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1. Image Reconstruction User Manual Version 1 0 Alpha Filipe Maia February 5 2007 Contents 1 Introduction 2 Learning by Example 21 First contact with Hawk 4 6 ace da RA A A A A A A 2 2 RING PrepLOCesSiING s s p a a a A Gk 3 Reference Jal Algorithims o a a eo ee a ae ee ee ed de ak 3 2 tuwrap conf Options 0004 Sane 2 E ee a ea E Chapter 1 Introduction Hawk is a collection of computer programs which aim at reconstructing an object from it s oversam pled diffraction pattern This usually means diffraction patterns from single particle diffraction as opposed to crystal diffraction An oversampled diffraction pattern is simply a diffraction pattern which can be sampled more finely than a crystal of the same sample This progrm makes use of many different algorithms which all take advantage of the fact that in real space an oversampled diffraction pattern causes the solution to be surrounded by an empty region which can be used be used to constraint the possible phases for the diffraction pattern Chapter 2 Learning by Example We re gonna start by trying to reconstruct a simple object a ring Im going to assume you have Hawk installed and all the programs are in the path If this is not the case please read the Installation chapter 2 1 First contact with Hawk For this reconstruction we re gonna start with a preprocessed diffraction pattern The preprocessing involves masking out2. make life more difficult Prepocessing might also be desirable to reduce image size throwing away redudant information in order to speed up calculation So in Hawk there s a program called process_image which will take your raw experi mental image and massage it so it becomes suitable for further processing You can start by taking a look at the raw image using a small utility bundled in called image_to_png and compare it to the preprocessed one image_to_png ring_raw h5 ring raw png CHAPTER 2 LEARNING BY EXAMPLE 5 display resize 600x400 ring_raw h5 amp image_to_png ring h5 ring png display resize 400x400 ring png amp a Figure 2 2 a Log scale colormap of the raw ring data b Log scale colormap of the processed ring data The first thing you ll probably notice is that the processed one doesn t look at all like rings and it s also much smaller One of the effects of preprocessing is to swap the quadrants of the picture with respect to the center of the diffraction pattern To do this it will try to figure out the center of the image by using the maximum of the self convolution as the center Alternatively it can also be specified by the user Figure 2 3 Quadrant swapping data for compatibility with FFTW Another interesting difference between the two images images is that the processed one is square while the raw is rectangular For the moment Hawk can only image with square image so the
3. new support 3 0 is a typical value e float patterson_threshold Defines the value that determines if a pixel is going to be used as initial support or not Pixels with a value greater than max autocorrelation patterson_threshold will be part of the support derived from the autocorrelation 0 04 is a typical value although this depends strongly on the image e float beta Relaxation parameter used in several algorithms including HIO and RAAR It can vary between 0 and 1 with 1 meaning no relaxation It s value is directly related with the instability and speed of the algorithms 0 9 is a typical value e int innerloop_iterations How many innerloop iterations to execute before executing an outer loop iteration 20 is a typical value e float added_noise How much noise to add to the input amplitudes The value is the stan dard deviation of the gaussian noise with mean 1 that is multiplied with the input ampltitude e float beamstop_radius This defines a circle centered in the middle of the image with a given radius and all the pixels lying inside that area will be marked as unknown e float support_intensity_threshold Defines the value that determines if a pixel is go ing to be used as support in the next iteration or not Pixels with a value greater than CHAPTER 3 REFERENCE 10 max blurred image support_intensity_threshold will be part of the support that is updated at every outerloop 0 20 is a t
4. to examine images is to use an excellent visualizer called VisIt produced by the LLNL and freely available for many platforms Please visit the page http www llnl gov visit for more information including installation details From now on i ll assume that you have Vislt installed VisIt cannot open the image format used by Hawk so we ll have to convert it to some standard format We ll use image_to_vtk to do just that image_to_vtk raw_ring h5 raw_ring vtk amp This will transform the image into a 2D structured points VTK file You can now start VisIt and load the file File Select File chooses the files and hit select Draw the image using Pseudo color select the file from the list box press open then go to Plots and choose pseudocolor and you maybe need to hit the Draw button now You should be able to see now the raw image figure You can now use use the Node picking tool to check the red values close to the center The highest value you ll find is 65535 but we should set the saturation limit somewhat below let lets say 55000 We should now try to determine more or less the background For this it s better to change the CHAPTER 2 LEARNING BY EXAMPLE u DB raw_rin Pseudocolor Var amplitudes k 4 655de 0 49158 04 32770 44 2 16380 04 0 000 Max 65540 041 O Min 0 000 Figure 2 5 Pseudocolor representation of the raw ring image color scale to logarithmic on the Active plots list click on the a
5. because the image we re using is much larger One important thing to check then is the autocorrelation vtk file This file unsurprisingly contains the autocorrelation of the input If you see a lot of blank space around the autocorrelation of the object you can usually CHAPTER 2 LEARNING BY EXAMPLE 8 further downsample the diffraction pattern to improve the speed of the algorith As long as most of the autocorrelation fits inside the image downsampling should not be a problem It should be noted though that decreasing the oversampling ratio will increase the noise so it s use depends on the signal to noise ratio of your particular dataset If you are tired of waiting for the solution you can kill the process and try out an image with a lower oversampling ratio Instead of downsampling 3x lets try with 10x and see what happens process_image i raw_ring h5 o pro2_ring h5 s 55000 g O a 10 Again create another directory copy uwrapc conf and ro2_ring h5 there and do the required changes in uwrapc conf Run uwrapc and check out the output Chapter 3 Reference 3 1 Algorithms 3 2 uwrap conf Options Options can be either floating point numbers marked as float integers marked as int or quoted textual strings marked as string e float initial_blur_radius The standard deviation of the starting radius of the gaussian in pixels used for blurring the real space image during the outerloop that is used to define a
6. input has to be cropped to make it square A last important difference is that the processed image has zeroes blue where the raw image has saturated pixels near the center of the diffraction pattern These zeroes are not really zeroes they are just unkown values Inside ring h5 besides the image itself there s also a mask that specifies which values have experimental meaning and which do not We can take a look at it by doing figure 2 5 image_to_png ring h5 ring png ring mask png amp CHAPTER 2 LEARNING BY EXAMPLE 6 display resize 400x400 ring mask png amp Figure 2 4 Ring image with mask next to it The blue represent unmeasured data and red the opposite You can see that there are quite a few regions with zero in the mask which correspond to exper imentally unkown intensities The area close to the corners of the mask correspond to saturated pixel detectors this area actually corresponds to the center of the detector The horizontal strip in middle of the mask is due to a completely different reason Because Hawk can only deal with square images the images are first made square by padding the smallest dimension with zeroes untill the image becomes square Obviously the padding values don t have any real meaning so they are masked out Now that we know a bit more about images and masks lets try to process our image We ll start by examining the image to determine at which point the detector seems to saturate An easy way
7. overexposed pixels removing background and beamstop and other trivialities which are nevertheless important but which we can learn more about later For the moment we ll focus on the inversion problem alone To begin with you need to go to the Hawk website and download the examples package if you haven t done it yet Then just decompress it and change your current directory to the newly created examples ring directory tar zxf examples tar gz cd examples ring Now inside this directory there should be two files called ring h5 and uwrapc conf The first file has the experimental data that we are trying to reconstruct It contains things like image intensity at each point a mask image center and other important information For a more detailed description of the format please check the file format reference The second one contains the options that are passed to the solver This is the file that controls the solver and is always named uwrapc conf Here s how it looks like File containing the diffraction pattern amplitudes_file ring h5 Threshold of the autocorrelation which defines the initial guess patterson_threshold 0 01000000 Threshold for defining the new support after each support update support_intensity_threshold 0 100000000 CHAPTER 2 LEARNING BY EXAMPLE 3 Number of iterations untill the minimum blurring is reached iterations_to_min_blur 4000 Reconstruction algorithm u
8. rrow on the left side of the first plot double click on the tree member Pseudocolor select Min and set it to 1 and then select log scale You can see that there seems to be plenty of signal all the way to high resolution and the background seems very small So we can safely set the background to 0 Another important thing to notice about this diffraction pattern is that it s quite smooth This means that it s higly oversampled To reduce computing time we can downsample it We can for example first try to downsample it by 3x So lets put all of this into a command process_image i raw_ring h5 o prol_ring h5 s 55000 g O a 3 This command will transform the intensities into amplitudes do the required fft shifts mask out all intensities above 55000 remove the background from our picture and downsample it by 3x It s always a good idea to visually inspect the output to make sure it is what you expect you have to convert it first with either image to_png or image_to_vtk when quantitative analysis is required We can now use the configuration file provided in the examples to try to reconstruct our new file So create a new directory for example prol and copy prol_ring h5 and uwrapc conf there Edit uwrapc conf to replace the amplitudes file value with prol ring h5 instead of ring h5 Now simply run uwrapc and check the result You ll notice that the iterations take a lot longer than with the ring h5 file provided This is
9. sed algorithm RAAR Use random intensities for the non zero part of the initial guess random_initial_intensities 1 Directory where to do the reconstructions work_directory Algorithm for support update support_update_algorithm fixed Make all amplitudes relative to maximum rescale_amplitudes 1 It s a simple key value configuration file All lines starting with are comments and not interpreted by the program Don t worry if you don t understand all lines It might be a good idea to take a look at the Basic Algorithm chapter if all this seems alien to you Now lets run the program and see what output it produces uwrapc A word of warning the program never stops so you are responsible to kill it when you re satisfied with the results Using another shell you can take a look at the files being created in that directory First a file called uwrapc confout will be created which lists all the options you chose plus the defaults that were used Don t be afraid by it s length many options are irrelevant for most reconstructions Another file created is diffraction png which contains a color coded representation of the pattern being phased The file autocorrelation png shows the patterson function of your diffraction pattern and the files initial_guess png and initial_support png are obviously the first guess for the iter ative algorithm and the first support respectively You should
10. take a quick look at them all to see if everything is running as expected Within some time the program start to output files named real_out xxxxxxx and support Xxxxxxx where the x s represent a number This is simply the output of the program after XXxxxxx iterations The output is stored in color coded png file for quick inspection and in h5 files for more rigorous future analysis The remaining file created by the program is uwrapc log and it contains numerous statistics useful for checking the evolution of the reconstruction You can look at this file using Grace which is freely available on the internet with the following command xmgrace nxy uwrapc log The most interesting plots are probably the Fourier Error and Real Space Error For more infor mation about the log file check the appropriate chapter CHAPTER 2 LEARNING BY EXAMPLE 4 After about 20000 iterations or so the program should have reached a stable solution so you can kill it You can check the final values of the Fourier and Real Space Errors in the log file and visually inspect the reconstructed image Hopefully it should look something like this Figure 2 1 Colormap representation of the reconstructed ring Congratulations you have just finished your first reconstruction 2 2 Ring preprocessing Prepocessing is necessary because unfortunately in the real word pixels saturate there s background noise there are beamstops and other problems that
11. ypical value although this depends strongly on the image int iterations_to_min_blur How many innerloop iteration untill the bluring radius de creases to it s minimal value Usually around 3000 float minimum_blur_radius Minimum bluring radius in pixels 0 7 is a usual value bool enforce_reality If not 0 the real space image will be forced to be real by setting it s imaginary part to 0 string logfile Name of the file where to write to log Usually uwrapc log int output_period Number of innerloops between writing image files int log_output_period Number of innerloops between writing output to the log file string algorithm Name of the algorithm to use Check section 3 1 for details
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