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FandPLimitTool User`s Manual

1. 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 3D Resolution Accuracy 3D Resolution Accuracy 3D Resolution Accuracy 3D Localization Accuracy 3D Localization Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Symmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Noise Aymmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Asymmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Noise Cartesian Parameterization Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization Airy Model Fundamental Limit Symmetric Parameterization Airy Model Pixelated with Poisson Noise Symmetric Parameterization Airy Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Airy Model Fundamental Limit 4symmetric Parameterization Airy Model Pixelated with Poisson Noise Asymmetric Parameterization Airy Model Pixelated with Poisson Gaussi
2. Figure 8 4 1 Calculation and Final confirmation Step 2 When the calculation is completed the Calculating button text will change back to Calculate Limits of Accuracy and the Results window will be brought in focus In addition the console window will be hidden when the calculation is over The console window can be accessed any time by selecting the Console option under the View Menu MUMDesignTool P Results PE 3D Localization Accuracy Born Vvolf Model Pixelated with Poisson Gaussian Noise Results Limit of the accuracy of y0 6 3512 nanometers y0 6 3512 nanometers z0 1522 174 nanometers Photon detection rate 0 87255 photons s Background level 538 056 photone pixells Figure 8 4 2 3D localization Accuracy results window 2D Resolution measure 9 2D Resolution measure This section provides an example of how to use the FandPLimitTool to calculate the accuracy with which the 2D location of two objects can be resolved from their image PREM The objects are assumed to be in focus with respect to the objective lens and the image of each object is assumed to be an Airy profile The calculation takes into account the stochastic nature of the photon detection processes and assumes the photons detected from the object to be Poisson distributed In addition the calculation also takes into account extraneous noise sources in particular the background component which is modeled as additive Po
3. FandPLimitToo l For single molecule localization and resolution MUMDesignTool Designing the focal plane spacing for multifocal plane microscopy UT SOUTHWESTERN Room ND6 310 6001 Forest Park Rd Dallas TX 75390 8576 1 214 648 1922 1 214 648 1259 Ward Ober Lab This document is a users manual for the Fundamental and Practical Limit Tool FandPLimitTool and the MUMDesignTool It explains how to calculate 2D and 3D localization accuracy limits as well as 2D and 3D resolution limits for single molecule microscopy data In addition it illustrates how to design the focal plane spacing for a multifocal plane microscopy setup with up to 10 focal planes Introduction FandPLimitTool For single molecule localization and resolution MUMDesignTool Designing the focal plane spacing for multifocal plane microscopy User s Manual Copyright 2004 2014 Ward Ober Lab http www wardoberlab com wardlab utsouthwestern edu Updated on June 30 2014 by Amir Tahmasbi Development Team Raimund J Ober Amir Tahmasbi Anish V Abraham Jerry Chao Sripad Ram Felix W Tang and E Sally Ward MUMDesignTool Contents Sken E A EE E E ee ee ee eee ee eee een 4 PV S IE WAI 2S oea gta oe lt n aaeri earn asso ena E duns gues E E N EE 6 WGI FOCI TNO cesses E E EEE pease E A E A E N EE E EA E O 7 WRIN e E E E E E NE E E E N E E 7 SOWIE OVT W oer nE e E E R O E A E 7 Pe
4. Trapezoidal v Additional parameters Double integration method Trapezoidal v Additional parameters Limits of summation lower limit upper limit 1 3000 specify x specify Limits of integration lower limit upper limit M A Figure 1 3 5 Noise factor calculation parameters Step 10 To improve screen clarity close the Advanced parameters window MUMDesignTool Remark 5 Closing the window is not in any way required by the application for the calculations to be performed and is only a suggestion in order to reduce the number of open windows and hence improve screen clarity You can access the window again at any time by clicking the Advanced Parameters option under the Parameters Menu in the main application window 1 4 Viewing and saving the parameter summary NOTE This is a new feature of the FandPlimitTool V1 2 Typically it is necessary to save the required and advanced parameters for later developments and to keep track of calculations This new feature provides a summary of the required and advanced parameters in a plane text format Step 1 Access the required inputs summary window by hitting the Parameter Summary option under View Menu BB Parameter Summary S al amp Summary Localization Accuracy 2D Airy Pixelated Poisson a Gaussian Basic Inputs Numerical Aparture 1 45 Wavelength 0 69 microns Exposure time Interval 0 0 13 s Magnification 100 Pixel Dimensio
5. 7 Sum Fix Plane lines g 1 2 v 3 v 4 6 W 7 W e v7 Ww 2 3 v 4 v5 7 We v 9 10000 photons Moise Parameter Setting ai Moise type Poisson Gaussian Branching py k 74 ane Markers B Background level 35 60 85 photons s pkt Examples Poisson geg PIT array pixel Readout noise std 8 5 7 e pixel Poisson Gaussian e g CCD OMO EM gain 250 100 110 Poisson Gaussian Branching teg EMCEE F Show Be ees E Reset Export Precise Mode Split windows taut sal EM model 1 1 1 1 Geometric model 2 High gain model 3 Gaussian model Done Photon 26 33 34 33 Figure 7 4 1 Entering the noise parameters Step 2 In Noise Parameter Setting Precise Mode window select the Poisson Gaussian Branching option in the Noise Type drop down menu This will consider background readout and branching noise for the calculations This option is suitable when using an EMCCD detector NOTE Holding the mouse pointer on this drop down menu will give a brief explanation as a tool tip text about the suitable option for different types of detectors see Figure 7 4 1 Step 3 Enter the values Background noise 35 60 85 the Readout noise std 8 5 7 the EM gain 250 100 110 and the EM model 1 1 1 Click OK when done The Precise Mode button
6. MUMDesignTool 11 2 Providing required parameters Step 1 Select the calculation option 3D Localization Accuracy Multifocal Pixelated with Poisson Gaussian Noise from the Calculate pull down menu in the main application window Step 2 The required parameters window which is visible by default will be updated accordingly If this window is not visible access it by clicking the Required Parameters option under the Parameters Menu in the main application window Step 3 In the Plane selection section of the Required parameters window select Plane 1 Step 4 In the Fundamental inputs Plane 1 section of the window enter the values for the various fields as follows Zo 0 5 Alpha 15 708 Object medium refractive index 1 515 Numerical aperture 1 3 Wavelength 0 52 Photon detection rate 10000 and Exposure time 0 13 BB Required Parameters GIE amp S 3D Localization Accuracy Multi focal Pixelated with Poisson Gaussian Noise Plane selection Plane 1 Plane 2 Fundamental inputs z0 0 5 microns Alpha 15 708 1 microns Immersion medium ref index 1 515 Numerical aperture 1 3 Wavelength 0 52 microns Photon detection rate 5000 photons s Exposure time 1 seconds Additional inputs Magnification 100 Photon detect rate ratio 0 5 0 5 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Symm
7. Trapezoidal hd Additional parameters Perform calculations Calculate Limits of Accuracy Calculate ha Limits of summation lower limit upper limit M A uze_defautt m Limits of integration lower limit upper limit MIA use_detautt m Figure 9 3 1 2D Resolution Accuracy advanced parameters window MUMDesignTool Step 2 In the Model profile calculations section of window access the Pixel integration method pull down menu and select Trapezoidal BR Advanced Pararneters Lo e BY Trapezo gt E EA x Gridding 2D Resolution Accuracy Airy Pixelated with Poisson Gaussian Noise Symmetric Parameterization Model profile calculations Pixel integration method Trapezoidal Additional parameters Background type Constant m Additional parameters Y Gridding 13 OK Cancel Figure 9 3 2 Pixel Integration Trapezoidal options Step 3 Click the Additional parameters button next to the Pixel integration method pull down menu In the dialog box that appears enter values for fields as follows XGridding 13 YGridding 13 Click OK when done Step 4 Access the Background type pull down menu and select Constant There are no additional parameters to be accessed via the Additional parameters button for the Constant option Step 5 In the Fisher information matrix calculations section of the window access the Single integration method and select
8. 0 0 5 Xo 13x4 5 100 yo 13x4 5 100 Pixel size 13 13 and ROI size 9 9 3D Localization accuracy measure Multifocal Plane Remark 17 The center of a 9 pixels x 9 pixels pixel array where the dimensions of each pixel is 13 um x 13 um is 4 5 x 13 um x 4 5 x 13 um To convert this location coordinates to the object space the coordinate values are divided by the magnification Hence the location coordinates are specified as 13x4 5 100 um x 13x4 5 100 um Step 6 In the Extraneous noise sources Plane 1 section of the window enter the values for the various fields as follows Background level 25 and Standard deviation 8 Step 7 In the Plane selection section of the Required parameters window select Plane 2 Then repeat step 6 for Plane 2 Remark 18 In case that the localization accuracy is required for an EMCCD detector the Use EM checkbox Should be checked and the desired value for the electron multiplication gain should entered in the EM gain field For more information see Remark 2 Step 8 In the Parameters to be estimated section of the window ensure that all check boxes for all parameters are checked 11 3 Providing advanced parameters NOTE All inputs in the Advanced Parameters window are optional The default values provided have been found to work adequately for typical imaging conditions Step 1 Access the advanced parameters window by clicking the Advanced Parameters option und
9. 2 and in case of using an EMCCD detector the stochastic electron multiplication noise that is modeled as a branching process 3 It is assumed that the pixels are rectangular in shape with no dead space between any two pixels Further the ROIs containing the images of the object are assumed to be rectangular arrays of pixels The object is assumed to be in the center of this rectangular pixel array and the location of the object is specified with respect to the object space Refer to 1 for more details regarding the design of focal plane spacing for a MUM setup 7 1 Summary of simulation conditions The following table summarizes the imaging conditions under which the calculations are performed Property VEIG Table 7 1 1 Summary of simulation parameters for the MUMDesignTool The MUMDesignTool 7 2 Providing the inputs and configuring the MUMDesignTool Step 1 Access the Configure Setting MUM Design Tool window by clicking the MUMDesignTool option under Tools Menu in the main application window or through its shortcut Ctrl M BB Configure Settings MUMDesignTool F PEE ET 3D Localization Accuracy Born VWolf Model Pixelated with Poisson Noise Simulation parameters Number of focal planes 2 z Photon detection rate 10000 photons s Photon count percentages 50 50 Immersion medium ref index 1 515 Numerical aperture 1 45 Wavelength 0 69 microns Exposure time 0 1 seconds Magnification
10. In the dialog box that appears enter the values Step size 0 0005 Lower limit 0 and Upper limit 1 Click OK when done Step 7 Access the Background type pull down menu and select Constant There are no additional parameters to be accessed via the Additional parameters button for the Constant option 3D Localization accuracy measure Multifocal Plane Step 8 In the Fisher information matrix calculations section of the window access the Single integration method pull down menu and select Trapezoidal Fisher information matrix calculations B Trapezo co E Single integration method Trapezoidal r Additional parameters Double integration method Trapezoidal i Aa step size Lower limit Limits of summation lower limit upper limit M4 use defaut qo Limits of integration lower limit upper limit M4 use _detaut i Upper limit 1 Alpha 2 x pi x numerical aperture f wavelength pi 3 1416 approx mA Cancel Trapezoidal integration step size 0 05 Figure 11 3 4 FIM Single Integration Trapezoidal options Step 9 Click the Additional parameters button next to the Single integration method pull down menu In the dialog box that appears enter the values Step size 0 0005 Lower limit 0 and Upper limit 1 Click OK when done Step 10 Access the Double integration method pull down menu in the same section of the window and select Trapezoidal Fisher inf
11. Trapezoidal Fisher information matrix calculations EJ Trapezo Lo E E Single integration method Trapezoidal Additional parameters Step size Double integration method Trapezoidal r Additional parameters 0 05 EPEETAN EEEE Moise factor calculation parameters Cancel Limits of summation lower limit upper limit MA use default m Limits of integration lover limit upper limit M4 use detaut Figure 9 3 3 FIM Single Integration Trapezoidal options Step 6 Click on the Additional parameters button next to the Single integration method pull down menu In the dialog box that appears enter Step size 0 05 Step 7 Access the Double integration method pull down menu in the Fisher information matrix calculations section of the window and select Trapezoidal Step 8 Click on the Additional parameters button next to the Double integration method pull down menu In the dialog box that appears enter the values XGridding 13 and YGridding 13 2D Resolution measure Fisher information matrix calculations BY Trapeze E m single integration method Trapezoidal ka Additional parameters m Griddi Double integration method Trapezoidal r Additional parameters 13 neang O Moise factor calculation parameters Y Gridding Limits of summation lover limit upper limit MiA use _defaut 13 Limits of integration lower limit up
12. Poisson Gaussian Noise Symmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Noise Aymmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Asymmetric Parameterization Gaussian Symmetric Model Pixelated with Poisson Noise Cartesian Parameterization Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization Airy Model Fundamental Limit Symmetric Parameterization Airy Model Pixelated with Poisson Noise Symmetric Parameterization Airy Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Airy Model Fundamental Limit Asymmetric Parameterization Airy Model Pixelated with Poisson Noise Asymmetric Parameterization Airy Model Pixelated with Poisson Gaussian Noise Aymmetric Parameterization Airy Model Fundamental Limit Cartesian Parameterization Airy Model Pixelated with Poisson Noise Cartesian Parameterization Airy Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization Born Volf Model Fundamental Limit Symmetric Parameterization Born Volf Model Pixelated with Poisson Noise Symmetric Parameterization Airy Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization V sx iV sy Vid V phi Vary a Parameter Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Values apply to both objects Fi
13. Sripad Ram E Sally Ward File Export View Parameters Tools About Ctrl A select a problem scenario 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Perform calculations Calculate Limits of Accuracy Calculate Model Image simulate Data Images Figure 6 2 2 About the FandPLimitTool MUMDesignTool 7 The MUMDesignTool This section describes how to use the MUMDesignTool a new software module in the new version of the FandPLimitTool to calculate and plot the Fisher information matrix FIM and the PLAM 1 along the z axis The MUMDesignTool is developed to help in designing the plane spacing for a multifocal plane microscopy MUM setup including up to 10 focal planes The MUMDesignTool provides two working modes The Rapid Mode takes into account the stochastic nature of the photon detection processes and assumes that the observed data is Poisson distributed 1 However this mode does not take into consideration other extraneous noise sources such as the background readout and stochastic signal amplification This mode yields a fast approach for the calculation of the FIM and the PLAM and allows changing the number of focal planes and their spacings in real time In addition the Precise Mode takes into account the extraneous noise sources such as the background noise which is independently Poisson distributed the readout noise which is modeled as independent additive Gaussian noise
14. l weeks gt 3000 Focal plane 4 18 3 amp Seen ocation parameters Z i o x0 0 325 microns Sum line yO 0 325 microns 2500 20 D a i 59 2000 1S Limit ruler Focal plane offset a 9 Number of focal planes 4 v 1500 358 n i D ss aa 2 f I gt 05 microns 2 aii 316 3 f ii f 1 microns N 6g A 15 microns 500 447 a 5 E 0 microns l 6 gt 9 microns ci 7 od Sdiri y E gt 0 microns 2 1 0 1 2 3 4 a i 0 microns Object z position yum 9 4f gt 0 microns 180 A 10 0 microns 160 Display options PDR Max 5 Ut Switch plots z0 x0 yO 10000 w T 120 Visibility 7 Sum Fix Y 10000 ma Plane lines 7 1 V 2 V 3 V 4 100 6 8 9 10 photons s 5 i 7 3 o Plane markers 7 1 7 2 7 3 V 4 7 5 80 6 V7 v 8 M 9 7 10 View mode Sum line 5 a Highlight region J Show 40 o fe tols 05 J 5 Reset l Enot Photon 9 0 Precise Mode Spli 25 25 25 25 3 2 1 0 1 2 3 4 Object z position pm Figure 7 3 1 MUMDesignTool Rapid Mode main window MUMDesignTool Step 1 In the Focal plane offset section of the window select 3 from the Number of focal planes pull down menu i 0 325 microns 2500 Vi y J TE U Limit rul
15. options section You will be asked to select a folder FL iwe x e n a Select a Folder Display optiong rs d POR hax Switch plots 0 z0 xO 6 yo Eo JY 10000 ime Desktop o Sum Fi Fix Y 10000 gt Libraries ane lines 7 4 F 2 73 4 5 a ae se Aa aaro photons p B Amir Tahmasbi Plane markers p 1 W 2 Wla l4 7 5 4 Computer le W 7 s v9 v1 0 4 fly Local Disk C3 Views mode defaut m aldi Arnir Highlight region Show b o Jei os amp T Folder mir Figure 7 3 4 Exporting the MUMDesignTool results MUMDesignTool Step 9 In the Browse For Folder window select a folder and click the OK button This will export the results as text files and the plots as pdf files 7 4 Precise Mode Once user has designed the plane spacing using the Rapid Mode the next step is to verify whether the designed spacing is appropriate in the presence of extraneous noise sources This verification is performed using the Precise Mode of the MUMDesignTool We next provide an example for this verification step Step 1 Click the Precise Mode button in the Display options section to calculate the accurate FIM and PLAMs along the z axis considering the extraneous noise parameters This will load the Noise Parameter Setting Precise Mode window as shown below Switch plots 6 z0 i xO C yO Fo Moise Parameter Setting Precise Mode 10000 Visibility
16. results 2 2 Plotting the limit of accuracy versus a parameter value Step 1 In the Multivalue Mode window click the Plot button This will open the Multivalue Plot Window shown in the following figure B muttival e amp s3 G Multivatue Plot o Photon detection rate photons s Limit of accuracy of x0 vs Photon detection rate Limit of accuracy of xO m 0 200 400 600 800 1000 Photon detection rate photons s Select plot Limit of accuracy of x0 vs Photon detection rate Figure 2 2 1 Multivalue results and plot windows Step 2 In the Multivalue Plot window access the Select Plot pull down menu and select Limit of accuracy of x0 vs Photon detection rate A plot of the limit of accuracy of x0 versus the photon detection rate will be shown as illustrated in the above figure Step 3 In the Multivalue Mode window click the Results button This will open the Multivalue Results Window shown in the above figure The selected values for the parameter will then be shown in a list box Clicking different lines of this list box will show the corresponding results in the Results Window MUMDesignTool 3 Simulating and visualizing model and data images Another new feature of the FandPLimitTool V1 2 is that user can now simulate and visualize model and data images of a single molecule associated with a desired problem scenario and a specific set of parameters A model
17. s Background level Poisson rate 100 Results and Parameters photons pixel s Model and Data Images sson Noise 3 x0 W y0 Parameters to be estimated 7 Alphat V Photon detection rate LaTex Report 7 Background level Alpha 2 x pi x numerical aperture i wavelength pi 3 1416 approx All Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Vary a Parameter Figure 5 1 2 Exporting the results and parameters NOTE Depending on the type of calculation i e singlevalue and multivalue the exported results text file may include one value or multiple values for the limit of accuracy of each parameter An example for the exported text file for a multivalue calculation is shown below s e Les G di t Amir Tahmasbi amp My Documents amp Exported files v Seorch Exported files p Organize Include in library Share with New folder w Favorites za r T 4 a al Results tet Notepad File Edit Desktop Downloads Recent Places Format View Help File Photon detection rate xd y0 Photon detection rate a Marne Date modified Type size af20 2014 2 30 PM af 20 2014 2 30 PM Text Document Text Document __ Parameters tet __ Results te a e aE g Farameters tt Notepad Edit Format Wiew Help ii Ls e jes Localization Accuracy 20 Airy Fundamental Limit 100
18. section of the window enter the values for the various fields as follows Zo 0 5 Object medium refractive index 1 515 Numerical aperture 1 3 Wavelength 0 52 Photon detection rate 10000 and Exposure time 0 13 Step 4 In the Additional inputs section of the window enter the values for the various fields as follows Magnification 100 Xo 13x4 5 100 yo 13x4 5 100 Pixel size 13 13 and ROI size 9 9 Remark 9 The center of a 9 pixels x 9 pixels pixel array where the dimensions of each pixel is 13 um x 13 um is 4 5 x 13 um x 4 5 x 13 um To convert this location coordinates to the object space the coordinate MUMDesignTool values are divided by the magnification Hence the location coordinates are specified as 13x4 5 100 um x 13x4 5 100 um Step 5 In the Extraneous noise sources section of the window enter the values for the various fields as follows Background level 1000 and Standard deviation 8 Remark 10 In case that the localization accuracy is required for an EMCCD detector the Use EM checkbox should be checked and the desired value for the electron multiplication gain should entered in the EM gain field For more information see Remark 2 Step 6 In the Parameters to be estimated section of the window ensure that all check boxes for all parameters are checked 8 3 Providing advanced parameters NOTE All inputs in the Advanced Parameters window are optional The default valu
19. text will change to Calculating and the application will temporarily become unresponsive while the calculations are being performed see figure below The console window will also be displayed NOTE The calculation could indeed take an hour to complete depending on the hardware capabilities of the platform on which the application is being executed Fp Console MUMDesigaTool Precise c Calculating the Fill and PLAM in Precise Mode M UMDesignTool modelobject 81 81 pro c m UMDesignTool MUM DesignTool moadelobjeact modelobjec gt modelobject gt modelobject gt modelobject gt modelobject MUR lesignTaol MUMDesignTool The MUMDesignTool ULI Visibility Ed sum lal Fix 10000 Plane lines F 1 F 2 F3 Z 4 ft 5 5 gt 5 g 40 photonsts Plane markers 1 W 2 Wla 7 4 7 5 Biv i 8 v4 9 x 1d View mode defautt Highlight region Show b o katol o8 f P oo Ol F Reset Export o Ept Photon Calculating Split windows 33 34 33 Figure 7 4 2 Calculation procedure in the Precise Mode Remark 8 Each element in the Background noise Readout noise std EM gain and EM model vectors corresponds to one of the focal planes For example in the above case the vectors have 3 elements associated with the 3 focal planes For more information about the different EM models see 3 Step 4 When the calculation is completed the Calculating butto
20. the Constant option 3D Resolution measure Born Wolf Model Step 8 In the Fisher information matrix calculations section of the window access the Single integration method pull down menu and select Trapezoidal Fisher information matrix calculations Single integration method Trapezoidal Additional parameters EJ Trapezo a mE Double integration method Trapezoidal Additional parameters Sten size Moise factor calculation parameters Limits of summation ower limit upper limit Mia Wse_defautt sa Lover limit Limite of integration lover limit upper limit Mas use _detaut mal Trapezoical integration step size 0 05 Upper limit 1 Alpha 2 x pi x numerical aperture wavelength pi 3 1416 approx tales apply to both objects Figure 10 3 4 FIM Single Integration Trapezoidal options Step 9 Click the Additional parameters button next to the Single integration method pull down menu In the dialog box that appears enter the values Step size 0 0005 Lower limit 0 and Upper limit 1 Click OK when done Step 10 Access the Double integration method pull down menu in the same section of the window and select Trapezoidal Fisher information matrix calculations i Trapezo HE xe single integration method Trapezoidal Additional parameters a S E Ez Double integration method Trapezoictal Additional p
21. the Defocus range section of the window enter the values for the various fields as follows Defocus start 2 Defocus increment 0 05 Defocus end 2 Step 4 In the configure setting MUM Design Tool window click the Done button The Done button text will change to Calculation in progress and the application will temporarily become MUMDesignTool unresponsive while the calculations are being performed During the calculation a console window will be shown to inform the user about the different steps of the calculation This console window will also display errors and warnings if there is any which is very useful for bug reporting purposes NOTE The calculation could indeed take half an hour to complete depending on the hardware capabilities of the platform on which the application is being executed Defocus range Defocus start 1 microns Detocus increment 0 1 microns Detocus end 1 microns Number of objects data points 21 Calculation in progress signTool signTool sign Toal signTaol signTaol sign Tool signTaol signTaol sign Toal signTaol signTaol sign Toa signTool signTaol Mmodelobject 21 21 processed modelobject 20721 processec modelobject 14 21 processec Mmoadelobject 18 21 processec moadelobject 17721 processec modelobject 16 21 processec moadelobject 15 21 processec moadelobject 14 21 processec modelobject 13 21 processec moadelobject 12 21 processec modelobje
22. the software the Results and Parameters option under the Export Menu becomes accessible Step 2 Select the Results and Parameters option under the Export Menu see figure below This will present a folder browser Step 3 Select a folder name in which you would like to save the results and parameters and click OK The results and parameters will be saved as two independent text files in the specified folder Fo Required Parameters Fundamental inputs Exporting results parameters images and report Le Co JS e 2D Localization Accuracy Airy Pixelated with Poisson Noise BB Results Sel ale ls Numerical aperture 1 45 Wavelength 0 69 Photon detection rate 1000 Exposure time 1 2D Localization Accuracy Airy f Pixelated with Poisson Noise microns Results Limit of the accuracy of photons s seconds x0 6 3716 nanometers Additional inputs yO 6 3716 nanometers Magnification 100 Location parameters x0 0 715 y0 0 715 Pixel size height width 13 13 ROI size height width 11 11 Alphat 0 000620 1 nanometers Photon detection rate 60 07 photons s Background level 9 98603 photons pixel s microns A amp uto center microns Alpha 2 x pi x numerical aperture wavelength pi 3 1416 approx microns X microns 7 eo eTe File View Parameters Tools Help no of pixels X no of pixels Extraneous noise source
23. the simulated model and data images and click OK The model and data images will be saved within two separate folders under the specified folder NOTE Depending on the type of calculation i e singlevalue or multivalue the exported model and data image folders may contain a sequence of images BB FandPLimitToo Browse For Folder File View Parameters Tools Help Select a folder to export the results parameters images Results and Parameters Model and Data Images sson Noise ME Desktop C Libraries B Amir Tahmasbi_ i Calculate Limits of Accuracy Calculate Model Image simulate Data Images 41 Papel ah x Local Disk C G labsoft labsoft S GA filetransfernew labsoft T LaTex Report Folder Amir Tahmasbi Make New Folder G amp MyDocuments Exported files gt v 4t Search Exported files Organize v Include in library v Share with New folder A A sv E z Name Date modified Type E Desktop n Datalmages 5 20 2014 4 25PM File folder ip Downloads dE Madellmages 5 20 2014 4 25PM File folder Recent Places Parameters bet 5 20 2014 2 30 PM Text Document E Results txt 5 20 2014 2 30 PM Text Document Libraries Documents Figure 5 2 1 Exporting the model and data images 5 3 Exporting a LeTex report NOTE A LeTex report can be generated only after performing a multivale calculation i e calculating the limits of accuracy when varying a para
24. viewer in Multivalue Mode Saving and loading the settings 4 Saving and loading the settings User can conveniently save and load the software settings which include the current problem scenario required and advanced parameters etc into and from the disk respectively This functionality is useful for retrieving the adjustments and results of a specific calculation after closing and reopening the software We next briefly describe how to make use of this important functionality 4 1 Saving the settings Step 1 To save the settings click the Save Settings option under the File Menu or use the shortcut Ctrl S see below This will present a dialog box to enter a file name The file extension is fim Enter your desired name and click Save BB FandPLimitToo lo eal Export View Parameters Tools Help Load Settings Ctrl L Save Settings Ctrl 5 Pixelated with Poisson Gaussian Noise Exit Ctrl Q Perform calculations Calculate Limits of Accuracy Calculate Model Image simulate Data Images Figure 4 1 1 Saving and loading the settings 4 2 Loading the settings Step 1 To load the settings click the Load Settings option under the File Menu or use the shortcut Ctrl L see Figure 4 1 1 This will present a dialog box to choose the desired file with extension fim Select a previously saved setting and press Open MUMDesignTool 5 Exporting results parameters images and report The FandPLimitT
25. 0 021005 0 021005 27 735 200 0 014853 0 014853 39 2232 300 0 012127 0 012127 46 0384 400 0 010503 0 010503 55 47 J00 0 0093939 0 0093939 62 0174 H00 0 0085754 0 0065 754 67 9366 700 0 0079393 0 0079393 753 5799 S00 0 0074265 0 0074265 78 4465 900 0 0070018 0 0070018 63 205 1000 0 0066425 0 0066425 87 7058 Basic Inputs Numerical Aparture wavelength 0 69 microns Exposure time Interval 0 0 13 5 magnification 100 Photon Detection Rate 1000 photons s Model parameters 0 325 0 325 13 2038 Advanced Inputs There are no advanced inputs for this calculate type a Figure 5 1 3 An example for the exported results and parameters MUMDesignTool 5 2 Exporting the model and data images Step 1 Exporting the model images is available upon performing at least one of the three different actions which are the calculation of the limits of accuracy see e g Section 1 the calculation of a model image see Section 3 1 and the simulation of data images see Section 3 2 On the other hand both model and data images can be exported only after simulating data images Once one of the mentioned calculations is performed the Model and Data Images option under the Export Menu becomes accessible Step 2 Select the Model and Data Images option under the Export Menu see figure below This will present a folder browser Step 3 Select a folder name in which you would like to save
26. 05 Lower limit 0 and Upper limit 1 Click OK when done Step 10 Access the Double integration method pull down menu in the same section of the window and select Trapezoidal Fisher information matris calculations Trapezo cl Ss Single integration method Trapezoidal ba Additional parameters A P Eza Double integration method Trapezoidal Additional parameters u Y Gridding Limits of summation lower limit upper limit Mis uze_defauk Limits of integration lower limit upper limit MiA use default Cancel Trapezoidal integration step size 0 05 Alpha 2 x pi x numerical aperture f wavelength pi 3 1416 approx Figure 8 3 5 FIM Double Integration Trapezoidal options Step 11 Click on the Additional parameters button next to the Double integration method pull down menu In the dialog box that appears enter the values XGridding 13 and YGridding 13 Step 12 The Fisher information matrix calculations section has a subsection titled Noise factor calculation parameters Enter the following values in this subsection Limits of summation 1 3000 Limits of integration 5000 5000 and Trapezoidal integration step size 0 05 Remark 11 The limits of integration and summation are initially set to default values which are automatically calculated based on the imaging conditions It is possible specify these limits by changing the value of the combo box to th
27. 100 x0 0 325 microns yO 0 525 microns Pixel size height width 13 13 microns X microns F FandPLimitTool f ROI size height width 5 5 no of pixels X no of pixels File Expert Wiews Parameters Help Defocus range MUMDesignTool Ctrl M Select a problem scenario Defocus start 1 microns s 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Defocus increment 0 1 microns Defocus end 1 microns Perform calculations Number of objects data points 21 Calculate Limits of Accuracy Calculate Model Image simulate Data Images Done Figure 7 2 1 The MUMDesignTool configuration window Step 2 In the Simulation parameters section of the window enter the values for the various fields as follows Number of focal planes 2 Total photon count 10000 Photon count percentage 50 50 Immersion medium refractive index 1 515 Numerical aperture 1 45 Wavelength 0 69 Exposure time 0 1 Magnification 100 Xo 13x4 5 100 yo 13x4 5 100 Pixel size 13 13 and ROI size 9 9 Note The center of a 9 pixels x 9 pixels pixel array where the dimensions of each pixel is 13 um x 13 um is 4 5 x 13 um x 4 5 x 13 um To convert this location coordinates to the object space the coordinate values are divided by the magnification Hence the location coordinates are specified as 13x4 5 100 um x 13x4 5 100 um Step 3 In
28. 100 sz 0 Pixel size 13 13 and ROI size 9 9 Remark 15 The center of a 9 pixels x 9 pixels pixel array where the dimensions of each pixel is 13 um x 13 um is 4 5 x 13 um x 4 5 x 13 um To convert this location coordinates to the object space the coordinate values are divided by the magnification Hence the location coordinates are specified as 13x4 5 100 um x 13x4 5 100 um Step 6 In the Extraneous noise sources Object 1 section of the window enter the values for the various fields as follows Background level 1000 and Standard deviation 8 Step 7 In the Plane selection section of the Required parameters window select Object 2 Then repeat steps 4 and 6 for the Object 2 10 3 Providing advanced parameters NOTE All inputs in the Advanced Parameters window are optional The default values provided have been found to work adequately for typical imaging conditions BR Advanced Pararneters eS fo E 3D Resolution Accuracy Born Vwolf Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization ae eed selection a ett Oobet2 OS Object 2 Object 1 fundamental inputs ew Alpha 15 708 Model profile calculations Pixel integration method Trapezoical kai Additional parameters Model integration method Trapezoidal Additional parameters Background type Constant Additional parameters Fisher information matris calculations FandPLimitToal Single integra
29. 12 pp 4457 4462 2006 7 S Ram A V Abraham E S Ward and R J Ober A novel 3d resolution measure for optical microscopes with applications to single molecule imaging Proc of SPIE vol 6444 2006
30. INKOW ssssseesssesssesssesseerseeerseearseenseseeansesanseeanstentsnsntaness 33 Figure 7 2 2 MUMDesignTool calculation IN progreSS ssssesessesssesseesssesseersesersesessesesseseenseeanseeetsteenenseeansess 34 Figure 7 3 1 MUMDesignTool Rapid Mode Main WINGOW sssssssssessesssessesesseeserseseseseeseessensesteatensesetensnses 35 Figure 7 3 2 Changing the number of focal planes in real time sessssssssusunsrsnsunununsnrnennunnnnnrnnnnunnnnnrnennnnnnnnrnnnns 36 Figure 7 3 3 The lateral elements of FIM and PLAM MUMDesignTool Rapid Mode scseeereeees 37 Figure 7 3 4 Exporting the MUMDeSIgNTOOI results ssssseeessseesseeetseessseseeensesersecenseeesaesetanseeanseeansnsensnsntansess 37 Figure 7 4 1 Entering the noise ParaMetess sssssssssssesssssssessssesseersecssseessseseeesecessecenseseeseseseeseeansesenseentsnsneansess 38 Figure 7 4 2 Calculation procedure in the Precise MOCe sssssssssessssessssseesseerseeesseenssesesnseeasseeanseeensnseteneess 39 Figure 74 32 MUMDesigntool Precise Mode siisvinssccarirrcninrevinetiserivinaweauacttiinentinretnanisinanarniaiemnenunaineianen 39 Figure 8 2 1 3D Localization Accuracy problem scenario and its required parameters window 41 Figure 8 3 1 3D Localization Accuracy advanced parameters WINGOW sssssssussrsrerenrunnnsnrnrnnunnnnnrnrnnnnnnnnrnnnna 42 Figure 8 3 2 Pixel Integration Trapezoidal OPtiON cssssssssesssesssssseessseeseeesesessesensesesseseean
31. M Single Integration Trapezoidal options Step 7 Access the Double integration method pull down menu in the Fisher information matrix calculations section of the window and select Trapezoidal Fisher information matrix calculations A 3 7 i T m a m Single integration method Trapezoidal v Additional parameters 2 tapez k gt a Fx Double integration method Trapezoidal Additional parameters X Gridding ma f E nthe Y Gridding Limits of summation lower limit upper limit M A use_defaut v 13 Limits of integration lower limit upper limit M A use_defaut v Figure 1 3 4 FIM Double Integration Trapezoidal options Step 8 Click on the Additional parameters button next to the Double integration method pull down menu In the dialog box that appears enter the values XGridding 13 and YGridding 13 Step 9 The Fisher information matrix calculations section has a subsection titled Noise factor calculation parameters Enter values Limits of summation 1 3000 and Limits of integration 5000 5000 in this subsection Remark 4 The limits of integration and summation are initially set to default values which are automatically calculated based on the imaging conditions It is possible specify these limits by changing the value of the combo box to the right of the limits of integration and summation fields Fisher information matrix calculations Single integration method
32. Results Plot Parameters to be estimated Alpha 2 x pi x numerical aperture fwvavelength pi 3 14176 approx Figure 2 1 1 Multivalue Mode setting window Step 2 In the Multivalue parameter section of window access the Parameter pull down menu and select Photon detection rate Step 3 In the Values field enter 100 100 1000 This will automatically define a vector containing 100 200 300 400 500 600 700 800 900 1000 Step 4 check the Auto center image for each calculation checkbox This will automatically center the particle in the ROI Step 5 In the main application window click the Calculate Limits of Accuracy button This will present a dialog box warning that the calculation may take a long time to complete Click Yes to proceed The Calculate Limits of Accuracy button text will change to Calculating and the application will temporarily become unresponsive while the calculations are being performed In addition the console window will become visible NOTE The calculation could indeed take a couple of hours to complete depending on the number of data points and hardware capabilities of the platform on which the application is being executed Varying a parameter multivalue mode Step 6 When the calculation is completed the Calculating button text will change back to Calculate Limits of Accuracy NOTE Steps 5 and 6 are explained in more details in Section 1 5 Executing the task and viewing
33. Xo and yo user can switch the FIM and PLAM plots to visualize the behavior of the corresponding coordinate along the z axis The embedded checkboxes help to hide or show different curves within the figures and enhance the visibility Moreover a desired region in the plot can be highlighted using other controls in this panel The Reset button in this panel resets the MUMDesignTool by recalling the Configure Setting MUMDesignTool Window The Split windows button shows the FIM and PLAM plots in new decoupled windows Also the Export button exports both the results as txt files and the plots as pdf files Finally the Precise Mode button runs the precise mode calculation of the MUMDesignTool to provide accurate results for the behavior of the FIM and PLAM curves This function will be discussed in detail later We next give an example for designing the focal plane spacing for a 3 plane MUM setup using the strong coupling spacing scenario for more information see 1 We assume that user has applied the steps in Section 7 2 Providing the inputs and configuring the MUMDesignTool Here are the steps 7 BB MUMDesignTool Rapid Mode a oR x File Help Simulation summary Refractive index Tube Length Numerical aperture Wavelength Exposure time 1 515 A 160 mm 1 45 0 69 microns O 1l seconds 100 oO co Focal plane 1 i te n D o o 5 0 wo Magnification Focal plane 2 Focal plane 3
34. ackground level 30 2715 photons pixel s Alpha 2 x pi x numerical aperture wavelength pi 3 1416 fapprox Figure 1 5 2 2D localization accuracy Results window MUMDesignTool 2 Varying a parameter multivalue mode Multivalue Mode is a new functionality designed for the calculation and visualization of the fundamental and practical limits on the 2D and 3D localization accuracy and resolution for a range of parameter values This section provides an example of how to use the Multivalue Mode to calculate the 2D PLAM for a range of an input parameter We assume that user has applied all the steps in Section 1 2D Localization Accuracy Limit 2 1 Providing inputs for the multivalue mode Step 1 Access the multivalue mode window by toggling the Vary a Parameter button at the bottom of the Required Parameters window Extraneous noise sourcels Background level Poisson rate 1000 photons pixels F alteaicetioce o kE 2D Localization Accuracy Airy Standard deviation 6 e fbixcel Pixelated with Poisson Gaussian Noise eee Electron multiplication parameters Muttivalue parameter F ne Uze EM EM gain 2 0082 Parameter Photon detection rate A EM model Geometric Values 100 200 300 400 500 600 Units photonsss Example 10 71 13 or 1011 1213 xO IM Alpha IW Background level E yO IV Photon detection rate W ASuto center image for each calculation
35. an Noise Aymmetric Parameterization Airy Model Fundamental Limit Cartesian Parameterization Airy Model Pixelated with Poisson Noise Cartesian Parameterization Airy Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization Born Volf Model Fundamental Limit Symmetric Parameterization Born Volf Model Pixelated with Poisson Noise Symmetric Parameterization Born V olf Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Muti focal Pixelated with Possion Noise Muti focal Pixelated with Possion Gaussian Noise 3D Resolution Accuracy Born VVolf Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Perform calculations Calculate Limits of Accuracy Calculate Model Image simulate Data Images Values apply to both objects Background level vary a Parameter Figure 10 2 1 3D Resolution Accuracy calculate type and its required parameters window Step 4 In the Fundamental inputs Object 1 section of the window enter the values for the various fields as follows Numerical aperture 1 3 Wavelength 0 52 Photon detection rate 10000 Object medium refractive index 1 515 d 0 1 phi pi 4 omega pi 3 and Exposure time 0 13 3D Resolution measure Born Wolf Model Step 5 In the Additional inputs section of the window enter the values for the various fields as follows Magnification 100 sx 13x4 5 100 sy 13x4 5
36. ange to Calculating and the application will temporarily become unresponsive while the calculations are being performed NOTE The calculation could indeed take half an hour to complete depending on the hardware capabilities of the platform on which the application is being executed BB FandPLimitTool File Export View Para A OWAARNING This calculation may take a long time to complete Are you sure Bou want to continue select a problem scenari 3D Resolution Accuracy Bo Perform calculations Calculating Calculate Model Image simulate Data Images Figure 10 4 1 Calculation and Final confirmation 3D Resolution Step 2 When the calculation is completed the Calculating button text will change back to Calculate Limits of Accuracy and the Results window will be brought in focus E Results k 2 E 3D Resolution Accuracy Born Vvolf Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Results Limit of the accuracy of ex 4 5562 nanometers sy 4 5082 nanometers az 33121041 nanometers d 41 7225 nanometers phi 0 017509 radians omega 12994251 radians Mat Mat Mab Figure 10 4 2 Results window 3D Resolution 3D Localization accuracy measure Multifocal Plane 11 3D Localization accuracy measure Multifocal Plane This section provides an example of how to use the FandPLimitTool to calculate the accuracy with which the 3D location of an object can be e
37. anseeanseeansneensnseeansens 51 Figure 9 4 2 Results window 2D Resolution esseessesssesessssseeserseessensesteesensesesansesesesensesesensuseeetensesesatansesntenseses 52 Figure 10 2 1 3D Resolution Accuracy calculate type and its required parameters windOW ssssssssssss 54 Figure 10 3 1 3D Resolution Accuracy advanced parameters WINKOW s sessssssessrsrrnenrnnnnsnrnrnnunnnnnrnrnrnnnnnnrnnnns 55 Figure 10 3 2 Pixel Integration Trapezoidal OPtiOns sssessssssssessecsssessesseersesesesessesesseseeensesansesessesensnseeansess 56 Figure 10 3 3 Model Integration Trapezoidal Options cssssssessssesrsseesesseerseeessesenseeesseseenseearseeatseeessesetaneess 56 Figure 10 3 4 FIM Single Integration Trapezoidal OPtiOns csssssessssesssssesseeerseserseessseseeesseeerseeanseeensneetensens 57 Figure 10 3 5 FIM Double Integration Trapezoidal Options csssssssesseseesseeersessseeessesseerseeerseeanseeenseentensens 57 MUMDesignTool Figure 10 4 1 Calculation and Final confirmation 3D Resolution sesesesssssseseesseeseesseseeseenseseeeterseentenees 58 Figure 10 4 2 Results window 3D Resolution ssessesssessesssseesesrssessenseseeesorsesecanseseeesensesesateeseeetansesesatansesetensnses 58 Figure 11 2 1 3D Localization Accuracy MUM calculate type and its required parameters window 60 Figure 11 3 1 3D Localization Accuracy MUM advanced parameters WINKOW ccsssseserseessersteeereees 61 Figure 11 3 2 P
38. arameters a Limits of summation lover limit upper limit MA Y Gridding 13 use detaut Limits of integration ower limit upper limit M A uze_defaut Trapezoidal integration step size 0 05 Alpha 2 x pi x numerical aperture J wavelength pi 3 1416 approx tales apply to both objects Figure 10 3 5 FIM Double Integration Trapezoidal options Step 11 Click on the Additional parameters button next to the Double integration method pull down menu In the dialog box that appears enter the values XGridding 13 and YGridding 13 Step 12 The Fisher information matrix calculations section has a subsection titled Noise factor calculation parameters Enter the following values in this subsection Limits of summation 1 3000 Limits of integration 5000 5000 and Trapezoidal integration step size 0 05 Remark 16 The limits of integration and summation are initially set to default values which are automatically calculated based on the imaging conditions It is possible specify these limits by changing the value of the combo box to the right of the limits of integration and summation fields MUMDesignTool 10 4 Executing the task and viewing results Step 1 In the main application window click the Calculate Limits of Accuracy button This will present a dialog box warning that the calculation may take a long time to complete Click Yes to proceed The Calculate button text will ch
39. astic nature of the photon detection processes and assumes the photons detected from the object to be Poisson distributed In addition the calculation also takes into account extraneous noise sources in particular the background component which is modeled as additive Poisson noise the readout noise of the detector which is modeled as independent additive Gaussian noise and the stochastic signal amplification noise which is present in EMCCD detectors 3 It is assumed that the pixels are rectangular in shape with no dead space between any two pixels Further the region of interest ROI containing the image of the object is assumed to be a rectangular array of pixels The object is assumed to be in the center of this rectangular pixel array and the location of the object is specified with respect to the object space Refer to 2 for details on determining the 2D localization accuracy in single molecule microscopy 1 1 Summary of imaging conditions The following table summarizes the imaging conditions under which the calculations are performed Property VEIG ET 1 Gaussian noisemean Joe Table 1 1 1 2D Localization Accuracy Summary of imaging conditions 2D localization accuracy measure 1 2 Providing required parameters Step 1 Select the problem scenario of 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise from the Calculate pull down menu in the main application window BB Requir
40. ation Step 3 In the Fundamental inputs section of the window enter the values for the various fields as follows Numerical aperture 1 45 Wavelength 0 69 Photon detection rate 10000 and Exposure time 0 13 Step 4 In the Additional inputs section of the window enter the values for the various fields as follows Magnification 100 Xo 13x4 5 100 yo 13x4 5 100 Pixel size 13 13 and ROI size 9 9 Remark 1 The center of a 9 pixels x 9 pixels pixel array where the dimensions of each pixel is 13 um x 13 um is 4 5 x 13 um x 4 5 x 13 um To convert this location coordinates to the object space the coordinate values are divided by the magnification Hence the location coordinates are specified as 13x4 5 100 um x 13x4 5 100 um Step 5 In the Extraneous noise sources section of the window enter the values for the various fields as follows Background level 1000 and Standard deviation 8 2D localization accuracy measure Remark 2 In case that the localization accuracy is required for an EMCCD detector the Use EM checkbox Should be checked and the desired value for the electron multiplication gain should entered in the EM gain field The default electron multiplication model is Geometric However different electron multiplication models e g High gain and Gaussian can be chosen from the EM model combo box based on the requirements By holding the mouse pointer on the EM model combo box a brief descrip
41. buted In addition the calculation also takes into account extraneous noise sources in particular the background component which is modeled as Poisson noise 1 the readout noise of the detector which is modeled as independent additive Gaussian noise 2 and the electron multiplication noise of an EMCCD detector which is modeled as a branching process 3 It is assumed that the pixels are rectangular in shape with no dead space between any two pixels Further the ROI containing the image of the object is assumed to be a rectangular array of pixels The object is assumed to be in the center of this rectangular pixel array and the location of the object is specified with respect to the object space Refer to 5 for details on determining the 3D localization accuracy in single molecule microscopy 8 1 Summary of imaging conditions The following table summarizes the imaging conditions under which the calculations are performed Property WETS Gaussiannoisemean OO 1 1 EM model Table 8 1 1 3D Localization Accuracy Summary of imaging conditions 3D Localization accuracy measure Born Wolf Model 8 2 Providing required parameters Step 1 Select the calculation option 3D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise from the Calculate pull down menu in the main application window Step 2 The required parameters window should be visible by default If it is not visible access it by clicking
42. ct 11 21 processec modelobject 10 21 processec modelobject 21 processec modelobject 8 21 proces Figure 7 2 2 MUMDesignTool calculation in progress Step 5 When the calculation is completed the MUMDesignTool Rapid Mode window will be brought in focus more details about this window will be discussed in the next section 7 3 Designing the plane spacing using the Rapid Mode Figure 7 3 1 shows the main window of the MUMDesignTool The Simulation summary section of the window represents a summary of the simulation parameters The Focal plane offset section of the window includes a pull down menu for selecting the number of focal planes as well as 10 slides to change the plane spacings Note that these settings can be performed in real time The right hand side panels which show the FIM and PLAM along the z axis for the MUM setup will be updated automatically by changing the plane spacing and other parameters The PDR section of the window assists us with choosing the total photon detection rate of the setup as well as the photon percentage for each focal plane Changing the number of planes will automatically update the photon percentages to be consistent with the total photon detection rate The MUMDesignTool The Display options section of the window provides controls for better calculation and visualization of the FIM and PLAM and also provides tools for exporting the results For instance using radio buttons Zo
43. damental inputs Object 1 Numerical aperture 1 3 Wavelength 0 51 Photon detection rate 10000 d 05 phi 0 7854 microns photons s microns radians Exposure time 0 13 seconds 3D Localization Accuracy Born VYolf Model Fundamental Limit 3D Localization Accuracy Born VYolf Model Pixelated with Poisson Noise 3D Localization Accuracy Born VVolf Model Pixelated with Poisson Gaussian Noise Additional inputs Magnification 100 Location parameters sx 0 325 microns sy 0 325 microns Pixel size height width 13 13 microns X microns ROI size height width 5 5 no of pixels X no of pixels Extraneous noise source s Object 1 Background level Poisson rate 1000 photons pixel s EM model Geometric Parameters to be estimated 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 2D Resolution Accuracy 3D Resolution Accuracy 3D Resolution Accuracy 2D Resolution Accuracy Perform calculations Gaussian Symmetric Model Pixelated with Poisson Noise Symmetric Parameterization Gaussian Symmetric Model Pixelated with
44. e right of the limits of integration and summation fields 3D Localization accuracy measure Born Wolf Model 8 4 Executing the task and viewing results Step 1 In the main application window click the Calculate Limits of Accuracy button This will present a dialog box warning that the calculation may take a long time to complete Click Yes to proceed The Calculate button text will change to Calculating and the application will temporarily become unresponsive while the calculations are being performed During the calculation a console window will be shown to inform the user about the different steps of the calculation NOTE The calculation could indeed take half an hour to complete depending on the hardware capabilities of the platform on which the application is being executed ols AO WARNING This calculation may take a long time to complete Are you sure wou want to continue E FandPLimitTool ole e File Export Wiew Parameters Tools Help select a problem scenario 3D Localization Accuracy Born Yolf Model Pixelated with Poisson Gaussian Moise Perform calculations Calculating Calculate Model Image simulate Data Images pisson Gauss Misture 6 of son Gauss Misture 5 of 6 Gauss Mixture 4 of 6 5 Mixture 3 of Ge fixture 2 of 6 Gauss Mixture 1 of Bb itialized Copyright 2 2004 2014 Ward Ober Lab For single molecule localization and resolution FandPLimitTool 1 2 Initializing the application
45. eceeeeseceeeeeeceeeeees 33 7 3 Designing the plane spacing using the Rapid Mode cccccccccsseccceeecceseeeeeneeeeeeceeeneceeeneeees 34 De CCS CIOS ico ssc pee E E E AEE 38 8 3D Localization accuracy measure Born Wolf Model cccccccccesssecceeceeseccceeaeeeeeeeeeaeeseeees 40 8 1 Summary OT imaging conditions scsiassiensosseassieveseswnisnedonnasisivensnseaiennaserseweiassiacessinanesvenieoinaeteess 40 8 2 Providing reguired parametel S ersirareininitr aer EEE TOE 41 8 3 Providing advanced parameters sseccssscccesscccesececenececenceceenceceuecessueceeeneeeeeuceseeecesseceseeeees 42 8 4 Executing the task and viewing results sssessesessensssreresrrrssrrrresrrersrrereserressreresrrreserereserresene 45 9 ZDARCSOWTOM Wig SRC r E red ota EE N E E OE EAE 47 9 1 Summary of imaging conditions essssesesssssensssreresrrrsssreresrrersrreressrerssreresererssreresrrreserereseeressne 47 92 Providing reguired parameters sererai ti e 48 9 3 Providing advanced parameters seoreacsiiieniriririer inite riter e EAEE Eeti 49 9 4 Executing the task and viewing results sssesseseseensesreresrrrssrreresrresssreresrrressreresrrreserereserresene 51 10 3D Resolution measure Born Wolf Model esssssssssssesssrensesrrrreessrerressrrrrressrrrressrrereeserrrressreeres 53 10 1 Summary of imaging Condi ONS serieren rier n ES A 53 10 2 Providing required PAarAMEteLS cccccssecccssecccsecccssccceececeececsn
46. eceeeueceeescessenceseueceseecensaees 54 10 3 Providing advanced parameters vccsccnucascocdsrosssenneasancccariaanedbaedsaeentsnevesoneneousedwaeesdadeosauned eas 55 10 4 Executing the task and viewing results ssssessesssrrnssrrrresrrrsssrrresrrerssrrresererssreresrrereseerese 58 11 3D Localization accuracy measure Multifocal Plane essesssesessesesrrrserrerssrrrssrrrresrrresrrererrrresene 59 11 1 Summary of imaging conditions esessessseeessreeresrrrssrreresrrresrrrrssrrressreresreressrersseereserersseerese 59 11 2 Providing reguired parameterne nn EEEE EAER 60 11 3 Providing advanced parameters ccccsseccesseccesecccsccceeececsececeneceseneceeencessuecesseceseuecesenees 61 11 4 Executing the task and viewing results essusessenssrrnssrrrrssrrrresreresrreresrrresrrressrereserereseerese 64 Roran O E EEE EEE EEEE E 65 MUMDesignTool List of figures Figure 1 2 1 Figure 1 2 2 Figure 1 2 3 Figure 1 3 1 Figure 1 3 2 Figure 1 3 3 Figure 1 3 4 Figure 1 3 5 Figure 1 4 1 Figure 1 5 1 Figure 1 5 2 Figure 2 1 1 Figure 2 2 1 Figure 3 1 1 Figure 3 1 2 Figure 3 1 3 Figure 3 1 4 Figure 3 2 1 Figure 3 2 2 Figure 3 2 3 Figure 4 1 1 Figure 5 1 1 Figure 5 1 2 Figure 5 1 3 Figure 5 2 1 Figure 5 3 1 Figure 6 1 1 Figure 6 2 1 Figure 6 2 2 Selecting the 2D Localization Accuracy calculate type csessssssssssssssssseesseesssesesersesarseeenseeeees 11 Required para
47. ection 5 Clicking the Parameter Summary option under the View Menu or hitting Ctrl P provides a summary of the required and advanced parameters in a plane text format This helps to conveniently review and save the parameters as a text file In addition clicking the Console option under the View Menu shows a console window in which the details of calculations will be listed This console window is also helpful for bug reporting purposes To calculate the limits of accuracy after specifying all desired parameters click the Calculate Limits of Accuracy button When the calculations are completed a Results window will be brought into view displaying the results The Results window can be accessed at any time by clicking the Results option under the View Menu or through its shortcut Ctrl R Similarly to calculate a model image after specifying all desired parameters press the Calculate Model Image A model image is an image profile that is devoid of stochasticity and noise To simulate realizations of this model image press the Simulate Data Images button Note that the simulated data images are corrupted by stochasticity and noise For instance depending on the Before you begin Pg desired set of parameters the image can be corrupted by extraneous noise sources such as background readout or stochastic signal amplification Finally clicking the MUMDesignTool option under the Tools Menu or hitting Ctrl M calls the MUMDesignTool application wh
48. ed Parameters 2 lol eo 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Fundamental inputs Numerical aperture 1 45 Wavelength 0 69 microns Photon detection rate 1 0000 photons s Exposure time 0 1 3 seconds Additional inputs 2D Localization Accuracy Airy Fundamental Limit Magnification 100 2D Localization Accuracy Airy Pixelated with Poisson Noise 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Location parameters ma 2D Localization Accuracy Gaussian Symmetric Fundamental Limit 0 0 325 i ii we tse microns Auimaanian 2D Localization Accuracy Gaussian Symmetric Pixelated with Poisson Noise y0 0 325 microns 2D Localization Accuracy Gaussian Symmetric Pixelated with Poisson Gaussian Noise 2D Localization Accuracy Gaussian Asymmetric Fundamental Limit 2D Localization Accuracy Gaussian Asymmetric Pixelated with Poisson Noise m 2D Localization Accuracy Gaussian Asymmetric Pixelated with Poisson Gaussian Noise ROI size height width 5 5 no of pixels X no of pixels 3D Localization Accuracy Born Wolf Model Fundamental Limit 3D Localization Accuracy Born Volf Model Pixelated with Poisson Noise Extraneous noise source s 3D Localization Accuracy Born VVolf Model Pixelated with Poisson Gaussian Noise 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Symmetric Parameterization 2D Resolut
49. er Focal plane offset z z0 Mumber of focal planes 3 ka Inf e 2 q F 05 micron T nm 5 ra a 5 t d microns p 4 15 microns microns microns Oo Oo riff _icrons Oo Oo Oo microns Object z positian um microns microns Figure 7 3 2 Changing the number of focal planes in real time Step 2 You will see an alert stating that Photon count percentages have been reset Click OK to proceed Step 3 In the Focal plane offset section of the window set the value of the plane spacing slider 2 to be equal to 0 6 microns Also set the value of the plane spacing slider 3 to be equal to 1 2 microns This will overlap the zero of the z0 FIM of each focal plane with the local maximum of that of the adjacent focal plane for more information see 1 As a result the FIM and PLAM curves will be updated Step 4 In the Display options section of the window select Sum line from the View mode pull down menu This will update the FIM such that only the sum line data points will be visible Step 5 In the Display options section of the window change the right hand side field of Highlight region to 0 6 and check the Show checkbox This will highlight the region between plane 1 and plane 2 for better visualization Step 6 In the Limit ruler section of the window set the z0 slider to 19 nm At this step you will see the Zo elements of the FIM and PLAM cur
50. er the Parameters Menu BB Advanced Parameters c E Ex 3D Localization Accuracy Mutti focal Pixelated with Poisson Gaussian Noise dvanced fundamental inputs A DO f Alpha 15 708 Update analytically Model profile calculations Pixel integration method Trapezoidal Additional parameters Model integration method Trapezoidal m Additional parameters Background type Constant Additional parameters Fisher information matrix calculations E FandPLimitTool Single integration method Trapezoidal Additional parameters File Expo Wiew Tools Help Double integration method Trapezoidal m Additional parameters Required Pararneters Ctrl U Select a problem Advanced Parameters Ctrl h 3D Localization Accuracy WiG TUCal PEREA WIT PUSSIN aS Limits of summation lover limit upper limit MAA use defaukt Perform calculations Calculate Limits of Accuracy Calculate hilo Limits of integration lover limit upper limit Mis use default Trapezoidal integration step size 0 05 Alpha 2 x pi x numerical aperture wavelength pi 3 1416 approx Figure 11 3 1 3D Localization Accuracy MUM advanced parameters window MUMDesignTool Step 2 The Advanced parameters window contains an Advanced fundamental inputs section The default value of the field in this section can be left unchanged Step 3 In the Model profile calculations section of window acces
51. ers window are optional The default values provided have been found to work adequately for typical imaging conditions Step 1 Access the advanced parameters window by clicking the Advanced Parameters option under the Parameters Menu in the main window MUMDesignTool BB Advanced Parameters S oo o es 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Model profile calculations Pixel integration method Trapezoidal v Additional parameters Background type Constant v Additional parameters Fisher information matrix calculations Single integration method Trapezoidal v Additional parameters Double integration method Trapezoidal v Additional parameters Limits of summation lower limit upper limit M A use_defaut Limits of integration lover limit upper limit M A use_defaut BB FandPLimitTool File Export View Tools Help Required Parameters Ctrl U blem Select a problem Advanced Parameters Ctrl N 2D Localization Accuracy Airy Prea Will PUISSUIT Gaussian Moise Perform calculations Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Figure 1 3 1 Advanced parameters window 2D Localization Step 2 In the Model profile calculations section of window access the Pixel integration method pull down menu and select Trapezoidal Step 3 Click the Additional param
52. es provided have been found to work adequately for typical imaging conditions Step 1 Access the advanced parameters window by clicking the Advanced Parameters option under the Parameters Menu BR Advanced Parameters ace E Bx 3D Localization Accuracy Born vvolf Model Pixelated with Poisson Gaussian Noise fundamental inputs Alpha 13 2036 Update analytically Model profile calculations Pixel integration method Trapezoidal Additional parameters Model integration method Trapezoidal Additional parameters Background type Constant Additional parameters Fisher information matris calculations E FandPLimitTool Single integration method Trapezoidal Additional parameters File Export View Tools Help Double integration method Trapezoidal __ Additional parameters Required Parameters Ctrl U Select a problem P Advanced Parameters Ctrl M 3D Localization Accuracy OON MAAE PAEREWA OSST Limits of summation lover limit upper limit M A uze_detault Limits of integration lower limit upper limit M A use default Perform calculations Trapezoidal integration step size 0 05 aig p a i Calculate Limits of Accuracy Calculate Mo Alpha 2 x pi x numerical aperture d wavelength pi 3 7416 approx Figure 8 3 1 3D Localization Accuracy advanced parameters window Step 2 The Advanced parameters window contains an Advanced fundamental inputs section The default va
53. esolution Accuracy Airy Model Pixelated with Poisson Noise Cartesian Parameterization 2D Resolution Accuracy Airy Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization 3D Resolution Accuracy Born VYolf Model Fundamental Limit Symmetric Parameterization 3D Resolution Accuracy Born Volf Model Pixelated with Poisson Noise Symmetric Parameterization 3D Resolution Accuracy Born VYolf Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization 3D Localization Accuracy Multi focal Pixelated with Possion Noise 3D Localization Accuracy Multi focal Pixelated with Possion Gaussian Noise Focal plane distance 0 0 5 Background level Poisson rate 25 photons pixel s EM model Geometric 3D Localization Accuracy Multi focal Pixelated with Possion Gaussian Noise Parameters to be estimated Perform calculations v x0 4 z0 Background level 7 yo Photon datection rate Calculate Limits of Accuracy Calculate Model Image simulate Data imagas Values apply to both objects Vary a Parameter Figure 11 2 1 3D Localization Accuracy MUM calculate type and its required parameters window Step 5 In the Additional inputs section of the window enter the values for the various fields as follows Magnification 100 Photon detection rate ratio 0 5 0 5 Focal plane distance
54. eters button next to the Pixel integration method pull down menu In the dialog box that appears enter values for fields as follows XGridding 13 YGridding 13 Click OK when done Fo Advanced Parameters m5 rS amp es z Trapezo o E E 2D Localization Accuracy Airy Gridding Pixelated with Poisson Gaussian Noise 3 Model profile calculations Y Gridding Pixel integration method Trapezoidal v Additional parameters 13 Background type Constant v Additional parameters Figure 1 3 2 Pixel Integration Trapezoidal options Step 4 Access the Background type pull down menu and select Constant There are no additional parameters to be accessed via the Additional parameters button for the Constant option Step 5 In the Fisher information matrix calculations section of the window access the Single integration method and select Trapezoidal Step 6 Click on the Additional parameters button next to the Single integration method pull down menu In the dialog box that appears enter Step size 0 05 2D localization accuracy measure Fisher information matrix calculations Single integration method Trapezoidal v Additional parameters Double integration method Trapezoidal Additional parameters Step size Limits of summation lower limit upper limit M A use_defaut Limits of integration lover limit upper limit M A use_defaut Figure 1 3 3 FI
55. etric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Aymmetric Parameterization Location parameters 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Asymmetric Parameterization x0 0 325 microns 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Cartesian Parameterization yO 0 325 microns 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization 2D Resolution Accuracy Airy Model Fundamental Limit Symmetric Parameterization 2D Resolution Accuracy Airy Model Pixelated with Poisson Noise Symmetric Parameterization Pixel size height wicth 13 13 microns xX microns 2D Resolution Accuracy Airy Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization ROI size height width 5 5 no of pixels X no of pixels 2D Resolution Accuracy Airy Model Fundamental Limit Asymmetric Parameterization 2D Resolution Accuracy Airy Model Pixelated with Poisson Noise Asymmetric Parameterization Extraneous noise source s Plane 1 2D Resolution Accuracy Airy Model Pixelated with Poisson Gaussian Noise Aymmetric Parameterization 2D Resolution Accuracy Airy Model Fundamental Limit Cartesian Parameterization 2D R
56. formation that are displayed in the console window are also stored in a log file fandp_log mia in the following path Console window log file and bug reporting C Users username AppData Roaming FandPLimitTool R foe ex GO d gt Computer Local Disk C Users amir AppData Roaming FandPLimitTool v 4 Search FandPlimitToot p Organize v Include in library v Share with New folder of A Favorites prs Name Date modified Type ME Desktop fandp_log mia 5 19 2014 5 21PM MIA File mi Downloads a E Recent Places Libraries E Documents a Music fe Pictures E Videos A 1 item Figure 6 2 1 Log file To report a bug that leads to an error or warning please send this log file to us More information about the current versions of the FandPLimitTool and the MUMDesignTool their homepages and licensing can be found in the corresponding About windows e g see below BB About FandPLimitTool FandPLimitT ool 1 2 For single molecule localization and resolution Copyright C 2004 2014 Ward Ober Lab All rights reserved MATLAB Copyright C 1984 2014 The MathWorks Inc All rights reserved FandPLimitT ool home page http www wardoberlab com software fandplimittool Please refer to license pdf for conditions of distribution and use FandPLimitT ool Developement Team Raimund J Ober Team Leader Amit T ahmasbi Anish Y Abraham Jerry Chao
57. gure 9 2 1 2D Resolution Accuracy calculate type and its required parameters window Step 2 The required parameters window which is visible by default will be updated accordingly If this window is not visible access it by clicking the Required Parameters option under the Parameters Menu in the main application window Step 3 In the Object selection section of the Required parameters window select Object 1 Step 4 In the Fundamental inputs Object 1 section of the window enter the values for the various fields as follows Numerical aperture 1 3 Wavelength 0 52 Photon detection rate 10000 d 0 1 phi pi 4 and Exposure time 0 13 2D Resolution measure Step 5 In the Additional inputs section of the window enter the values for the various fields as follows Magnification 100 sx 13x4 5 100 sy 13x4 5 100 Pixel size 13 13 and ROI size 9 9 Remark 12 The center of a 9 pixels x 9 pixels pixel array where the dimensions of each pixel is 13 um x 13 um is 4 5 x 13 um x 4 5 x 13 um To convert this location coordinates to the object space the coordinate values are divided by the magnification Hence the location coordinates are specified as 13x4 5 100 um x 13x4 5 100 um Step 6 In the Extraneous noise sources Object 1 section of the window enter the values for the various fields as follows Background level 1000 and Standard deviation 8 Remark 13 In case that the localiza
58. ich will be discussed in detail later in this tutorial Before you begin Before following this tutorial please make sure that the software has been correctly installed and started Please refer to the FandPLimitTool Installation Guide for instructions on installing and starting the application WARNING User defined functions The Advanced Inputs Window has fields where the user is required to select which function to use to perform a certain part of the calculation In the options available for such fields the User Defined option is also often available This option allows the user to specify the names of their own custom function for performing the associated part of the calculation However in the executable version of the program this option is not fully supported Users cannot specify the names of their own functions for the user defined options as such functions will not have been compiled along with the original program to generate the executable and therefore will not be recognized by the executable version of the program MUMDesignTool 1 2D localization accuracy measure This section provides an example of how to use the FandPLimitTool to calculate the accuracy with which the 2D location of an object can be estimated from its image PLAM The object is assumed to be in focus with respect to the objective lens and the image of the object is assumed to be an Airy profile The calculation takes into account the stoch
59. image is in fact the image profile of a single molecule or two single molecules in case of a resolution problem in the absence of stochasticity and extraneous noise A simulated data image on the other hand is a realization of a model image and is corrupted by stochasticity and extraneous noise sources such as background readout and stochastic signal amplification The following sections provide examples for calculating and visualizing model and data images respectively We assume that user has applied all the steps in Section 1 2D Localization Accuracy Limit 3 1 Calculate a model image NOTE For some of the problem scenarios mostly fundamental limits a model image may not be available In such cases the Calculate Model Image button will be grayed out and as such a model image cannot be calculated E FandPLimitToo File Export View Parameters Tools Help select a problem scenario 20 Localization Accuracy Airy Fundamental Limit Perform calculations Calculate Limits of Accuracy Calculate Model Image simulate Data Images Figure 3 1 1 Unavailable model and data images Step 1 If a model image is available for current problem scenario in the main application window click the Calculate Model Image button The Calculate Model Image button text will change to Calculating Model Image and the application will temporarily become unresponsive while the calculations are being performed Simulating and visualizing
60. imitTool ROI size height width 11 11 no of pixels X no of pixels File View Parameters Tools Help Extraneous noise source s Results and Parameters Se Background level Poisson rate 100 photons pixel s Model and Data Images 2D 3 Noi LaTex Report ied tata All Ctrl E Parameters to be estimated W x0 4 Alpha V Background level FJ FJ i sie i yO ea nn eee ae Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Alpha 2 x pi x numerical aperture it wavelength pi 3 1416 approx Figure 5 3 1 Exporting a LaTex report Step 3 Select a folder in which you would like to save the LaTex report and click OK A tex file together with several eps images will be saved within a folder named LaTex Report under the specified folder 5 4 Exporting everything simultaneously NOTE If all the required calculations are performed the export All option becomes available and user can export everything simultaneously Step 1 Select the All option under the Export Menu This will present a folder browser Step 2 Select a folder name in which you would like to export all the results including the limits of accuracy the simulated model and data images and the LaTex report and then click OK MUMDesignTool 6 Console window log file and bug reporting The FandPLimitTool V1 2 is equipped with a new console window and a log file The console
61. ing conditionS s sessssessrsresrernseerennsrenne 59 Introduction Introduction This document is a user s manual for the FandPLimitTool V1 2 and MUMDesignTool V1 0 It provides detailed instructions for performing five specific calculations which are representative of the types of calculations that can be performed with this application Moreover it provides detailed information about how to use the MUMDesignTool to design the focal plane spacing for a multifocal plane microscopy MUM setup 1 Consider the following terminology which will be used multiple times throughout this document FLAM fundamental localization accuracy measure PLAM practical localization accuracy measure FREM fundamental resolution measure PREM practical resolution measure What is new We have added several new features to the FandPLimitTool V1 2 which make it more powerful and faster than its previous version V1 1 The new features are listed as follows and each option will be discussed in detail later e A new software module the MUMDesignTool is incorporated with the package which provides tools to design the focal plane spacing for multifocal plane microscopy e New functionality that allows the calculation of the 3D resolution measure e A new function called vary a parameter is added to the software which allows users to calculate and plot the limits of accuracy for a range of different experimental parameters e New functionality tha
62. ion Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization Readout Gaussian noise parameters 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise 4ymmetric Parameterization Standard deviation a e pixel 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise 4symmetric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Cartesian Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization E Use EM EM gain 2 0082 2D Resolution Accuracy Airy Model Fundamental Limit Symmetric Parameterization JE 2D Resolution Accuracy Airy Model Pixelated with Poisson Noise Symmetric Parameterization m Pixelation parameters Pixel size height width 1 3 13 microns X microns Background level Poisson rate 1 000 photons pixel s EM model Geometric 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Parameters to be estimated x0 Alpha Background level Perform calculations g EU Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Alpha 2 x pi x numerical aperture VayaParameter i wavelength pi 3 1416 approx Vary a Parameter Figure 1 2 1 Selecting the 2D Localization Accuracy calculate type MUMDe
63. ise Results Limit of the accuracy of yO 2 5687 nanometers D 2 5587 nanometers z0 12 7615 nanometers Photon detection rate 0 29457 photonsis Background level 57 667 photonapixels Figure 11 4 2 Results window 3D localization MUM References 1 A Tahmasbi S Ram J Chao A V Abraham F W Tang E S Ward and R J Ober Designing the focal plane spacing for multifocal plane microscopy Opt Express vol 22 no 14 pp 16706 16721 2014 2 R J Ober S Ram and E S Ward Localization accuracy in single molecule microscopy Biophys J vol 86 pp 1185 1200 2004 3 J Chao E S Ward and R J Ober Fisher information matrix for branching processes with application to electron multiplying charge coupled devices Multidim Sys Sig Proc vol 23 no 3 pp 349 379 2012 4 J Chao E S Ward E and R J Ober A software framework for the analysis of complex microscopy image data IEEE Trans Inform Technol Biomed vol 14 no 4 pp 1075 1087 2010 5 m S Ram R J Ober and E S Ward How accurately can a single molecule be localized in three dimensions when imaged through a fluorescence microscope Proc of SPIE vol 5699 pp 426 435 2005 6 S Ram E S Ward and R J Ober Beyond Rayleigh s criterion A resolution measure with application to single molecule microscopy Proc Natl Acad Sci USA vol 103 no
64. isson noise the readout noise of the detector which is modeled as independent additive Gaussian noise 2 and the electron multiplication noise of an EMCCD detector which is modeled as a branching process 3 It is assumed that the pixels are rectangular in shape with no dead space between any two pixels Further the ROI containing the image of the objects is assumed to be a rectangular array of pixels The midpoint between the objects is assumed to be at the center of this rectangular pixel array and the location of the midpoint between the objects is specified with respect to the object Space Refer to 6 for details or determining the 2D resolution accuracy in single molecule microscopy 9 1 Summary of imaging conditions The following table summarizes the imaging conditions under which the calculations are performed Property Object 1 Object 2 waooo o i om oS S SOS Gaussian noisemean Joe OOOO SO Table 9 1 1 2D Resolution Accuracy Summary of imaging conditions a MUMDesignTool 9 2 Providing required parameters Step 1 Select the calculation option 2D Resolution Accuracy Airy Pixelated with Poisson Gaussian Noise Symmetric Parameterization from the Calculate pull down menu in the main application window Fo Required Parameters S Sea ls 2D Resolution Accuracy Airy Pixelated with Poisson Gaussian Noise Symmetric Parameterization Object selection Object 1 C Object 2 Fun
65. isture 1 of 6 Application initialized All rights reserved Figure 9 4 1 Calculation and Final confirmation MUMDesignTool NOTE During the calculation a console window will be shown to inform the user about the different steps of the calculation The calculation could indeed take half an hour to complete depending on the hardware capabilities of the platform on which the application is being executed Step 2 When the calculation is completed the Calculating button text will change back to Calculate Limits of Accuracy and the Results window will be brought in focus In addition the console window will be hidden when the calculation is over The console window can be accessed any time by selecting the Console option under the View Menu E Results E 2D Resolution Accuracy Airy Pixelated with Poisson Gaussian Noise Symmetric Parameterization Results Limit of the accuracy of ex 5 9669 nanometers sy 2 9669 nanometers g 11 7311 nanometers phi 0 023825 radians Figure 9 4 2 Results window 2D Resolution 3D Resolution measure Born Wolf Model 10 3D Resolution measure Born Wolf Model This section provides an example of how to use the FandPLimitTool to calculate the accuracy with which the 3D location of two objects can be resolved from their image PREM The image of each object is assumed to be 3D Point Spread Function The calculation takes into account the stochastic nature of the ph
66. ixel Integration TrapeZoidal OPtiOns csssessssssseessserssessesssersesessesesseeesseseenseearseeansteensnseeensess 62 Figure 11 3 3 Model Integration TrapeZoidal Options cssssssssessserssessessseeseeersesessesesseseeasseearsesessneetsnsneensess 62 Figure 11 3 4 FIM Single Integration Trapezoidal OPtions sssssssssessssssesseesseessesessesseeesesrseeenseeesseseeenees 63 Figure 11 3 5 FIM Double Integration TrapeZoidal Options cssessssesseeesseeesseeesseenssesseensesesseeesseeetsesneeneess 63 Figure 11 4 1 Calculation and Final confirmation 3D localization MUM esssssssesssesserseseesersteeeeneeees 64 Figure 11 4 2 Results window 3D localization MUM cssssessssesssssssessersssssessesteesenseseeasseseeeeenseseeatansesetensnaes 64 List of tables Table 1 1 1 2D Localization Accuracy Summary of imaging conditionS s s sssessssssrenrunsnennrnnnnnnrnrnnnnnnnnrnenns 10 Table 7 1 1 Summary of simulation parameters for the MUMDeSIgNTOOI cceeseseesseeeeeseesesenseeeneenseees 32 Table 8 1 1 3D Localization Accuracy Summary of imaging conditionS s s sssesssssernrunsesrnrununnnrnennnnnnnnrnenns 40 Table 9 1 1 2D Resolution Accuracy Summary of imaging CONCITIONS se ssssssssssssrensnrunnnsnrnnnnnnnnnrnnnnnnnnrnnnns 47 Table 10 1 1 3D Resolution Accuracy Summary of imaging conditioOnS s sssessesserenrunsesrnnnnunnnrnrnnnnnnnnrnnnns 53 Table 11 1 1 3D Localization Accuracy MUM Summary of imag
67. lculate pull down menu in the main application window Step 2 The required parameters window which is visible by default will be updated accordingly If this window is not visible access it by clicking the Required Parameters option under the Parameters Menu in the main application window Step 3 In the Object selection section of the Required parameters window select Object 1 Fpl Required Parameters 3D Resolution Accuracy Born VVvolf Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization as selection Object 1 Object 2 Lo Lo amp es Fundamental inputs Object 1 Numerical aperture 1 3 Wavelength 0 52 Photon detection rate 10000 microns photons s Immersion medium ref index 1 515 d 05 phi 0 7854 radians omega 1 5708 radians microns Exposure time 0 13 seconds m Additional inputs Magnification 100 Location parameters sx 0 325 microns sy 0 325 microns z 0 microns Pixel size height width 13 13 microns X microns ROI size height width 5 5 no of pixels X no of pixels Extraneous noise source s Object 1 Background level Poisson rate 1000 photons pixel s EM model Geometric Parameters to be estimated Visx Wisy Misz Wla iphi V omega Photon detection rate 1 Photon detection rate 2
68. leted the Simulating X Data Images button text will change back to Simulate Data Images and the display tool will be brought in focus Step 4 In the viewer window you can visualize the data images and change the visual effects You can also visualize different realization by scrolling the slider to the right in the Viewer Slider window NOTE The viewer belongs to our previously developed Microscopy Image Analysis Tool MIATool For more information please see 4 Remark 7 In case that the Simulate Data Images functionality is used together with the Multivalue Mode the viewer will show a stack of data images associated with the different values of the Multivalued parameter In this case user can visualize images that correspond to different model by scrolling the slider to MUMDesignTool the left in the Viewer Slider window as shown below On the other hand different realizations data images of a specific model can be accessed using the slider to the right see below Window 1x 1y 3 Adj Pixel 19562 Orig Pixel 113 File Edit View Insert Tools Desktop Window Help nagdl kiARAV9VDEZ ABA 08 Hes ba ba e b a Ce e js 35 _ _ Details Open Tools Mode Normal Channel All Display Standard Multiplicity Single Options Parallel Free Dim 1 Apply Save Overlay Open Player Open Zoom Tool Open Montage Tool Figure 3 2 3 Simulated image
69. lor you De Eeee E 9 WARNING User defined TUNCUONS seusensesssoiscnsiri daii a 9 1 2D localization accuracy measure ssssssesesresesrressrreresrresssreressrrrssreresereessreresetreserereseeressreeeseerese 10 1 1 Summary of imaging conditions sssesssessseesesrerssrerssrrerssreresrrrrssreresereresreressreresrrresereresrrressee 10 1 2 Providing required parameterS essesssessreessressrrrssrersrrssrrrssreesrersrrresrersrersreroesrersereserresreeseeree 11 1 3 Providing advanced parameters cccssscccseccceseccceseccenccceuececeececseceeeuecesecesauecesseceseneeeeees 13 1 4 Viewing and saving the parameter SUMMALY ccccccsssecccceseccecenscceceesececeueceeseeceeseusesetsuneess 16 1 5 Executing the task and viewing results ccccccsssccccessececeesecccceeeceeeeesececeunecesseneceeeeuseeetseneess 16 2 Varying a parameter multivalue MOE ccccccccccesssecceeceeeeccesceeeeeccceeeeeeeeeeteeeeseeeeseueeeeeeeeeas 18 2 1 Providing inputs for the multivalue mode cccccesseccccesscceceesececeesececeeeeeceseuseceseegeceeseeeeeetas 18 2 2 Plotting the limit of accuracy versus a parameter value ccccccceeseccccessecceeesececeeeeceeeeeeeeeeas 19 3 Simulating and visualizing model and data images ccsesccccssseccceesececeesecceeeseceeeuseceseueceesenes 20 Jh rs 210 cio Wage 0 01a gic eee ee ne eee een ener nee eer eee eee 20 Fe C010 coo cecal a8 2 21 eee eee eee ee
70. lue of the field in this section can be left unchanged 3D Localization accuracy measure Born Wolf Model Step 3 In the Model profile calculations section of the window access the Pixel integration method pull down menu and select Trapezoidal Advanced fundamental inputs AAA Alpha 13 2038 Update analytically By Trapezo a peel amp Griddin Model profile calculations gt Papp a Pixel integration method Trapezoidal ka Additional parameters o Y Gridding Model integration method Trapezoidal Additional parameters 13 Background type Constant Additional parameters ce Figure 8 3 2 Pixel Integration Trapezoidal options Step 4 Click the Additional parameters button next to the Pixel integration method pull down menu In the dialog box that appears enter the values XGridding 13 and YGridding 13 Click OK when done Step 5 Access the Model integration method pull down menu in the same section of the window and select Trapezoidal Pixelated with Poisson Gaussian Noise Born Wolf Model Bd Trapezo sco E aE fundamental inputs SS QZ step size Alphat 13 2038 Update analytically 0 0005 l Lower limit Model profile calculations pp A o Pixel integration method Trapezoidal Additional parameters Upper limit Model integration method Trapezoical x Additional parameters j Background type Constant ka Additional parameters Figure 8 3 3 Model I
71. meter Exporting results parameters images and report Step 1 Perform a multivalue calculation for the limits of accuracy see Section 2 Once the calculation is performed and the results are available within the software the LeTex Report option under the Export Menu becomes accessible Step 2 Select the LeTex Report option under the Export Menu see figure below This will present a folder browser 2 Multivalue Plot GIE x Limit of accuracy of x0 vs Photon detection rate 0 014 M BB Required Parameters o If E DS m ao 2D Localization Accuracy Airy Pixelated with Poisson Noise Fundamental inputs BB MultivalueMode OS ol olf ss Numerical aperture 1 45 2D Localization Accuracy Airy Wavelength 0 69 microns Pixelated with Poisson Noise Photon detection rate 10000 photons s Multivalue parameter Exposure time 1 seconds Limit of accuracy of xO microns Parameter Photon detection rate X pand o Nn Additional inputs Values 1000 2000 3000 4000 5000 i Magnification 300 Units photons s Example 10 1 13 or 10 11 1213 2000 4000 6000 8000 Location parameters Photon detection rate photons s xO 0 23833 microns 7 Auto center image for each calculation Select plot lo ee Results Plot of accuracy of x0 vs Photon detection rate Pixel size height width 13 13 microns X microns BB FandPL
72. meters window 2D Localization csesssseseessseseessesseseenseeeeaseseeetenseseeatenseeetensnses 12 Electron multiplication PAFAMETELS csscssssesrssessseseeeeseeersecenseseteseeenseeenseeensesetansesensesensteetensetenens 13 Advanced parameters window 2D LOCAaliZatiON csssssesesssssseseessseesenseseeeseesesesenseseeatenseeetensnses 14 Pixel Integration Trapezoidal Options ssssssessssessssessseseeerseeersesesseeesseseeeesesarsesensesensesesanseeanseeenaes 14 FIM Single Integration Trapezoidal Options cssssssesssssesssesseesssessseseseesesersesenseeessesetensesanseeenaes 15 FIM Double Integration Trapezoidal OPtions cssessssssesssessssessseseseesesrsesesseenssesesenseeanseeanaes 15 Noise factor Calculation parameters csscesesssessssessssessseseeeeseeersesessesesesetarseserseeessesetansetansesanseeetenss 15 Viewing and saving the parameter summary 2D Localization ssssseseessseeesesseseerseeeeeneees 16 Calculation and Final confirmation ccsesesesseeseeceesssseseeeseseceeseseseseseseseeseseseeesasasseseseessesatanensseses 17 2D localization accuracy Results WINGOW sssssssesssssssesserseeersesesseseeessesenseeensesetaesetansetansesensnseees 17 Multivalue Mode setting WINGOW cssssssssssssssssssessessssssesersteasseeessesesseseeessesansesensesessesetansetanseeanaes 18 Multivalue results and plot WINKOWS ssscssssesssessssesssesseerseeasseeessesesesesoesesarseserstentansetansetanseeenaes 19 Una
73. model and data images BB FandPLimitTool File Export View Parameters Tools Help select a problem scenario 2D Localization Accuracy Airy Pixelated with Poisson Noise Perform calculations Calculate Limits of Accuracy BR FandPLimitTool File Export View Parameters Tools Help select a problem scenario 2D Localization Accuracy Airy Pixelated with Poisson Noise Perform calculations Calculate Limits of Accuracy j is Simulate Data Images Figure 3 1 2 Calculate a model image Step 2 When the calculation is completed the Calculating Model Image button text will change back to Calculate Model Image and the display tool will be brought in focus B Window 1x 10 y 7 Adj Pixel 0 Orig Pixel 100 lt ola B viewer Slider 1 eleal z File Edit View Inset Tools Desktop Window Help USGAES k ARVDVDEA A 08 im 1 1 HDE ostete Open Tools Mode Normal z Channel All Display Standard z Multiplicity Single v Options Parallel Free Dim 1 Apply Save Overlay Open Player Open Zoom Tool Open Montage Tool v Figure 3 1 3 Model image viewer Step 3 In the viewer window you can visualize the model image and change the visual effects MUMDesignTool NOTE The viewer belongs to our previously developed Microscopy Image Analysis Tool MIATool For more i
74. n text will change back to Precise Mode and the MUMDesignTool Precise Mode window will be brought in focus see figure below F MUMDesignTool Precise Mode USGAS ARUTDe OE Fisher Information Matrix FIM 2500 plane 1 plane 2 plane 3 2000 z0 element of FIM 14m 500 1 0 5 0 0 5 1 1 5 2 Object z position um x0 element of FIM 14m 0 5 0 0 5 1 Object z position um en yO element of FIM 14m 2 1 0 5 0 0 5 1 1 5 2 Object z position um Practical Localization Accuracy Measure PLAM 45 an an te nm M nm Limit of the accuracy of z0 nm Object z position um Limit of the accuracy of x0 nm QJ mn 3 ho mn hJ _ mn 0 5 0 0 5 1 Object z position um need s3 Q9 M m 20 Limit of the accuracy of yO nm 2 1 0 5 0 0 5 1 1 5 2 Object z position um Figure 7 4 3 MUMDesignTool Precise Mode MUMDesignTool 8 3D Localization accuracy measure Born Wolf Model This section provides an example of how to use the FandPLimitTool to calculate the accuracy with which the 3D location of an object can be estimated from its image PLAM The image of the object is assumed to be a 3D Point Spread Function profile The calculation takes into account the stochastic nature of the photon detection processes and assumes the photons detected from the object to be Poisson distri
75. nformation please see 4 Remark 6 In case that the Show Model functionality is used together with the Multivalue Mode the viewer will show a stack of images associated with the different values of the Multivalued parameter In this case user can visualize the different model images by scrolling the slider to the left in the Viewer Slider window as shown below The current value of the parameter e g Magnification 150 will also be shown in the viewer window see below E Window 1x 6 y 11 Adj Pixel 661 Orig Pixel 101 lt lt gt gt poboada B viewer Slider 1 2 fe lle iss File Edit View Insert Tools Desktop Window Help Ugs k ABAVDEL Aa 0H im 5 1 H I S a Details Magnification 150 Open Tools Mode Normal z Channel All Display Standard Bd Multiplicity Single v 4 1 2 Options Parallel Free Dim 1 Apply Save Overlay Open Player Open Zoom Tool Open Montage Tool Te Figure 3 1 4 Model image viewer in Multivalue Mode Step 4 To improve screen clarity close the Model Image Viewer using the standard exit buttons on any of the viewer windows 3 2 Simulate data images NOTE For some of the problem scenarios mostly fundamental limits a data image may not be available In such cases the Simulate Data Images button will be grayed out and as such a data image cannot be simulated this is shown in Figure 3 1 1 S
76. ng results Step 1 In the main application window click the Calculate Limits of Accuracy button This will present a dialog box warning that the calculation may take a long time to complete Click Yes to proceed The Calculate button text will change to Calculating and the application will temporarily become unresponsive while the calculations are being performed During the calculation a console window will be shown to inform the user about the different steps of the calculation NOTE The calculation could indeed take half an hour to complete depending on the hardware capabilities of the platform on which the application is being executed WB FandPLimitTool S Mixture 2 of 6 Wixture 1 of 6 Wixture 25 of 25 File Export View Parameters Tod BM Warning select a problem scenario Oi Wixture 2 SEE WARNING This calculation may take a long time to complete Are you sure Oi Mixture 2 3D Localization Accuracy Multi focal Pix you want to continue nis fixture 2 m Perform calculations Calculating Figure 11 4 1 Calculation and Final confirmation 3D localization MUM Step 2 When the calculation is completed the Calculating button text will change back to Calculate Limits of Accuracy and the Results window will be brought in focus In addition the console window will be hidden when the calculation is over B Results o x 3D Localization Accuracy Multifocal Pixelated with Poisson Gausstan No
77. ns 13 13 microns Photon Detection Rate 10000 photons s I Model parameters 0 325 0 325 13 2038 Background Noise 1000 photons s p Readout Noise 8 e p Advanced Inputs Pixel Integ Fume Trapezoidal Pixel Integq Gridding 13 13 Save as text Bi FandPLimitTool os tse File Export Parameters Tools Help Parameter Summary Ctrl P Results Ctrl R 2D Localizatic Saussian Noise Console Select a pri Perform calculations Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Figure 1 4 1 Viewing and saving the parameter summary 2D Localization Step 2 You will see the summary of the required and advanced parameters in a plane text format This summary can be saved on the disc as a txt file by hitting the Save as text button 1 5 Executing the task and viewing results Step 1 In the main application window click the Calculate Limits of Accuracy button This will present a dialog box warning that the calculation may take a long time to complete Click Yes to proceed The Calculate button text will change to Calculating and the application will temporarily become unresponsive while the calculations are being performed During the calculation a console 2D localization accuracy measure window will be shown to inform the user about the different steps of the calculation This console window will also display errors and warnings if there is a
78. nt Model integration method r Additional parameters Advanced fundamental inputs Object 1 2A eee 5 es Trapezo E Alphat 15 708 Figure 10 3 2 Pixel Integration Trapezoidal options Step 4 Click the Additional parameters button next to the Pixel integration method pull down menu In the dialog box that appears enter values for fields as follows XGridding 13 YGridding 13 Click OK when done Step 5 Access the Model integration method pull down menu in the same section of the window and select Trapezoidal selection Object 1 0 Object 2 BI Trapezo gt E E Aa fundamental inputs Object 1 Step Size Alpha 15 708 Update analytically Lower Limit Model profile cea ice gg eat be gs AMAA 0 Pixel integration method Trapezoidal T Additional parameters Upper Limit Model integration method Trapezoidal Additional parameters 1 Background type Constant m iti Additional parameters Figure 10 3 3 Model Integration Trapezoidal options Step 6 Click the Additional parameters button next to the Model integration method pull down menu In the dialog box that appears enter the values Step size 0 0005 Lower limit 0 and Upper limit 1 Click OK when done Step 7 Access the Background type pull down menu and select Constant There are no additional parameters to be accessed via the Additional parameters button for
79. ntegration Trapezoidal options Step 6 Click the Additional parameters button next to the Model integration method pull down menu In the dialog box that appears enter the values Step size 0 0005 Lower limit 0 and Upper limit 1 Click OK when done Step 7 Access the Background type pull down menu and select Constant There are no additional parameters to be accessed via the Additional parameters button for the Constant option Step 8 In the Fisher information matrix calculations section of the window access the Single integration method pull down menu and select Trapezoidal MUMDesignTool Fisher information matrix calculations EJ Trapezo ol mE Single integration method Trapezoidal Additional parameters Step size Double integration method Trapezcidal Additional parameters 0 0005 L linit Ssesosccecuesses aes Moise factor calculation parameters oe T Limits of summation lover limit upper limit M A use defaut Limits of integration lower limit upper limit hr oai ial use defaut 1 Trapezoidal integration step size 0 05 cone Alpha 2 x pi x numerical aperture J wavelength pi 3 1416 approx Figure 8 3 4 FIM Single Integration Trapezoidal options Step 9 Click the Additional parameters button next to the Single integration method pull down menu In the dialog box that appears enter the values Step size 0 00
80. ny which is very useful for bug reporting purposes NOTE The calculation could indeed take half an hour to complete depending on the hardware capabilities of the platform on which the application is being executed BJ warning o eae WARNING This calculation may take a long time to complete Are you sure you want to continue Be FandPLimitToo File Export View Parameters Tools Help Select a problem scenario 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise z Perform calculations Calculating Calculate Model Image simulate Data Images xture 2 of 2 xture 1 of 2 ed 104 2014 Ward Ober Lab For single molecule localization and resolution FandPLimitTool 1 2 Initializing the application Figure 1 5 1 Calculation and Final confirmation Step 2 When the calculation is completed the Calculating button text will change back to Calculate Limits of Accuracy and the Results window will be brought in focus In addition the console window will be hidden when the calculation is over The console window can be accessed any time by selecting the Console option under the View Menu Bi Results lt gt o meal 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Results Limit of the accuracy of x0 6 349 nanometers yO 6 349 nanometers Alpha 0 000686 1 nanometers Photon detection rate 746 5606 photons s B
81. ool V1 2 provides very flexible tools for exporting the results of calculations simulated images and even a report file More specifically user can export the results and parameters of a desired problem scenario the simulated model and data images and a LeTex report that can be generated when performing a multivale calculation i e when varying a parameter The simulated model and data images can also be exported when varying a parameter In such cases a sequence of images will be exported In this section we discuss different steps of exporting various results 5 1 Exporting the results and parameters NOTE To export the desired outputs such as results images and a report appropriate calculations has to be performed prior to exporting If the results model and data images and a LeTex report are not available the corresponding menu options under the Export Menu will be grayed out see below After the appropriate calculation is performed the corresponding menu option becomes accessible BB FandPLimitTool File Export View Parameters Tools Help Results and Parameters Model and Data Images LaTex Report All Calculate Limits of Accuracy el Image Simulate Data Images Figure 5 1 1 Exporting is not available Step 1 Perform either a standard see e g Section 1 or a multivalue see Section 2 calculation for the limits of accuracy Once the calculation is performed and the results are available within
82. ormation matrix calculations Single integration method Trapezoidal ka Additional parameters Double integration method trapezoidal Additional parameters my ee Trapezo Lo mE Moise factor calculation parameters P x Gridding Limits of Summation lower limit upper limit MIA use default E Limits of integration lower limit upper limit MA use default Y Gridding Trapezoidal integration step size 0 05 13 tAlpha 2 x pi x numerical aperture wavelength pi 3 1416 approx Cancel Figure 11 3 5 FIM Double Integration Trapezoidal options Step 11 Click on the Additional parameters button next to the Double integration method pull down menu In the dialog box that appears enter the values XGridding 13 and YGridding 13 Step 12 The Fisher information matrix calculations section has a subsection titled Noise factor calculation parameters Enter the following values in this subsection Limits of summation 1 3000 Limits of integration 5000 5000 and Trapezoidal integration step size 0 05 Remark 20 The limits of integration and summation are initially set to default values which are automatically calculated based on the imaging conditions It is possible specify these limits by changing the value of the combo box to the right of the limits of integration and summation fields MUMDesignTool 11 4 Executing the task and viewi
83. oton detection processes and assumes the photons detected from the object to be Poisson distributed In addition the calculation also takes into account extraneous noise sources in particular the background component which is modeled as additive Poisson noise the readout noise of the detector which is modeled as independent additive Gaussian noise 2 and the electron multiplication noise of an EMCCD detector which is modeled as a branching process 3 It is assumed that the pixels are rectangular in shape with no dead space between any two pixels Further the ROIs containing the images of the object are assumed to be rectangular arrays of pixels The object is assumed to be in the center of this rectangular pixel array and the location of the object is specified with respect to the object space Refer to 6 for details on 3D resolution accuracy in single molecule microscopy 10 1 Summary of imaging conditions The following table summarizes the imaging conditions under which the calculations are performed Property Object 1 Object 2 aooo i om OoOO oS S Gaussian noisemeen Joe OOOO S SO Table 10 1 1 3D Resolution Accuracy Summary of imaging conditions Location of object in ROI sx sy 0 585 um 0 585 um MUMDesignTool 10 2 Providing required parameters Step 1 Select the calculation option 3D Resolution Accuracy Point Spread Function Born Wolf Model Pixelated with Poisson Gaussian Noise from the Ca
84. per limit MiA use _defaut coe Figure 9 3 4 FIM Double Integration Trapezoidal options Step 9 The Fisher information matrix calculations section has a subsection titled Noise factor calculation parameters Enter values Limits of summation 1 3000 and Limits of integration 5000 5000 in this subsection Remark 14 The limits of integration and summation are initially set to default values which are automatically calculated based on the imaging conditions It is possible specify these limits by changing the value of the combo box to the right of the limits of integration and summation fields 9 4 Executing the task and viewing results Step 1 In the main application window click the Calculate Limits of Accuracy button This will present a dialog box warning that the calculation may take a long time to complete Click Yes to proceed The Calculate button text will change to Calculating and the application will temporarily become unresponsive while the calculations are being performed WB FandPLirnitTo BY Warning File Export q A WARNING This calculation may take a long time to complete Are you sure Select a prob e pou want to continue Calculating Calculate Model Image simulate Data Images xture 5 of 24 5 Mixture 4 of 25 sauss Mixture 3 of 25 Sauss Mixture 2 of 25 ture 1 of 25 ture 6 of 6 6S Mixture 5 of 6 Sauss Mixture 4 of Bf S Mixture 3 of 6 wture 2 of 6 Gauss M
85. r 22 4 Saving and loading the settings ceeccccsssccccessecccceseceeceeecceeeesececeeeceeeeneceeseusecessuaecessunecessenes 25 Dd GAN IAS MeS NE e gees vanonmansee toesbetaeeemseessuiee casnnreescuedenauar aren cieneanenonaeeietes 25 42 Loading the settings ee ne ee 25 5 Exporting results parameters images and report essssssssesesressrrsssrrssrtesrrrssrresrerserrserersreeserresns 26 5 1 Exporting the results and parameters crremeitorkierea cE E ees 26 5 2 Exporting the model and data iMageS ccccccssccccssseccccsscceeeesececeeseceeeeeseceseusecesseneceesaeeeeetas 28 5 3 Exporting a LeTex report ssssesssssesssssessrrsrrssrsresresresrrsrrsrrsrrssrerroreosrosesreoressessessreseeseeseeseese 28 5 4 Exporting everything simultaneouSly sssesssessesesrersssreresrrrssrreresrresssreresererssreresrrressrereserresene 29 6 Console window log file and bug reporting sesssssessesesrreserreresrrrsssreresrrerssreresrrerssreresrrrresrerese 30 6 1 The console window ac circ es Senses cess cn seca Sons vcs cae ct nsession 30 Introduction 6 2 The log file ANd DUG re POFrtiNg cecccccsssccccesseccceesececceecceeeesececsueceeeeeecesseeecessuesessuneceesees 30 7 TIe MUMD SS FO OC aoc ceca case saa tee E AES 32 Fels SUiinary O1 Stitt lACIO MC ONC IONS searen niria sa varaneeuucacassnbets taenenee a neeueeeeesads 32 7 2 Providing the inputs and configuring the MUMDesignTool ccceseccccees
86. roceed These parameters by default are visible to the user when software starts They can also be accessed by clicking the Required Parameters option under the Parameters Menu or through its shortcut Ctrl U Although default values are always provided for all required parameters users must modify the fields to suit their desired imaging conditions BB Required Parameters KAE er eae i FandPLimitTool gt lec pee File Export View Parameters Tools Help 2D Localization Accuracy Airy Fundamental Limit Select a problem scenario Fundamental inputs 2D Localization Accuracy Airy Fundamental Limit v Numerical aperture 1 45 Wavelength 0 69 microns Perform calculations Photon detection rate 10000 photons s Exposure time 0 13 Seconds Calculate Limits of Accuracy alculate Model Image mulate Data Images Parameters to be estimated v x0 v yO Photon detection rate Vary a Parameter Advanced parameters on the other hand are optional inputs that govern the numerical routines involved in performing the required calculations These parameters are optional the default values supplied for these inputs will work for typical imaging conditions Advanced parameters can be accessed by clicking the Advanced Parameters option under the Parameters Menu or through its shortcut CtrI N For details about specifying values for advanced parameters please refer to Section 1 to S
87. s the Pixel integration method pull down menu and select Trapezoidal Advanced fundamental inputs Alpha 15 708 Update analytically E Trapezo o E Model profile calculations Aaa Y Gridding 6 m Gridding Pixel integration method Trapezoidal Additional parameters Trapezoidal Additional parameters User Defined m Additional parameters Model integration method Background type ewe Figure 11 3 2 Pixel Integration Trapezoidal options Step 4 Click the Additional parameters button next to the Pixel integration method pull down menu In the dialog box that appears enter values for fields as follows XGridding 13 YGridding 13 Click OK when done Step 5 Access the Model integration method pull down menu in the same section of the window and select Trapezoidal 3D Localization Accuracy Mutti focal Trapezo ec Pixelated with Poisson Gaussian Noise A P m fundamental inputs Step Size Alpha 15 706 Update analytically Lower Limit Model profile calculations Pixel integration method Trapezoidal Additional parameters Upper Limit Model integration method Trapezoical Additional parameters User Detined Additional parameters Background type Figure 11 3 3 Model Integration Trapezoidal options Step 6 Click the Additional parameters button next to the Model integration method pull down menu
88. seeanseeatstennsnsetansess 43 Figure 8 3 3 Model Integration Trapezoidal Options sssssssssssesssesssesseerseessesesseeesseseeerseeanseeanseeensnseteneens 43 Figure 8 3 4 FIM Single Integration Trapezoidal OPtiONn ssssssssessssessssseeeseerseeesseeessesseeeseearseeensesetsnsetaneess 44 Figure 8 3 5 FIM Double Integration Trapezoidal OptiOnS s s sssssussssrsnurununsnrnnununnnnnrnnnnunnnnnrnnnnnnnnnnrnnnnnnnnnnrnnnna 44 Figure 8 4 1 Calculation and Final confirmation ceeessssesssseesseeesseeesseeeeseseeeesecesseeerseseesesetansesarseeanstentsnsntensens 45 Figure 8 4 2 3D localization Accuracy results WINdOW s s sessssssrurununsnnnununnnnnrnnununnnnnrnnnnnnnnnunnnnnnnnnnunnnnnnnnnnnn nenna 46 Figure 9 2 1 2D Resolution Accuracy calculate type and its required parameters windoW sesser 48 Figure 9 3 1 2D Resolution Accuracy advanced parameters WiINdOW se sssssssursrsrenenrunnnnnrnrnnunnnnnrnrnnnnnnnnrnnnna 49 Figure 9 3 2 Pixel Integration Trapezoidal OPtiON csssesssesessseesssesseesssesseerseeessesenseeesesesensesanseeatstennsnsetensess 50 Figure 9 3 3 FIM Single Integration Trapezoidal OPtiONn sssssessseesesseeeseeerseeesseeesseseeenseeanseeensteensnseeansess 50 Figure 9 3 4 FIM Double Integration Trapezoidal OptiOns sssssssessssesssesseeersessseeessesseerseeesseeanseeenseeetensess 51 Figure 9 4 1 Calculation and Final confirmation ccsessssessssseesseeerseeesseeessesseonsesenseeesseseseset
89. signTool Step 2 The required parameters window which is visible by default will be updated accordingly If this window is not visible access it by clicking the Required Parameters option under the Parameters Menu in the main application window BB Required Parameters oS fol amp ss 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Fundamental inputs Numerical aperture 1 45 Wavelength 0 69 microns Photon detection rate 10000 photons s Exposure time 0 13 seconds Additional inputs Magnification 100 Location parameters x0 0 325 microns yO 0 325 microns Pixel size height width 13 13 microns xX microns ROI size height width 5 5 no of pixels X no of pixels Extraneous noise source s Background level Poisson rate 1000 photons pixel s BB FandPLimitTool File Export View Tools Help Required Parameters Ctrl U Select a problem EM model Geometric p Advanced Parameters Ctri N 2D Localization Accuracy ary Prea wm PUISSOr Gaussian Noise Parameters to be estimated Perform calculations 7 x0 7 Alpha V Background level yo Photon detection rate Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Alpha 2 x pi x numerical aperture wavelength pi 3 1416 approx Vary a Parameter Figure 1 2 2 Required parameters window 2D Localiz
90. stimated from the images acquired by a 2 plane MUM setup PLAM The images of the object are assumed to be 3D Point Spread Function profiles The calculation takes into account the stochastic nature of the photon detection processes and assumes the photons detected from the object to be Poisson distributed In addition the calculation also takes into account extraneous noise sources in particular the background component which is modeled as additive Poisson noise the readout noise of the detector which is modeled as independent additive Gaussian noise and the electron multiplication noise which in modeled as a branching process It is assumed that the pixels are rectangular in shape with no dead space between any two pixels Further the ROIs containing the images of the object are assumed to be rectangular arrays of pixels The object is assumed to be in the center of this rectangular pixel array and the location of the object is specified with respect to the object space Moreover it is assumed that the photon detection process at each detector is independent of that of other detectors Refer to 1 and 7 for details on determining the 3D localization accuracy in multifocal plane microscopy MUM 11 1 Summary of imaging conditions The following table summarizes the imaging conditions under which the calculations are performed Property Plane 1 Plane 2 Table 11 1 1 3D Localization Accuracy MUM Summary of imaging conditions
91. t allows simulating single molecule model and data images e New functionality that allows determining limits of accuracy in the presence of stochastic signal amplification i e when using an electron multiplying CCD EMCCD detector e The code is significantly optimized The software therefore runs much faster than the previous version e Exporting tools are enhanced and user can now export the results parameters simulated model and data images and graphs as text image and LaTex report files respectively e Summary ofall input parameters can be explored within the software e Enhanced user interface design e A console window and a log file to facilitate bug reporting Software overview The FandPLimitTool allows users to determine the fundamental and practical limits of 2D and 3D localization accuracy and resolution for a variety of imaging conditions The software has been E MUMDesignTool built using object oriented programming methodologies and has been designed for flexibility to accommodate new models and numerical calculation routines in the future Each calculation supported by this application requires a different set of parameters The parameters are divided into two categories Required parameters and Advanced parameters Required parameters are those parameters that specify the imaging conditions under which the calculations are to be performed Users must provide values for these parameters before a calculation can p
92. tep 1 If a data image is available for current problem scenario in the main application window click the Simulate Data Images button This will present a dialog box to enter the desired number of data images i e realizations of current model Simulating and visualizing model and data images BB FandPLimitTool bo eee File Export View Parameters Tools Help Select a problem scenario 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Perform calculations Calculate Limits of Accuracy Calculate Model Image Simulate a set of images realizations given a model and in the presence of stochasticity and extraneous noise E Number of Data Images o amp pee Please enter the number of data images realizations 35 Figure 3 2 1 Enter the number of data images Step 2 Enter the desired number of data images Click OK to proceed The Simulate Data Images button text will change to Simulating X Data Images where X is the number of desired images specified by user The application will temporarily become unresponsive while the calculations are being performed a2 FandPLimitTool File Export View Parameters Tools Help Select a problem scenario 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise Perform calculations Calculate Limits of Accuracy Calculate Model Image Figure 3 2 2 Simulating data images Step 3 When the calculation is comp
93. the Required Parameters option under the Parameters Menu BB Required Parameters Sl lola S 3D Localization Accuracy Born Vvolf Model Pixelated with Poisson Gaussian Noise Fundamental inputs z0 0 01 microns Object medium refractive index 1 515 Numerical aperture 1 45 Wavelength 0 69 microns Photon detection rate 10000 photons s Exposure time 0 13 seconds Additional inputs P 2D Localization Accuracy Airy Fundamental Limit Magnification 100 2D Localization Accuracy Airy Pixelated with Poisson Noise 2D Localization Accuracy Airy Pixelated with Poisson Gaussian Noise 2D Localization Accuracy Gaussian Symmetric Fundamental Limit x0 0 525 microns 2D Localization Accuracy Gaussian Symmetric Pixelated with Poisson Noise y0 0 325 microns 2D Localization Accuracy Gaussian Symmetric Pixelated with Poisson Gaussian Noise 2D Localization Accuracy Gaussian Asymmetric Fundamental Limit 2D Localization Accuracy Gaussian Asymmetric Pixelated with Poisson Noise 2D Localization Accuracy Gaussian Asymmetric Pixelated with Poisson Gaussian Noise ROI size height width 5 5 no of pixels X no of pixels 3D Localization Accuracy Born VVolf Model Fundamental Limit S qs 3D Localization Accuracy Born VYolf Model Pixelated with Poisson Noise Extraneous noise source s 3D Localization Accuracy Born VVolf Model Pixelated with Poisson Gaussian Noise 2D Resolution Accuracy Ga
94. tion accuracy is required for an EMCCD detector the Use EM checkbox Should be checked and the desired value for the electron multiplication gain should entered in the EM gain field For more information see Remark 2 Step 7 In the Object selection section of the Required parameters window select Object 2 Then repeat steps 4 and 6 for the Object 2 Step 8 In the Parameters to be estimated section of the window ensure that all check boxes for all parameters are checked 9 3 Providing advanced parameters NOTE All inputs in the Advanced Parameters window are optional The default values provided have been found to work adequately for typical imaging conditions Step 1 Access the advanced parameters window by clicking the Advanced Parameters option under the Parameters Menu BB Advanced Parameters ea e 2D Resolution Accuracy Airy Pixelated with Poisson Gaussian Noise Symmetric Parameterization Model profile calculations __ Pixel integration method Trapezoidal m Additional parameters Background type Constant m Additional parameters EA FandPLimitTool File Export View Tools Help Fisher information matrix calculations Required Parameters Ctrl U select a problem single integration method Trapezoical Additional parameters Advanced Parameters Ctrl N SSS 2D Resolution Accuracy Airy MOIE PAEAN Wirt POISSOr Sass Double integration method
95. tion method Trapezoical Additional Additional parameters Ea File Export View Tools Help Double integration method Trapezoidal ka Additional parameters Required Parameters Ctrl U Select a problem P Advanced Parameters Ctrl M Limits of summation lower limit upper limit Mi use_defautt 3D Resolution Accuracy GUNT MIAE PAETAE YI FESUN Limits of integration lower limit upper limit M A use_defaut Perform calculations Calculate Limits of Accuracy Calculate hic Trapezoidal integration step size 0 05 Alpha 2 x pi x numerical aperture wavelength pi 3 1416 Capprox Values apply to both objects Figure 10 3 1 3D Resolution Accuracy advanced parameters window Step 1 Access the advanced parameters window by clicking the Advanced Parameters option under the Parameters Menu MUMDesignTool Step 2 Skip the Object selection and Advanced fundamental inputs Object 1 sections of the window Their fields do not need to be changed as they are automatically calculated from the values entered in the Required Inputs window Step 3 In the Model profile calculations section of window access the Pixel integration method pull down menu and select Trapezoidal x Gridding Model profile cea bg beth ss Aaa aA E Pixel integration method Y Gridding 13 Trapezoidal Additional parameters Trapezoidal Additional parameters Background type Consta
96. tion of each option is shown on a tool tip text For more information about different electron multiplication models consult 3 Extraneous noise source s Background level Poisson rate 1000 photons pixel s V Use EM EM gain 2 0082 EM model Geometric ala Geometric High gain Geometric standard geometric electron multiplication High gain exponential electron multiplication Gaussian S l Use only with high EM gain iv y0 v Photon detection rate Gaussian Gaussian approximation of output of electron multiplication Parameters to be estimated v x0 J Alpha Alpha 2 x pi x numerical aperture i wavelength pi 3 1416 fapprox Vary a Parameter Figure 1 2 3 Electron multiplication parameters Step 6 In the Parameters to be estimated section of the window ensure that all check boxes for all parameters are checked Step 7 To improve screen clarity close the Required parameters window Remark 3 Closing the window is not in any way required by the application for the calculations to be performed and is only a suggestion in order to reduce the number of open windows and hence improve screen clarity You can access the window again at any time by clicking the Required Parameters option under the Parameters Menu in the main application window 1 3 Providing advanced parameters NOTE All inputs in the Advanced Paramet
97. ussian Symmetric Model Pixelated with Poisson Noise Symmetric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Symmetric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise 4ymmetric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Asymmetric Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Noise Cartesian Parameterization 2D Resolution Accuracy Gaussian Symmetric Model Pixelated with Poisson Gaussian Noise Cartesian Parameterization 2D Resolution Accuracy Airy Model Fundamental Limit Symmetric Parameterization 2D Resolution Accuracy Airy Model Pixelated with Poisson Noise Symmetric Parameterization Location parameters Pixel size height width 13 13 microns X microns Background level Poisson rate 1000 photons pixel s EM model Geometric 3D Localization Accuracy Born VYolf Model Pixelated with Poisson Gaussian Noise Parameters to be estimated Perform calculations z0 V Background level Ww eee ae Calculate Limits of Accuracy Calculate Model Image Simulate Data Images Vary a Parameter Figure 8 2 1 3D Localization Accuracy problem scenario and its required parameters window Step 3 In the Fundamental inputs
98. vailable model and data iMageS ssssssssesssessssessessesesesessecessesesseseearsesensesesseseeansetanseeanseeetanss 20 AI CUAUS A Modelimi ge saraa 21 Mode MSS OVS aac aha tin vate tnierscrisiisa an EAD 21 Model image viewer in MultivalUe MOde sssssssesssseesseerssessseseserseeesseeesstseseseeanseeetstennsnenteneess 22 Enter the number of data IMACS srecruncisnicvervarenessuranratunaciiseruenieconiiwiaesinarisiuneciivernaxanetontiaennaenisniastias 23 Simulating dala IMMaAp EEsperia naa aE aaa ara TENES NEAN aa Ea A i 23 Simulated image viewer in Multivalue Mode s s s sessssrsnsurunsnrnsnrununnnrnnunununnnrnnununnnnnrnnunnnnnnnrnnnnnnnnnne 24 Saving and loading the SOTUN ES vsisicsiscevisainsiniiuievcaisiavianeeraneendaiansiuiaennanereaivsonviuanvanavaaveiwnuiauaiaueninannianties 25 Exporung 1S MOL GV aia Dl rundincciminannnn n A 26 Exporting the results and parameters ssssssessssessssssssssseerseeessesesseseeesecenseeessesesaesesansesensesensnsntensess 27 An example for the exported results and parameters cssssssessseseesseersecesseessseseeensesenseeerseeetes 27 Exporting the model and data iMageS csssssssessssessseeeeseeessseesseseeesecassesesseseeesesansesansesensnentansess 28 Expone a La lex TED OM capena a EA 29 5 ai 9 118 0 0 nr ener enenrrr nnn E E E ee eee 30 OS FINS oarra E A E EE E E 31 About the Fane LIMI TOOL uieii aa a a aaan avisiate 31 Introduction Figure 7 2 1 The MUMDesignTool configuration W
99. ves Step 7 To see the xo elements of the FIM and PLAM curves in the Display options section select the x0 radio button The FIM and PLAM curves will be updated accordingly as can be seen in the following figure The MUMDesignTool File Help Simulation summary 1 515 160 imm E 3 Focal plane 1 1 45 0 69 microns Focal plane 2 O 1 seconds a F Focal plane 3 100 Sum line Refractive index Tube Length Numerical aperture Wavelength Exposure time Magnification Location parameters 0 585 microns 0 585 microns Limit ruler Focal plane offset Number of focal planes 3 x0 element of FIM 1 um Limit of the accuracy of xO nm a E E microns microns microns microns i microns microns Object z position pm microns microns microns Display options Switch plots z0 x0 yO Visibility Plane lines Sum F Fix Y w1 V2 E3 6 7 5 Plane markers 7 1 7 2 3 5 6 7 5 photons s View mode default v Limit of the accuracy of xO nm Highlight region Show o e l os e E i 3 Photon Precise Mode Split windows 33 34 33 D 0 5 Object z position pm Figure 7 3 3 The lateral elements of FIM and PLAM MUMDesignTool Rapid Mode Step 8 To save the calculated data points and the plots click the Export button in the Display
100. window which can be accessed directly within the software not only can provide users with the details of calculations in real time but also is very useful for identifying warning errors and reporting bugs The information that are shown in the console window are also stored in a log file 6 1 The console window As mentioned earlier during the long calculations a console window is automatically displayed to inform the user about different steps of the calculation This console window can also display errors and warnings if there is any which is very useful for bug reporting purposes Step 1 To access the console window at any time select the Console option under the View Menu Step 2 To hide the console window simply close it using the standard close button Note that closing the console window will not stop storing the information in the log file BB FandPLimitTool File Export Pararneters Tools Help Parameter Summary Ctrl P Results Ctrl R 2D Localizatir Gaussian Moise Console Select a pri Perform calculations Calculate Limits of Accuracy Calculate Model Image simulate Data Images 2 ole le imture 2 of 2 dure 1 of 2 ture 1 of2 ture 2 of 2 All rights reserved Copyright 2 2004 2014 ward Ober Lab For single molecule localization and resolution FandPLimitTool 1 2 Initializing the application Figure 6 1 1 Console window 6 2 The log file and bug reporting The in

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