 Data Acquisition Card National Instruments 26 110 55 1 26 110 55 CCD Camera Edmund Optics 47 812 82 1 47 812 82 Note Prices are in Mexican Pesos As a whole a system like this in the market including shipping expenses and taxes would cost around US 126 636 39 see attached quotation which translates to 1 717 685 86 in mexican pesos 103 As for the system we propose the approximate costs would be as follows Power Supply 15 1 000 00 1 1 000 00 3 Amperes Lock in Amplifier 300 00 3 900 00 Monochromator 29 596 47 1 29 596 47 White light from UV to Light source 23 424 89 1 23 424 89 NIR Polarizer Glan Thompson 5 886 74 2 11 773 48 Beam Splitter 3 730 08 1 3 7
83. ith rapid changing samples Aspnes 1976 Nevertheless when calibrating and taking measurements care must be taken to preserve a constant temperature level since liquid crystals are sensitive to temperature variations and may affect the obtained results Carey 1996 2 2 3 Phase modulation polarimeters These systems use modulators that are controlled by an electrical signal The most commonly used element is the photoelastic modulator PEM The system presented here is of this type It consists basically of a dual phase modulator and a fixed analyser A diagram of the element setup is presented in the following figure 0 45 0 PEM1 PEM2 A Detector Fig 2 3 Dual PEM Stokes polarimeter which measures all four Stokes parameters where PEM1 and PEM2 are photoelastic modulators and A denotes an analyser The two photoelastic modulators in the polarisation analyser are operated at slightly different resonant frequencies thus generating a beat signal that modulates the polarised component of the incident light Typically these frequencies are in the range of tens of kilohertz One of the main advantages of this system over both rotating and oscillating element polarimeters is speed Although they all require an electrical signal for control and acquisition purposes the response of PEMS is significantly faster than any motor or liquid crystal cell Nevertheless the overall cost of the device increases significantly given the
84. ll Stokes polarimeter Mathematical Analysis and Interpretation 3 3 Control and CommunicatiON ooooooninnnccnnncccnnnn 3 01 ESA CONTO susi 3 9 2 PEM CONTO psico 3 3 3 Signal Analysis 3 4 Main Labview Program and User Interface Chapter 4 Results 4 1 Characterisation of elements and system 4 1 1 LCVR characterisatiON oo ononnnn c 4 1 2 Characterisation of Polarisation State Generator 4 2 Characterisation of the systeM eeee 4 2 1 Results for different media and comparison to ideal reSPONSE ccceeeeeeeeeeeeeeeeeeeeeeees 4 2 2 Repeatability and Precision 4 2 3 Analysis of system performance through gradual variation of a single factor Chapter 5 Conclusions 5 1 System Performance 000 cececeeeeeeeeeedeeeeeeeecee 5 2 System limitations ennenen eener 5 3 Future AAA usar aver ncieteay toes 5 3 1 LOCK IM ampli vta 5 3 2 Data acquisition CalO ooooooooccccnncncnccccnncnos 5 3 3 PEM based PG dad 5 3 4 Mechanical SySteM ceeeeeeeeeeeees 5 3 5 Readings for wider areasS cccee 5 3 4 Spectral VAMOS tutti References 2c aise ek ee eee ee ees ee ADPIC orien eds Analysis for transmitted light intensity for a dual photoelastic modulator system ADDED tt Transmission Laser Ellipsometer Business Plan 63 63 66 68 72 73 75
85. lysis of system performance through gradual variation of a single factor In order to determine the system s susceptibility to changing surrounding conditions a series of measurements varying the ambient light intensity were taken Using a quarter waveplate retarder as a media a simple light dimmer to control the illumination and a radiometer to monitor the varying light intensity the 16 Mueller matrix elements were obtained and recorded for eight different intensities The obtained results are shown in the figure below Mueller Matrix Elements with various Light Intensities m00 em01 1 5 m02 m03 m10 m11 m12 m13 m20 m21 m22 m23 m30 1 5 poe e m32 m33 Figure 4 11 Elements for the Mueller matrix corresponding to a quarter waveplate retarder throughout a series of measurements with various light intensities Element Value Light Intensity W cm2 From figure 11 we can see that those elements that should be approximate to one present a relatively constant behaviour with its values fairly close to 1 As for the elements that should ideally be zero vary somewhat among themselves though they are all small However we may also notice that they don t share a 75 common sign either some of them being negative and the other positive This suggests a certain amount of inaccuracy in the measurements Furthermore although the curves do present a
86. m equations 3 13 and 3 15 respectively It can also be concluded that this configuration will have a larger sensitivity towards circularly polarised light 49 100 80 FT fi KHz Figure 3 11 Fourier spectrum of the modulated intensity signal using the circular polarisation sensitive configuration for three different states of polarisation linearly polarised light and right circularly polarised light Afterward the ellipticity of the incident polarisation was varied whilst keeping the orientation constant y 37 8 Figure 12a illustrates the error in calculating from equations 3 12 to 3 15 In this case the Stokes parameter for circularly polarised light V is recovered better than those for linearly polarised light Q and U This result is to be expected because the sensitivity to circular polarisation of the configuration The largest error is that of Q To obtain the results shown in figure 3 12b the orientation y of elliptically polarised light was changed while keeping the ellipticity constant y 0 5 The error for the calculated Stokes parameters behaves exactly as in the previous analysis Thus it may be stated that the system detects the Stokes parameter V with higher accuracy 50 a p Figure 3 12 Difference between calculated and incidence Stokes parameters while varying a the ellipticity and b the orientation of the incident light beam 3 3 Control and Communication 3 3 1 LCVR Cont
87. mmed microprocessor which will in turn be implemented in the final circuit board The signal generation filtering and signal conditioning will be managed with operational amplifiers and other active and passive elements yet to be determined VIII Cost analysis and comparison The total cost for the circuits elements is shown above Both the detector circuits and the card circuits are considered Element System ee Qty Total Details Instrumentation Amplifier for IC AD823AN 180 00 5 900 00 better performance Photodiodes FDSO10 558 83 4 2 235 33 Must be identical 33 2 KW resistors 1 00 6 6 00 1 4 watt 101 100 KW resistor 1 00 4 4 00 1 4 watt 1pF capacitor 3 00 2 6 00 ceramic 60 V 7 5 pF capacitor 3 00 2 6 00 ceramic 60 V 100 nF capacitor 3 00 2 6 00 ceramic 60 V Metallic encasing 30 00 2 60 00 For noise reduction PIC18F4553 120 00 1 120 00 40 PIN PDIP MASTER PROG 450 00 1 450 00 universal programmer for Pics SOCKET 6 00 1 6 00 40 PIN QUARTZ CRYSTAL 12 00 1 12 00 20 MHZ USB CONNECTOR 12 00 1 12 00 USB CONECTOR B TYPE USB CABLE 54 00 1 54 00 OA amp B BREADBOARD 93 00 1 93 00 CABLE mtr 12 00 2 24 00 UTP CONNECTORS 8 00 15 120 00 w screws RED LEDS 3 00 2 6 00 3mm GREEN LEDS 3 00 2 6 00 3mm Micro switch 4 00 4 16 00 Switch 2 termin FENOLIC PL
88. mong the three compared data which varies from 10 to 20 This value is related to the sampling frequency that was used during the experiment With the purpose of optimising the system s overall performance the effect of different variables such as ambient light distance between modulators mechanical noise metal encasing input voltage for the photoreceiver and quality of the analyser By establishing 2 different levels for each of the afore mentioned factors and by means of a 2 factorial design with a IV level resolution a statistical analysis that allowed us to determine which of the six factors contributes more to the performance of the system and which if any is crucial to its optimal response was carried out The following table shows the two levels used for each of the factors analysed during the study Factor High Level Low Level Ambient Light 1 0 Distance between Em 12 cm modulators Mechanical Noise 1 0 Metallic Encasing 1 0 Input Voltage 15 V 12V Analyser Calcite Glass Table 1 Varying factors during the experiments and their respective low and high values 86 Note The values shown as 0 and 1 represent the absence o presence of said factor respectively By using these values and randomly varying each factor a data matrix was generated hence obtaining a total of 16 different tests each with a different combination of values Furthermore with the purpose o
89. mplification the signal is sent to two separate stages One stage directly multiplies or mixes the noisy signal with the reference signal The other one also multiplies the noisy signal but this time with the reference signal 90 out of phase So for instance if the reference signal is a Sine this other signal would be a Cosine 30 Both outputs are then fed to low pass filters tuned to eliminate all AC components and keep only those with frequencies close to zero which would be the DC component The actual process and complete circuit is somewhat more complex than the description above Since the signal may be buried in several others with various frequencies both greater and smaller more than one filter may be required either low pass or high pass after the gain stage and others just before the final output Finally a band suppressing notch filter is sometimes recommended to be used right after the amplifying stage to eliminate a reduced range of specific frequencies whose amplitude is greater or equal to the one that is being extracted yet significantly apart in frequency terms from the desired signal otherwise one might accidentally eliminate the signal along with the unwanted noise It must also be noted that the process of phase sensitive detection demands an exact phase synchronisation between the reference signal and the modulation of the light beam Chabay 1975 With this in mind it is advisable to use the very same el
90. mplifier the obtained signal is analysed and the polarisation state is thus determined and displayed by the software With this knowledge different characteristics about the sample may be obtained such as composition and concentration In the final instrument the detector will be replaced by a CCD camera for analysis of a wider spectrum and variety of samples The device is to encompass as well a monochromator enabling a wide selection of wavelengths from ultraviolet to infrared in order to broaden the scope of materials that can be studied Finally a special mount will be designed to enclose all the constituting elements of the device and to provide mechanical mobility both manual and automatic to different parts so as to provide greater flexibility and versatility to the device IV Justification The need for this device Although similar instruments are already available in the market the instrument will enable analysis in both transmission and reflection as opposed to most of those already on sale Furthermore what is probably the most attractive feature of this system the instrument and proposed analysis will provide for a far more economic instrument enabling easier access to the system This way we are confident 96 different areas of the industry and research fields will be interested in acquiring such an instrument Lastly we strive to produce a high speed response capable of competing with other existing systems
91. nd phase A reference sinusoidal signal tuned to frequency and phase of the desired one must be used Though signal generators or oscillators provide a reasonably stable signal the generated frequency varies by a few hertz through time For this application this variation will not do since we are aiming to lock the signal that is buried in noise Therefore a phase locked loop PLL is also required to ensure that the reference signal is precisely tuned and whose frequency is continuous Basically the PLL along with passive components with calculated values is fed the sinusoidal signal at a specific frequency The circuit then feeds back the signal to the PLL and stabilizes the frequency so as to ensure that it is fixed at the desired value Care must be taken to select the adequate values for the passive components Otherwise the obtained frequency will not match the desired one Formulae have been provided for this purpose and whenever the results render a non commercial value for resistors and or capacitors trimpots are often advisable to ensure frequency accuracy 2 6 1 Lock in Amplifier Principle of Operation The reference signal is fed to the lock in via one input channel and to a phase locked loop whereas the noisy signal and fed to another one The noisy signal then enters an optional amplifying stage because usually the amplitude of the desired signal is too small usually in the range of mili or nanovolts After the a
92. nput of the reference signal for the lock in amplifier The digital control switch from figure 14 represents a simple digital switch that in this case will be one of the acquisition cards digital outputs Five of these terminals were used for each of the signals The relay is fed by a 12 V source the same as the detector so that no additional voltage sources are required The function generator emulates the reference signal from the PEM controller and the response was monitored in an oscilloscope A computer simulation using Multisim is shown in the figure below in both the ON and OFF state ON state OFF state Figure 3 15 Software simulation for the switching device 54 Finally the overall connection diagram including LCVRs PEM controllers switch DAQ source and detector is depicted in figure 3 16 Ref Signals Detector To LCVR 1 GND To LCVR 2 mo Bojeuy 1KHz Figure 3 16 Connection diagram for the system 3 3 3 Signal Analysis RS 232 Interface Control Program Basic Serial Write and Read vi The program enables data communication in and out of the serial rs232 port allowing the user to control the transmission rate number of bits to read or write and the port number to use The program is already an example from the Labview library and merely used as an addition to the overall program for communication with the lock
93. nted horizontally between both of them The PEM modulation is controlled with a square signal at a frequency of 47 KHz with different phase retardances that can be modified by the users via a control provided by the PEM manufacturer An important property of these photoelastic modulators is that the beam must enter the PEM at the precise centre of the crystal given that according to the manufacturer the modulation varies sinusoidally throughout the crystal as it moves away from the centre This was tested and proved to be correct Thus if the beam enters the crystal in some other point that is not the centre the obtained curves will not be the ones expected For this reason a black cardboard mask was made for both modulators that cover the windows the crystals are in and with a small orifice in the exact centre so as to ensure the incident beam enters the PEM at the right point Using a mathematical analysis software in this case Mathcad the ideal light intensity transmission curves corresponding to several different polarisation states passing through the system were estimated in order to predict the response that was to be obtained during experimental trials The experimental setup for these tests is shown in Fig 2 Fig 3 2 Experimental setup used for the characterisation of the photoelastic modulator Two of the ideal curves are presented in figure 3 3 for two different amplitude phase retardations half and 1 5 wave
94. ntil the user presses the OK button before continuing with the next measurement until the specified number of readings has been completed 57 After each measurement the polarisation ellipse Stokes vector ellipticity and orientation are displayed for the user to see Controls and File Path for data logger status indicator Write the file path in which you want to create the datalog or create new file TXT or ASCII File Path C Documents and SettingslAdministrador EscritoriolLIA txt 7 Controls Sequence Results Results Il BO co DO ThetaBOThetaCO ThetaDo V Measuring data XY Graph 103991 S9MOIS Stop and Quit Ellipticity angle Table where results are displayed Polarisation Elipse and degree of polarisation Figure 3 19 User interface for automatic measurement sequence Once the measurements are finished the program displays the readings in a data table for perusal whilst sent to a data log ASCII or TXT file The different columns containing information on the four Stokes parameters are also drawn in graphics for better analysis and simplicity purposes Nevertheless the above program is only one half of the entire project since the measuring stage must work in synchronicity with the state generator constituted by the already mentioned LCVRs Thus the state generating program which sequentially generates four of the six fundamental polarisation states was implemented in th
95. o lt 2 T lt 7 E e Orientation second measurement N o o al o o o al o Amplitude V Comparison between the obtained curves for orientation The lilac curve gt E E 2 2 u corresponds to LCVR1 and the blue curve to LCVR2 Bllipticity 0 6 0 4 va 0 NO AA NA Amplitude V Figure 4 3 Comparison between the obtained curves for ellipticity of outcoming beam The lilac curve corresponds to LCVR1 and the blue curve to LCVR2 Although a slight phase difference is evident one can also clearly see that both curves are very similar to each other However it must be noted that even a slight deviation in alignment and orientation may cause a certain amount of error in the obtained data Once having established the correct performance of both LCVRs the stage for the polarisation state generator was set up As stated in previous chapters this stage consists on a linear polariser followed by two LCVRs the first oriented at 45 and the other at 0 A picture of the setup for the PSG may be seen in Fig 4 4 65 Figure 4 4 Experimental setup for the polarisation state generator based on two liquid crystal variable retarders 4 1 2 Characterisation of Polarisation State Generator With all the constituting elements working as a single system the next step is to test and make the appropriate measurements in order to ensure its correct performance Hence a series
96. ocated between the PSG and PSA The PSA 24 then follows the sample with a PEM oriented horizontally a second PEM at 45 and finally a fixed analyser at 0 PSG PSA 0 45 0 o 45 0 A A A 94 Y Ti y i 4 Source P PEM1 PEM2 Sample PEM3 PEM4 A detector Fig 2 5 Complete Mueller polarimeter based on photoelastic modulators The same notation as in the previous figure is used for the constituting elements 2 4 3 Oscillating Element Polarimeter Yet another setup for measuring the Mueller matrix has been proposed based on the use of four LCVRs De Martino 2003 Uberna 2006 Although still under development the results obtained thus far seem promising The PSG stage generates a sequence of four different retardations before the beam enters the sample Different retardation values have been tested each based on the work of different authors and criteria A set of four values has been proposed by the authors with which the most accurate results have been obtained The experimental setup for the instrument is presented as follows PSG PSA Oy 0 Source P LCVR1 Levr2 Sample LCVR3 LCVR4 A detector Fig 2 6 Complete Mueller polarimeter based on liquid crystal variable retarders LCVR 6 and its different subindexes represent various possible orientations of the elements 23 2 4 4 Applications of a Mueller Polarimeter Whether in transmission or reflection certain materials can affect the polarisation
97. opic when stressed and will thus induce the same kind of birefringence as an anisotropic crystal like calcite A picture of the constituting elements of a photoelastic modulator is shown in figure 1 7 A piezoelectric transducer is a block of crystalline quartz cut at a specific orientation 18 Xcut A metal electrode is deposited on each of two sides and the transducer is cut in such a way that it resonates at a specified frequency F The resonance is uniaxial and is directed along the long axis of the crystal A block of fused quartz is cemented to the end of the transducer The length of the fused quartz is such that it also has F as the fundamental longitudinal resonance When both elements are cemented together resonance of the transducer causes a periodic strain in the fused quartz Jellison 2005 Signal Input ya PRZ gt SN N J A A Figure 1 7 The components ofa photoelastic modulator 1 4 Dual PEM Systems in Polarimetry A dual Photoelastic modulator system can obtain all 16 elements of the Mueller Matrix provided the four incident polarisation states of the incoming beam are known which describes the polarisation properties of a material Goldstein 2003 The typical configuration for such an ellipsometer would be tuning the first PEM P1 at frequency F and orientation of 0 and the second PEM P2 tuned at frequency F2 where Fz is slightly different from F Furthermore P2 must have an o
98. pse vi program gathers the calculations form the previous program draws and displays the corresponding polarisation ellipse from the specified data and sends it back to the main program for the user to better visualise the readings 3 4 Main Labview Program and User Interface The program may be divided in two parts the manual and the automatic The manual part comprises Boolean and numeric controls for direct communication with the LIA The amplifiers manual provides the user with a set of instructions for different adjustments measurements and specifications that can be controlled during a measurement These commands were implemented in the program by means of the Basic serial write and read vi see previous section These controls include manipulation of sensitivity time constant filters reference floating or grounded reference signal internal or external reset autophase autoreserve and autogain These last three are of 56 particular importance since all three must be pressed in sequence autoreserve autogain autophase for the lock in to perform the measurement accurately The rest of the aforementioned controls are mainly used to avoid overloading and minimise noise Furthermore the program reads and monitors the LIA s state overload unlocked upon pressing a Boolean control and displays the information by means of text boxes or Boolean indicators depending on the data type The user also has the option of sending
99. reference signal used to locate a specific component of the system s output signal it follows that the reference must have the same frequency as the one we wish to measure Furthermore the reference must be perfectly synchronised to the other for the lock in to happen Fortunately each PEM controller has two signal outputs which are the square signal at which the PEM is being driven with a frequency f and a second square signal at twice the frequency f Thus we have therefore a total of four signals f 2f f2 and 2f2 The subindexes 1 and 2 refer to the two PEMs one driven at 45Hz and the other at 47Hz Finally the chopping frequency must also be taken into account given that it is modulating the signal as well though in this case in matter of amplitude A switching device was hence developed intended to be controlled by the computer and sequentially switch among all four signals to be fed to the lock in amplifier for the different amplitudes to be measured and sent in turn to the computer Simply put the device feed the different reference signals to the lock in amplifier one at a turn through one same output Figure 14 shows the schematic diagram for a single switch The switching device is constituted by five of this 33 Function Generator uu Oscilloscope oe gt y 7 as ral s sa We 9 A l Digital Control gt J 4 Switch one loo a Figure 3 14 Digital switch used to control the i
100. rientation of 45 P2 is then followed by a linear polariser at 0 as shown in figure 1 8 12 0 45 0 0 45 A 5 Ps LevrRi Levee Sample PEM1 PEM2 A detector Figure 1 8 Polarimetric system based on photoelastic modulators PEM y PEM A is a linear polariser analyser 1 4 1 Applications of a Dual Modulator System Whether in transmission or reflection certain materials can affect the polarisation state of light that interacts with them This is due to intrinsic qualities and properties of said materials such as optical activity chirality and reflectivity Applications for Dual PEM Systems range from the medical to the military Depending on the wavelength and other parameters the system enables analysis and characterisation of different materials most of them organic in nature but also certain reflecting materials Such materials are used in medical analysis holography food processing and pharmaceutics among others Dual PEM polarimeters are used in astronomy to study light polarisation from nearby stars and sunspots Another useful application of this system is in optical fibres When a fibre is bent it generates mechanical stress which in turn causes the polarisation state of the light travelling through the fibre to change Light polarisation may also vary depending on the environment the fibre is in Polarimeters are hence used to monitor the polarisation state of light coming out of the fibre Hind
101. rm measurements in reflection as well as in transmission for future stages of the instrument Finally it must be determined whether a single point or a wide area is to be analysed Thus an appropriate mount for either laser or camera must also be implemented 5 3 5 Readings for wider areas As stated above one possibility of future stages of the project is to analyse more than one point within the sample That is a wider area in which different changes may be taken place in different points of the sample A CCD camera is 79 to be bought and will be used instead of the photoreceiver Image processing might thus be necessary in the future and the control program and calculations should be modified accordingly 5 3 4 Spectral range Finally the instrument is intended to work within a wide spectral range At the moment the instrument only detects red light at a wavelength of 1 632 8 nm If the spectral range is to be widened a white light source must be used along with a monochromatic so that selection of wavelength is available Furthermore the camera which is to replace the photoreceiver must be sensitive to all the desired wavelengths so that measurements are possible 80 References Aspnes D 1976 Rotating compensator analyzer fixed analyzer ellipsometer Analysis and comparison to other automatic ellipsometers Journal of Optical Society of America Vol 66 No 9 Azzam R 1977 Fourier Photoellipsometers and Photopolar
102. rol Each LCVR is driven by a square signal with variable amplitude that ranges from 0 to 8 V rms and a frequency of 1KHz Great care must be taken not to apply any DC voltage to the LCVR for it could cause irreversible damages to its chemical constitution Therefore when a square wave signal of at least 1 KHz is not being applied the voltage must be that of 0 V With this in mind a LabView program was developed for characterisation and control of the retarders This program is explained in greater detail in the section below Program control VI Since there are two LCVRs to be controlled two independent analog outputs were required Given that the necessary frequency is not too high the performance that the NI DAQ 6229 see previous section provides was more than enough for the feat to be achieved A recently implemented feature of the Labview platform enables the user to output two analog signals either with the same or different characteristics simultaneously Hence synchronous control of both LCVRs was possible 51 A sequence of two analog outputs with varying amplitude from O to 8 V was developed in order to monitor and determine the required amplitude values to obtain the main six polarisation states These states include Linear polarisation at 0 Horizontally polarised light Linear polarisation at 90 Vertically polarised light Linear polarisation at 45 Linear polarisation at 45 Circular right polari
103. ry the further it travels The period of time in which the phase of a light wave remains on average constant is known as coherence time Given that it is possible to define a polarisation state only when both components of light maintain the same relative phase one with respect to the other it is possible to say that polarisation of light is only possible when the light is coherent Furthermore a single ray of light consists of two independent oppositely polarised rays When passed through a birefringent doubly refractive crystal such as calcite two emerging rays can be observed This is due to the fact that in a birefringent crystal these two rays experience different refractive indexes If then a second crystal is used through which both rays pass through by means of rotation one of the beams can be completely extinguished whereas the other one s intensity is maximised By rotating the second crystal again another 90 the first ray reappears at maximum intensity and the second one vanishes Finally if the crystal is to be reoriented at an angle of 45 the intensities of the two rays are equal These two rays are then said to be polarised Collet 2005 The two rays represent the S and the P polarisation states The S and P notations come from the German words for parallel paralelle and perpendicular senkrecht This way a light beam can be represented by two components the P polarisation component usually d
104. s Instrument 2005 Intrinsic qualities of materials have an effect on the way light interacts with them Properties and characteristics such as stress defects reflectivity and polarisation loss may be determined with the instrument by measuring the polarization state of light after passing through a material Other applications include thin film characterisation as well as laser test and measurement 13 1 5 Polarisation in Nature 1 5 1 Why is the sky blue In other planets and satellites in outer space the sky appears black and the stars are visible throughout all day regardless of the position of the Sun Nevertheless here on Earth the daytime sky appears blue and stars are not visible Whereas during night when the Sun is set the stars are clearly visible and the sky appears to be black Why is this John Tyndall explained this phenomenon by showing that scattering of sunlight thus polarising it to a certain degree takes place in the upper atmosphere Pye 2001 Furthermore he demonstrated that small particles in the atmosphere scatter light of short wavelengths more strongly than those of larger wavelengths Thus the blue color is predominantly scattered rather than say the red one Lord Rayleigh further estimated that the atmosphere need not necessarily contain solid or liquid particles for the scattering to occur A large enough amount of gas molecules will also suffice for blue light to be scattered As it may be
105. s VECTOFS oooccncccnccccccccncccconcccnonanannnnnnnnnnnnnnnnnnnnnonnnnnnnnnnnnnnnnnnnnennnnnnnos 62 Figure 3 22 Automatic measurement user panel displaying the Mueller matrix of the sample under Study iocomoiniioinimci a datan 62 Figure 4 1 Labview program for controlling the input square signal used to characterise the LOVE A A 64 Figure 4 2 Comparison between the obtained curves for orientation 65 vil Figure 4 3 Comparison between the obtained curves for ellipticity of OUECOMUIMG DC ANN concceesesaseatceactce seed sect eencrentaiw veces neque esuneade cae aneseaeeedeccencencestbenceadsexet 65 Figure 4 4 Experimental setup for the polarisation state generator based on two liquid crystal variable retardersS ccccccseeeeeeeeeeeeeeeeeeeeeeeeeeeeenees 66 Figure 4 5 Experimental setup for the polarisation state analyser based on two photoelastic MOdulatorS oooooooooocconcccnncccnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 68 Figure 4 6 Curves representing the last three stokes vectors for each of the linear polarisations with varying orientation from 0 to 180 69 Figure 4 7 Curves representing the last three Stokes vectors for each of the elliptical polarisations oriented a 90 and ellipticities varying from Figure 4 8 The sixteen Mueller Matrix elements averaged throughout five different measurements along with their respective error for a A 2 retarder seinen e
106. sation Circular left polarisation The monitoring procedure consisted in fixing one of the LCVRs at a specific amplitude of the square signal while sequentially varying the other and registering the resulting polarisations states of the outcoming beam knowing beforehand the polarisation state of the incoming beam The same process was then repeated with the other LCVR The resulting table provided the required information and the determined amplitude values required to achieve the aforementioned states of polarisation were hence implemented in the program A screenshot of the control program is shown below The amplitude values and their respective resulting polarisation state with an incoming horizontally polarised beam are shown AA apks aoar Cath Tew ut A Pa pan Pommnanen oom eee _ 3 Uea ven E OS Sue Unreal a a Em Cooder meda T ee ames Figure 3 13 Control program for dual LCVR system After having the amplitude values determined four out of these six polarisation states were selected and a new program generating all four states sequentially was made 52 3 3 2 PEM Control Switch Control Given that four different signals must be used as reference for the lock in amplifier to detect and measure the necessary amplitudes for the signal analysis As previously mentioned the photoelastic modulators are each controlled by separate device provided by the manufacturer along with the PEMs Since the
107. t one as it provides a greater number of measurements but the detection and data acquisition need to have a very fast response Stepper motors or servo motors are often the preferred choice for these polarimeters though systematic errors and encoder performance may affect the precision and reliability of the obtained data Giudicotti 2007 Different mechanical 18 setups have been used usually involving a quarter wave plate retarder and or an analyser mounted on a rotation stage driven by a motor Two of these setups are shown below on figure 2 The mechanism on the left shows a motor band system that enables automatic rotation of the base in which the waveplate is mounted The second mechanism proposes a system of two gears One of them is mounted on the motor whereas the second one serves the double purpose of rotating stage and mount for the retarder Needless to say the latter example is more accurate as long as both gears are perfectly compatible in matter of diameter number of teeth relationship Nevertheless at least the gear in which the waveplate is mounted ought to be custom made for the plate to fit properly in the exact centre Mini steppers have also been used successfully providing greater accuracy in the measurements Ord 1977 The measurements are then taken using the angular position of the transmission axis of the rotating element as reference hence determining the initial point of the graphic generated by the
108. tate include changes in the amplitude phase direction of the orthogonal field components and transference of energy from polarised states to the unpolarised state Goldstein 2003 Each of these elements may be in turn represented by a particular Mueller Matrix For instance a linear polariser with its axes along the x and y directions may be represented by the following Mueller Matrix pp pop 0 0 e p p 0 0 L Px Py PTP 2 6 2 0 0 2P P 0 0 0 0 2 PD where 0 lt p 51 and px and py are the attenuation coefficients of the polariser For simplification purposes an alternate notation may also be used where the same Mueller Matrix defined in 2 6 can be rewritten as 2 7 oowy gt Coop by SONS GSS oo Where 22 AE o p 2 7a 1 B zP p 2 7b 1 C ze PeP 2 7C Furthermore each of the Mueller Matrix elements describes a different property of the material it represents Among such properties it is possible to determine the diattenuation differential attenuation of orthogonal polarisations for both linear and circular polarisation states depolarisation coefficient and linear retardance assuming a thin film Thus the properties are represented as follows Tuchin 2009 Kim 1987 P LD LD CD LD CB LB mE LD P CB LB 2 8 LD CB p LB CD LB LBy Pp Where P Isotropic Absortion LDo Linear Diattenuation 0 or 90 LDas Linear Diatt
109. te having equal amplitudes Also if E Ey and dx by 1 3 Polarising Elements 1 3 1 Linear Polarisers Linear polarisers can transmit light whose electric field vector oscillates within the plane that contains the polariser s axis This plane s orientation can be varied by rotating the polariser If the plane is horizontal the polariser is called a horizontal linear polariser If the electric field of the light passing through the polariser s got a component that is orthogonal to the polariser s transmission axis it will suffer attenuation of said component Whenever a linear polariser is placed in front or behind another linear polariser both of them with their axes placed orthogonally to each other crossed polarisers all light should ideally be extinguished 1 3 2 Glan Thompson Prism The Glan Thompson prism configuration is shown in figure 1 4 The prism is polished in such a way that the optical axis is located in the plane of the entrance face as well as parallel to the diagonal cut This prism has several advantages Since light enters the crystal normal to the surface and to the optic axis both the ordinary and the extraordinary rays move normal to the surface without deviating For traditional Glan Thompson prisms both halves are glued together Note that the separating material between both halves of the prism does not necessarily have to have a refraction index which is intermediate to the ordinary and extraordinary ra
110. thogonal components in the same degree for any given polarisation regardless of the orientation of propagation is said to be isotropic in nature 1 3 5 Birefringent Plate Retarders Birefringent plate retarders can cause a phase difference between two orthogonal polarisations It is also possible to modify the polarisation state using anisotropic absorption elements Ss Figure 1 5 A quarter waveplate retarder Consider a linearly polarised light beam that passes through a birefringent crystal or waveplate Given that linearly polarised light is formed by two components Eq 1 3 this causes the two components to experience slightly different refractive indexes If we have a plate of thickness d and assuming that the wavelength remains the same before and after passing through the medium the wavelength in the crystal may be defined as 2 n where n is the crystal s index of refraction Thus the total number of waves in the plate is d A n If each of the mutually orthogonal components is affected by a different refraction index the phase difference after exiting the plate can be defined as d n nj 1 5 A 6 2n 10 Where ni and nj are the two different refractive indexes affecting the components hence causing for them to pass through the plate at different speeds Tompkins 2005 1 3 6 Liquid Crystal Variable Retarder LCVR Liquid crystal variable retarders are real time continuously tunable
111. tion a chopper may be added to the optical system rotating at a much lower frequency around 500 Hz thus providing for a greater signal to noise ratio Guo 2007 33 2 6 3 Why design and implement a LIA when there are commercial ones available There is a wide variety of commercially available lock in amplifiers that work within a specific frequency range Although it is advisable to use a commercial LIA for calibrating and testing the instrument it is nevertheless important that the final installment of the complete system include its own LIA Design and construction of a lock in specifically for the application at hand may be more desirable for a number of reasons Firstly the cost of a commercial lock in is significant and by purchasing it the total cost of the instrument under development is consequently increased Also when working with a specific set of single values precious time and calibration procedure may be saved with a circuit built to the exact instrument s specifications whereas with a commercial lock in a lengthy procedure involving warm up adjustment and calibration must take place before any actual measurements can be obtained Finally the whole automation process may be hindered or negatively affected by the limitations of the commercial lock in Although most of these devices have a built in system for computer interfacing and programming the port or other specifications and protocols might not necessarily b
112. ts it takes up too much time to lock the signal measure the amplitude and send the data to the PC Since the amplifier is designed for measuring signals with a wide range of frequencies and amplitudes it provides different time constants cut off frequencies and various options that the user can manipulate according to the signal they are trying to measure Since we have specific frequencies and signals to measure a lock in amplifier specifically designed for the system and measurement requirements might speed up the process since it would have a fixed time constant and cut off frequencies for the filters predefined so there would be no need for in the moment adjustments to be performed via PC or manually A good option would be designing an amplifier for each of the four signals to measure using each of the four reference signals This would then enable not only to have fixed parameters and save processing time but it would allow for the four signals to be measured simultaneously without the need for switching 78 and waiting one signal at one frequency to be measured before the next one can be read as is the case right now This would undeniably enhance the instrument s response and make the system non dependant from third party equipment by integrating it all in the same instrument It must be noted that these quadruple lock in amplifier was indeed contemplated and its design and implementation begun Nevertheless due to time an
113. uch as linear and circular birefringence and linear and circular diattenuation The system uses a silicon photodiode as a means of detecting the incident beam and its behaviour The photoreceiver encompasses along with the photodiode a preamplifying stage and a lock in amplifier for signal detection and analysis The system is controlled via a computer and a data acquisition card from National Instruments The control program was developed in Labview and allows the user to take measurements either manually step by step or with an automatic sequence The applications for this measurement device include material analysis for the development of optical devices characterisation of optical tissue detection of polluting substances and pharmaceutics quality control among many others Nombre de la Tesis POLAR METRO DE MUELLER COMPLETO BASADO EN RETARDADORES DE CRISTAL LIQUIDO Y MODULADORES FOTOELASTICOS Defensor Ing Alicia Fernanda Torales Rivera Asesor Dr Geminiano Mart nez Ponce Dra Cristina Solano Postgrado Maestr a en Optomecatr nica El polar metro de Mueller implementado funciona en transmisi n y esta compuesto por dos m dulos un generador y un analizador de estados de polarizaci n PSG y PSA respectivamente El PSG est constituido por un sistema dual de placas retardadoras variables de cristal l quido LCVR dispuestos de tal manera que pueden generar cualquier estado de polarizaci n al combinar los retardos
114. ure 6 Residuals vs test number used for verifying independence Once again if the residuals turn out to be independent no definite pattern should be observable along the horizontal axis If we look at figure 6 we can also conclude that this condition is also met thus validating our results 90 BIBLIOGRAPHY 1 R W Collins An C Chen Rotating polarizer and analyzer ellipsometry en Handbook of ellipsometry Eds H G Tompkins E A Irene William Andrew Pub Nueva York 2005 G E Jellison F A Modine Polarization modulation ellipsometry en Handbook of ellipsometry Eds H G Tompkins E A Irene William Andrew Pub Nueva York 2005 D Goldstein Polarized light 2nd ed Estado Unidos de Am rica Marcel Dekker 2003 p 562 H Guti rrez Pulido R De la Vara Salazar An lisis y dise o de experimentos 2a ed M xico McGraw Hill 2008 p 180 182 91 Appendix B Transmission Laser Ellipsometer Business Plan Dr Geminiano Martinez Ponce Dr Cristina Solano Sosa Eng Alicia F Torales Rivera October 5 2009 92 Transmission Laser Ellipsometer Theory Photoelastic Modulator PEM A photoelastic modulator causes a phase shift to change sinusoidally as a function of time This phase shift is obtained by making the two perpendicular components of light pass through a waveplate at different speeds This is achieved by inducing a time varying birefringence by way of a time
115. waveplates An LCVR is composed of two plates separated by a few micrometers This space is filled with nematic liquid crystal which is a birefringent material whose birefringence can be adjusted by means of a variating applied voltage Electrodes are located in specific places among the retarder so as to enable an electric field to be applied between both plates and hence the liquid crystal Upon application of the voltage the molecules within the liquid crystal gradually reorientate themselves until they are perpendicular to the plates As the voltage increases the molecules continue reorientating causing a reduction in birefringence and consequently in retardation Meadowlark 2009 Fused Silica _ Alignment layer Spacer LC Molecules Maximum retardance V 0 Fused Silica Alignment layer SS PAULA Spacer LC Molecules Minimum retardance V gt gt 0 Figure 1 6 Schematic representation of the principle of operation of an LCVR 11 1 3 7 Photoelastic Modulator PEM A photoelastic modulator causes a phase shift between the orthogonal components of a light beam to change sinusoidally as a function of time This phase shift is obtained by making the two perpendicular components of light pass through a waveplate at different speeds This is achieved by inducing a time varying birefringence by way of a time varying stress in a normally isotropic material An isotropic material will become anisotr
116. y using a lock in amplifier tuned and synchronised at the adequate frequencies If these conditions are met the Stokes parameter lap is proportional to the DC term in the Ip signal obtained by the photoreceiver Qap can be found from the amplitudes of the signals at frequencies 2 and 1 2 Uap is proportional to the amplitude of the signal at frequency 22 Finally Vap is calculated using the amplitudes of the signals at frequencies w and 21 m2 These amplitudes are obtained from L 21 0 3 12 2 Re 2 _ y J2 Re I a J 6 I J 6 I 3 13 ap ap Qp U 42 Re I 2 P SO I E 3 14 ap 48 J2 Im 1 0 _ 42 ImIQa to ap 7 3 15 J l J 8J 8 L where 1 At Mo fI exp ior dt 3 16 At 2At is the integration time and i 1 Numerical Evaluation The numerical evaluation of the full Stokes polarimeter was made using Mathcad The modulator frequencies have been set at f 42KHz and f 47KHz where 27f The integration time of the lockin was set at At 0 2ms A criterion for selecting the frequencies at which the lock in amplifier should be tuned is to identify the stronger signals through the analysis of the Fourier spectrum of equation 3 11 In figure 3 11a the figure spectra of the signals when linearly polarised with orientation y 0 and 7 4 and right circularly polarised light are shown From this it is evident that Qap and Vap will be obtained fro
117. y to know which polarisation state is entering the sample as well as which state is exiting it thus enabling calculation of which polarisation changes occurred during the process As in the case of Stokes polarimeters there are different elements available for both the PSA and PSG stages these being either rotating elements or phase modulating devices As in the previous section only complete Mueller polarimeters will be mentioned 2 4 1 Rotating element polarimeter A rotating element polarimeter capable of measuring all 16 elements of Mueller matrix is formed by a fixed polarimeter followed by a rotating retarder which together constitute the PSG stage The sample is located in the middle of both PSG and PSA stages The PSA stage is similarly formed by a rotating retarder followed by a fixed analyser The following diagram illustrates this setup PSG PSA Ah OO Q Q ot n Source P R1 Sample R2 A Detector Fig 2 4 Rotating element Mueller polarimeter where P denotes the polariser A is an analyser and R1 and R2 are retarders 2 4 2 Phase Modulating Polarimeter This system uses photoelastic modulators PEM as a means for controlling and determining the state of polarisation of a light beam The arrangement consists on a fixed polarimeter oriented at 0 a PEM oriented at 45 followed by a second PEM oriented horizontally These elements together constitute the PSG stage of the system Again the sample is l
118. ys What is required is that the angle is such that one of the two rays suffers total internal reflection and the other one does not B fos Figure 1 4 Glan Thompson prism Perspective A and cross sectional B The optic axis is shown by the double headed arrows in A and by the matrix of points in B 1 3 3 Dichroic Sheet Polariser In dichroic sheet polarisers the molecules within a plastic sheet are re orientated in such a way that their transition dipole moments are aligned along a specific axis Thus light polarised in this same axis is absorbed whereas light polarised orthogonally is transmitted 1 3 4 Retarders Retarders make the absolute phases of two orthogonal polarisation components to be varied after propagation as a function of thickness A common example is the quarter wave plate retarder 2 4 which increases by 90 the phase of a linear polarisation relative to another Retardance is an effect caused by the refractive index As light is transmitted from vacuum to another material the speed of light is reduced by a factor of 1 n where n is the refractive index of the material Since the frequency remains constant when the light passes from one medium to another this results in a faster variation of the phase angle of light within a body than in vacuum Consequently any transparent body increases the phase of light in comparison to the one it has outside the body A body that provokes retardation between or

Chapter 1 - Biblioteca CIO

Contents

Download Pdf Manuals

Related Search

Related Contents