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%BACK_PROJ backpropagate the updated projections (multilayer slices) into
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%the full 3D volume, call thi function separatelly for real and imaginary
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%part of the projections
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%
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% volData_upd = back_proj(projData_upd,theta,Npx_vol)
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%
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% Inputs:
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% **projData_upd - stacked 2D array, linearized difference of the complex-valued projections, ie log( P_new .* conj(P_orig) ./ |P_orig|^2)
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% **theta - scalar, angle of the provided projection
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% **Npx_vol - dimensions of the full volume
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% *returns*
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% ++volData_upd - 3D array, linearized update of the tomographic volume
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% Academic License Agreement
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%
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% Source Code
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%
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% Introduction
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% • This license agreement sets forth the terms and conditions under which the PAUL SCHERRER INSTITUT (PSI), CH-5232 Villigen-PSI, Switzerland (hereafter "LICENSOR")
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% will grant you (hereafter "LICENSEE") a royalty-free, non-exclusive license for academic, non-commercial purposes only (hereafter "LICENSE") to use the PtychoShelves
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% computer software program and associated documentation furnished hereunder (hereafter "PROGRAM").
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%
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% Terms and Conditions of the LICENSE
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% 1. LICENSOR grants to LICENSEE a royalty-free, non-exclusive license to use the PROGRAM for academic, non-commercial purposes, upon the terms and conditions
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% hereinafter set out and until termination of this license as set forth below.
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% 2. LICENSEE acknowledges that the PROGRAM is a research tool still in the development stage. The PROGRAM is provided without any related services, improvements
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% or warranties from LICENSOR and that the LICENSE is entered into in order to enable others to utilize the PROGRAM in their academic activities. It is the
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% LICENSEE’s responsibility to ensure its proper use and the correctness of the results.”
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% 3. THE PROGRAM IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR
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% A PARTICULAR PURPOSE AND NONINFRINGEMENT OF ANY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS. IN NO EVENT SHALL THE LICENSOR, THE AUTHORS OR THE COPYRIGHT
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% HOLDERS BE LIABLE FOR ANY CLAIM, DIRECT, INDIRECT OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY ARISING FROM, OUT OF OR IN CONNECTION WITH THE PROGRAM OR THE USE
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% OF THE PROGRAM OR OTHER DEALINGS IN THE PROGRAM.
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% 4. LICENSEE agrees that it will use the PROGRAM and any modifications, improvements, or derivatives of PROGRAM that LICENSEE may create (collectively,
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% "IMPROVEMENTS") solely for academic, non-commercial purposes and that any copy of PROGRAM or derivatives thereof shall be distributed only under the same
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% license as PROGRAM. The terms "academic, non-commercial", as used in this Agreement, mean academic or other scholarly research which (a) is not undertaken for
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% profit, or (b) is not intended to produce works, services, or data for commercial use, or (c) is neither conducted, nor funded, by a person or an entity engaged
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% in the commercial use, application or exploitation of works similar to the PROGRAM.
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% 5. LICENSEE agrees that it shall make the following acknowledgement in any publication resulting from the use of the PROGRAM or any translation of the code into
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% another computing language:
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% "Data processing was carried out using the PtychoShelves package developed by the Science IT and the coherent X-ray scattering (CXS) groups, Paul
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% Scherrer Institut, Switzerland."
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%
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% Additionally, any publication using the package, or any translation of the code into another computing language should cite
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% K. Wakonig, H.-C. Stadler, M. Odstrčil, E.H.R. Tsai, A. Diaz, M. Holler, I. Usov, J. Raabe, A. Menzel, M. Guizar-Sicairos, PtychoShelves, a versatile
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% high-level framework for high-performance analysis of ptychographic data, J. Appl. Cryst. 53(2) (2020). (doi: 10.1107/S1600576720001776)
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% and for difference map:
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% P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379–382 (2008).
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% (doi: 10.1126/science.1158573),
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% for maximum likelihood:
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% P. Thibault and M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 063004 (2012).
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% (doi: 10.1088/1367-2630/14/6/063004),
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% for LSQ-ML:
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% M. Odstrčil, A. Menzel, and M. Guizar-Sicairos, Iterative least-squares solver for generalized maximum-likelihood ptychography, Opt. Express 26(3), 3108 (2018).
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% (doi: 10.1364/OE.26.003108),
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% for mixed coherent modes:
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% P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature 494, 68–71 (2013). (doi: 10.1038/nature11806),
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% and/or for multislice:
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% E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, X-ray ptychography with extended depth of field, Opt. Express 24, 29089–29108 (2016).
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% (doi: 10.1364/OE.24.029089),
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% and/or for OPRP:
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% M. Odstrcil, P. Baksh, S. A. Boden, R. Card, J. E. Chad, J. G. Frey, W. S. Brocklesby, Ptychographic coherent diffractive imaging with orthogonal probe relaxation.
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% Opt. Express 24.8 (8360-8369) 2016. (doi: 10.1364/OE.24.008360).
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% 6. Except for the above-mentioned acknowledgment, LICENSEE shall not use the PROGRAM title or the names or logos of LICENSOR, nor any adaptation thereof, nor the
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% names of any of its employees or laboratories, in any advertising, promotional or sales material without prior written consent obtained from LICENSOR in each case.
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% 7. Ownership of all rights, including copyright in the PROGRAM and in any material associated therewith, shall at all times remain with LICENSOR, and LICENSEE
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% agrees to preserve same. LICENSEE agrees not to use any portion of the PROGRAM or of any IMPROVEMENTS in any machine-readable form outside the PROGRAM, nor to
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% make any copies except for its internal use, without prior written consent of LICENSOR. LICENSEE agrees to place the following copyright notice on any such copies:
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% © All rights reserved. PAUL SCHERRER INSTITUT, Switzerland, Laboratory for Macromolecules and Bioimaging, 2017.
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% 8. The LICENSE shall not be construed to confer any rights upon LICENSEE by implication or otherwise except as specifically set forth herein.
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% 9. DISCLAIMER: LICENSEE shall be aware that Phase Focus Limited of Sheffield, UK has an international portfolio of patents and pending applications which relate
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% to ptychography and that the PROGRAM may be capable of being used in circumstances which may fall within the claims of one or more of the Phase Focus patents,
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% in particular of patent with international application number PCT/GB2005/001464. The LICENSOR explicitly declares not to indemnify the users of the software
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% in case Phase Focus or any other third party will open a legal action against the LICENSEE due to the use of the program.
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% 10. This Agreement shall be governed by the material laws of Switzerland and any dispute arising out of this Agreement or use of the PROGRAM shall be brought before
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% the courts of Zürich, Switzerland.
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function volData_upd = back_proj(projData_upd,theta,Npx_vol)
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projData_upd = gpuArray(projData_upd); % difference after ptycho update
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assert(isreal(projData_upd), 'Inputs are assumed to be real valued')
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Nlayers = size(projData_upd,3);
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% permute to see it from the top direction
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projData_upd = permute(projData_upd, [2,3,1]);
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% interpolate back to the full size
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if Nlayers == 1
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% faster option for single layer
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volData_upd = repmat(projData_upd* (Nlayers/Npx_vol(2)) ,[1,Npx_vol(2),1]);
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else
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%% periodic boundary
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binning = ceil(Npx_vol(2)/Nlayers/4); % in order to reduce computational requirements, use a combination of interpolation FFT and simple and fast upsampling
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Nl_upsample = Npx_vol(2) / binning;
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assert(Nl_upsample == round(Nl_upsample), 'Volume size cannot be split for binning')
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% revert the 0.5px offset along the beam direction , process real and imag part separatelly
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% to avoid mixing
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projData_upd = projData_upd * (Nlayers/Nl_upsample/binning);
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%% %%% centered FFT interpolation %%%
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% pre-fft transform
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projData_upd = fft(projData_upd,[], 2);
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% apply 0.5 pixel shift
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projData_upd = utils.imshift_fft_ax(projData_upd,0.5,2, false);
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% interpolate to the full size
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volData_upd = utils.interpolateFT_ax(projData_upd,Nl_upsample,2, false);
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% post-ifft transform
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volData_upd = real(ifft(volData_upd,[], 2));
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% finally quickly upsample to the full required size
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volData_upd = utils.unbinning_2D(volData_upd, [1, binning]);
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end
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% back rotate to the basic orientation , use bilinear interpolation
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% because it is much faster than FFT rotation
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volData_upd = utils.imrotate_ax(volData_upd, -theta, 3, 0, 'bicubic');
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end
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