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HRTEM Exit Wave Reconstruction Package

1. eoo Check Aligned Images Previous Time between each frame 1 60 sec Save Aligned Images Export Images Data Type Integer 2 Bytes U is Mac Byte ordering PC Byte ordering Export To check the alignment one can step through the images one by one or play the series as a movie with a specified time interval between frames The aligned images can be resaved back to the original filenames Save Aligned Images or exported in a different or same format Export to a new set of files Gerchberg Saxton This is the basic starting point for performing the exit wave reconstruction The images can be aligned at this point or they can have previously been aligned through the Align Image Series command Regardless for experimental images the align checkbox should be checked as this will allow the software to do further sub pixel alignment as part of the reconstruction algorithm Invoking this menu command brings up the following dialog _ Experimental Image Series Base Name File Name Select First Image ATFS ATFS 001 First Focus A 2965 images in series 19 Sampling A px 0 20549 Series Focus step A 24 0 10 Customize Reconstruction Stop when change in fit is less than 0 250 cycles 3 Simulated Images no alignment noise processing Align C Show live update of reconstructed wave fu
2. reconstructed ex ked a default select lection can be moved around Once IS INVO ion menu command Correct When the Aberrat will be placed on it wave This se dow shows the ampl the ex Ihe user image d phase tude image an in h parameter ad wi ked selects wh INVO Keys hf arrow le Illy updated for the new and can modity it with the left and ri UST j tude and phase IC t isfactory sett Image are con values of the selected parameter Once The ampl ings are found the new it wave If the selection gets deleted the ent parameters can be applied to 14 IS indow ION W created if the aberrat ICa tomati ble to also show the correspond focus from the current exit wave with the ION IS QU a new default select ted image for any d aberration correct impose ing compu IS possi open It given 15 Propagated Complex Wave 1 Exit Wave Amplitude CT m ORR Er Amp Standard Deviation 0 0623 Phase Min 0 261 Phase Max 0 426 Image Focus A 0 Amp Ave Peak Width 9982 27 Phase Range 0 687 Amplitude Max 0 9973 Use Left and Right Arrow Keys to Control Selected Property Shift Plane of Focus Lens Abberations Mag A Incr A Abberrations Mag A Incr Angle Incr 9 Focus Plane 0
3. Reconstruct Will as it says start the reconstruction algorithm The time required for the reconstruction is a function of the image size the number of images and the number of iterations If the option to show amplitudes of computed images is selected the software will display a window where the computed and experimental images are shown side by side for comparison This window is shown below It should be noted that the values for the cross correlation coefficient and chi square below are values obtained for the entire image The reconstruction and refinement algorithm uses values obtained from a central region which is half of the actual image in size or the region specified in the customize reconstruction window 10 Propagated Reconstructed Wave Experimental Image Amplitude i Reset ed Il Propagated Focus 2952 0 Assigned Focus 2952 0 Previous Next The actual output of the algorithm is a complex reconstructed exit wave 11 Al y ee Display Modulus Square Display Real Part Display Imaginary Part Display Modulus Display Phase Yy v gt a7 or Fyt r ry r F N 2 e M A P vu gt La d e 4 La DN 142 T ie T m M 2 36 am
4. 5 Two fold 0 10 O 0 10 Three fold 0 1000 O 0 10 0 200 O 0 10 Low Resolution TIE Method takes take 3 or more low resolution images taken at different values of focus and attempts to reconstruct the complex low resolution exit wave The algorithm is based on the Transport of Intensity equation and can be used on low resolution images for imaging magnetic domains etc 16 TIE Low Resolution Exit Wave Reconstruction Experimental Image Series Base Name File Name Select first image in series j Image Focus step 300000 images Image number Increment 1 vi Align Images 4 Customize Show Aligned Images Cancel Reconstruct Shiske Filler Restoration The Shiske filter relies on the assumption that the observed signal the image is related to the object the projected potential in a linear fashion through a transfer function This holds true to a good approximation for the Fourier coefficients of the potential and the image within the validity of the Weak Phase Object Approximation WPOA In the WPOA the specimen is thin enough so that the object is thought of as a phase function operating on the phase of the electron wave function Multiple scattering is ignored and the propagation of the wavefield within the specimen is also ignored In addition most of the electrons are considered not scattered the central beam in the diffraction pattern i
5. a starting exit wave from each image back propagated to the exit plane of the specimen The exit wave is an average of the exit wave generated from each image in the series Initially the amplitude of the complex wave in the image plane is set to the amplitude of each image and a phase of zero This complex wave is then propagated back to the exit plane through the contrast transfer function of the microscope The exit wave is then forward propagated through the microscope yield computed images for each focus value The computed images are compared to the experimental images and a fit is calculated This constitutes one iteration Amplitudes of the propagated waves are reset to those of the image and then propagated back to the exit plane for the next iteration At the end of one cycle the software will look for new focus values that optimizes the fit with the experimental images and new cycle will begin with a new sequence of iterations The calculation will continue until the number of cycles and iterations have been reached or until the change in fit has reached a set limit If the limit is not reached within the given number of cycles the software will ask if the calculation should continue At any point the calculation can be stopped by pressing Apple Apple period If this is done once the software has begun the iterations the current iteration will continue to the end and the reconstructed wave at that point will be shown
6. the potential found from the Shiske restoration This lirative comparing qud lar case all the methods would lead essentially the same interpretation of the atomic structure No claims are made ICU t in th t show howi Is mean is par 20 to the validity of the approximations underlying the different methods True Image Gerchberg Saxton 21
7. HRTEM Exit Wave Reconstruction Package User Manual CONTENTS INSTALLATION 3 INTRODUC TION Dot 3 j RECONSTRUCTION PACKAGE MENU COMMANDS 4 IV USE OF COMMANDS 5 I ALIGN IMAGE SERIES Il GERCHBERG SAXTON 1 ABERRATION CORRECTION IV LOW RESOLUTION TIE METHOD V SHISKE FILTER RESTORATION COMPARISON OF RECONSTRUCTION METHODG 16 Installation The reconstruction package will automatically be available as the hardware key will be programmed to enable the optional package The reconstruction package will accessible through the sub menu Exit Wave Reconstruction under the Process Menu A separate menu item Shiske Filter Restoration will also appear under the Process Menu Introduction This Package constitutes an extension to MacTempasX Total Resolution LLC and provides a number of functions for reconstructing the complex electron exit wave from a series of High Resolution Transmission Electron Microscope HRTEM images taken at different foci The approach used for reconstructing the complex exit wave is based on the Gerchberg Saxton algorithm The Shiske Filter Restoration method is based on an optimum filter approach for restoring the
8. Select First Image ATFS ATFS 001 dat First Focus 2965 images 13 Sampling px 0 205490 Series Focus step 24 0 Customize vi Align Simulated Images no alignment noise processing Cross correlation Restoration Filter Noise Constant gt 0 0 010000 9 Phase correlation Cut off 0 67 1 Microscope Parameters Pre Alignment Noise Filter s Voltage kV Delta 30 Wiener Filter iwi Low Frequency Filter Cs mm 0 6000 Divergence mrad 0 20 4 Frequency Cut off 0 10 1 Cs5 mm 0 00 gi nA R2 1 High Frequency Filter PhasePlate rr ooo 10 001 0 001 Frequency Cut off 150 2E Post Reconstruction Filter Resolution 1 1 25 wi Low Frequency Filter 0 10 1 Cancel In the image below there has been imposed a low frequency cut off corresponding 5 Angstroms 19 77 Comparison of Reconstruction Methods V It is interesting to try to compare the solutions one finds by using different methods in this case the results from True Image Gercberg Saxton and Shiske filtering True Image and Gerchberg Saxton attempts to restore the exit wave while Shiske restoration tries to restore the potential In the images below we are ly the phase of the exit wave from the two exit wave reconstruction methods with
9. ame aans ATFS 001 dat images Image number Increment 1 Check Image Series C3 Align by cross correlation Align By Phase Correlation Phase Correlation Parameters Frequency Cut off 0 67 1 Sampling 0 20000 A Pixel Optional Focus Shift voltage 200 300 kV Use Select first image to specify the first image in a series of images For raw binary images the user needs to specify the data type any byte offset and any necessary byte swap of the data Verify that the base name is correct as the software tries to guess the structure of the base name for the series based on the r Import Raw Image Import from ATFS 001 dat O O Format Length 2097152 aay Text ETTEREN Data Type Lines Are Rows i Get Size By Counting l ee Size Binary 7mm Offset O Width 11024 Angle Swap Data Bytes Height 1024 90 yt Simulation Sampling Width 0 Height 0 Angle 90 00 Cancel Use Check Image Series to verify that the images have been read in correctly and that all the images are suitable for use in the reconstruction Image Series Inspection Window View f Image Fourier Transform Displayed Image ATFS 001 dat Previous Next Click Align to start the alignment of the image series Once the image alignment procedure is completed the following window is displayed
10. m which can be split into an amplitude and a phase image Illy would look like the default display of the complex ISUQ image vi The Amplitude wave A complex image can be shown in different form By right button clicking ing the layed allow iso or Control click on the image a pop up menu will be d 2 2 a O p D 5 g N E n c O O O ua EE c Q C zx w uc 9 O Q 0 o0 o Ift one were to perform the operation mathematical operation Exit Wave 1 the phase of the exit wave should closely correspond to what can be calculated from the s wave approach One can do this operation with the image calculator or with the scripting package if installed Alternatively one do a linked Fourier transform of the exit wave place an annular mask in the Fourier transform and make the inner ring such that it eliminates the inner part of the Fourier spectrum The resulting phase image for the above calculation would look as shown below in a somewhat contrast enhanced image 13 untitled A2 Correction Ion Aberrat ts may not be ff In order to possibly correct for any to apply a phase plate to the focus value and other aberration coe ing The start imum accuracy ith opti w these parameters t ini ined determ ble Is DOSSI In change t wave
11. nctions a Cross correlation 1 On completion show image wavefunction amplitudes Phase correlation Cut off 0 57 1 Restoration Filter Noise Constant gt 0 0 010000 Show Aligned Images Microscope Parameters Voltage kV Divergence mrad 0 20 PhasePlate m 0 00 Cs mm D60 55 mm 000 Ri 1 2 1 Focus Spread 30 00 Lens Aperture 1 125 0 001 0 001 Pre Alignment Noise Filter s Post Reconstruction Filter C Wiener Filter wi Low Frequency Filter 0 10 Low Frequency Filter 0 10 C High Frequency Limit 150 l Cancel After selecting the first image in the series the rest of the information needs to be filed out according to the experimental conditions The image series is specified by the first image to be used in the reconstruction and the number of images in the series The starting focus and the focus step must be set correspond to assumed values for the experiment The software will try to refine the focus values as part of the reconstruction If the images come with a sampling as from a calibrated Gatan Image file the sampling will be set accordingly Otherwise the sampling of the image must be specified All the Microscope Parameters must be set if they differ from the default values supplied by the software The package will normally default to working with experimental images containing noise and in need of alignme
12. nt However this can be over ridden by clicking on the Simulated Images checkbox For experimental images noise filtering can be applied as well as a high frequency cut off Options exist to have a live update of the reconstructed image after each iteration and to show the wave function amplitudes in the image plane as determined by the algorithm By selecting Customize a specified area can be chosen to be used for determining the alignment By default an area centered in the image and of a dimension which is half of the image dimension is used Individual focus values for the images can also be set at this point if those are known As mentioned earlier the software will try to search for focus values that optimizes the fit between calculated images from the reconstructed exit wave with the experimental images E ed 91 27 Optimum Area for Alignment 9 Selection Width Height 512 512 Entire Image View Image C Fourier Transform Displayed Image ATFS_001 dat Customize focus Image Focus 72965 0 Reset View Restoration Filter Noise Constant This constant must be non zero in order to not blow up noise in regions where the contrast transfer function of the objective lens is very small The default value will probably suffice in most cases Max Number of Iterations cycle and Max Number of Cycles The reconstruction algorithm is comprised of a series of iterations The first step is to compute
13. s strong Within the WPO approximation one can write 1 9 E V 2 H g n g where H is a transfer function associated with the microscope V is the potential projected of the specimen and lis the fourier coefficients of the recorded image A noise term is added which is to be considered uncorrelated with the object we are trying to reconstruct In the equation above we are statin g that we can record a number of different images for different values of the transfer function H and noise given the same object V We want to find the best estimate of the potential given N images recorded at different conditions of the microscope lens We want to express the estimate by the application of a set of filters such that the estimated potential can be written VG FG 17 Thus what we try to find is the optimal solution for a filter function which minimizes the difference between the estimated solution and the true potental which we seek to find 2 Minimize lt X FOLO V e gt i The solution filter function operating on each image of the form _ H g 2 H GY In the WPOA the function is proportional the contrast transfer function of the microscope sin x 2 Below is an example of the use of the Shiske filter restoration on the same experimental images of gold used in the Gerchberg Saxton exit wave retrieval algorithm 18 Experimental Image Series Base Name File Name
14. specimen projected potential from a focus series of HRTEM images lil Reconstruction Package Menu Commands zi 2 Text Window Help Image Calculator THC FFT Linked Fourier Spectrum GF Hanning Masked FFT Soft Circular Masked FFT X tr 38F Inverse FFT d Power Spectrum Edit Mask X 1r 88M Apply Mask s Fourier Filters p Spatial Filters j Transform Statistics Calibrate X Extract From Complex b Correlation Convolution p Azimuthal Average Template Matching Peak Lattice Analysis p Average Motif Change Image Origin Geometric Phase Analysis Diffraction Pattern Quantification Crystallographic Image Processing 5 Exit Wave Reconstruction p Align Image Series Shiske Filter Restoration Gerchberg Saxton Focus Determination Low Resolution TIE Method v Always Create New Image Aberration Correction Process MacTempas process menu Exit Wave Reconstruction Align Image Series Gerchberg Saxton Low Resolution TIE Method Aberration Correction Shiske Filter Restoration IV USE OF COMMANDS Align Image Series Will align a series of images either by the use of the cross correlation function or the phase correlation function Optionally with the phase correlation function a known focus step can be used to assist in the alignment procedure Align Image Series Experimental Image Series Base Name File N

HRTEM Exit Wave Reconstruction Package

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