%ML Maximum Likelihood refinement % % Publications most relevant to the Maximum Likelihood refinement % + M. Guizar-Sicairos and J. R. Fienup, "Phase retrieval with transverse % translation diversity: a nonlinear optimization approach," Opt. Express 16, 7264-7278 (2008) % + P. Thibault and M. Guizar-Sicairos, "Maximum-likelihood refinement for % coherent diffractive imaging," New J. Phys. 14, 063004 (2012). % Academic License Agreement % % Source Code % % Introduction % • This license agreement sets forth the terms and conditions under which the PAUL SCHERRER INSTITUT (PSI), CH-5232 Villigen-PSI, Switzerland (hereafter "LICENSOR") % will grant you (hereafter "LICENSEE") a royalty-free, non-exclusive license for academic, non-commercial purposes only (hereafter "LICENSE") to use the cSAXS % ptychography MATLAB package computer software program and associated documentation furnished hereunder (hereafter "PROGRAM"). % % Terms and Conditions of the LICENSE % 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 % hereinafter set out and until termination of this license as set forth below. % 2. LICENSEE acknowledges that the PROGRAM is a research tool still in the development stage. The PROGRAM is provided without any related services, improvements % 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 % LICENSEE’s responsibility to ensure its proper use and the correctness of the results.” % 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 % A PARTICULAR PURPOSE AND NONINFRINGEMENT OF ANY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS. IN NO EVENT SHALL THE LICENSOR, THE AUTHORS OR THE COPYRIGHT % 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 % OF THE PROGRAM OR OTHER DEALINGS IN THE PROGRAM. % 4. LICENSEE agrees that it will use the PROGRAM and any modifications, improvements, or derivatives of PROGRAM that LICENSEE may create (collectively, % "IMPROVEMENTS") solely for academic, non-commercial purposes and that any copy of PROGRAM or derivatives thereof shall be distributed only under the same % 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 % 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 % in the commercial use, application or exploitation of works similar to the PROGRAM. % 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 % another computing language: % "Data processing was carried out using the cSAXS ptychography MATLAB package developed by the Science IT and the coherent X-ray scattering (CXS) groups, Paul % Scherrer Institut, Switzerland." % % Additionally, any publication using the package, or any translation of the code into another computing language should cite for difference map: % P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy, Science 321, 379–382 (2008). % (doi: 10.1126/science.1158573), % for maximum likelihood: % P. Thibault and M. Guizar-Sicairos, Maximum-likelihood refinement for coherent diffractive imaging, New J. Phys. 14, 063004 (2012). % (doi: 10.1088/1367-2630/14/6/063004), % for mixed coherent modes: % P. Thibault and A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature 494, 68–71 (2013). (doi: 10.1038/nature11806), % and/or for multislice: % 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). % (doi: 10.1364/OE.24.029089). % 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 % 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. % 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 % 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 % 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: % © All rights reserved. PAUL SCHERRER INSTITUT, Switzerland, Laboratory for Macromolecules and Bioimaging, 2017. % 8. The LICENSE shall not be construed to confer any rights upon LICENSEE by implication or otherwise except as specifically set forth herein. % 9. DISCLAIMER: LICENSEE shall be aware that Phase Focus Limited of Sheffield, UK has an international portfolio of patents and pending applications which relate % 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, % in particular of patent with international application number PCT/GB2005/001464. The LICENSOR explicitly declares not to indemnify the users of the software % in case Phase Focus or any other third party will open a legal action against the LICENSEE due to the use of the program. % 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 % the courts of Zürich, Switzerland. function [ p, fdb ] = ML( p ) import utils.* global opt_time fdb.status = core.engine_status; core.errorplot; opt_time = 0; verbose(3, 'Starting non-linear optimization') if p.probe_mask_bool if p.probe_mask_use_auto verbose(3, 'Using a probe mask from probe autocorrelation.'); to_threshold = -real(auto); else verbose(3, 'Using a circular probe mask.'); [x,y] = meshgrid(-p.asize(2)/2:floor((p.asize(2)-1)/2),-p.asize(1)/2:floor((p.asize(1)-1)/2)); to_threshold = (x.^2 + y.^2); clear x y end to_threshold_flat = reshape(to_threshold, [prod(p.asize) 1]); [~, ind] = sort(to_threshold_flat); probe_mask_flat = zeros([prod(p.asize) 1]); probe_mask_flat(ind(1:ceil(p.probe_mask_area * prod(p.asize)))) = 1; p.probe_mask = reshape(probe_mask_flat, p.asize); clear to_threshold to_threshold_flat dummy ind probe_mask_flat else p.probe_mask = ones(p.asize); end % Taking care to pass some needed functions in p fnorm = sqrt(prod(p.asize)); % Arranging optimization vector xopt = []; % Optimization vector if p.opt_flags(1) == 1 for obnum = 1:p.numobjs xopt = [xopt; real(p.object{obnum}(:)); imag(p.object{obnum}(:))]; end end if p.opt_flags(2) == 1, xopt = [xopt; real(p.probes(:)); imag(p.probes(:))]; end xopt = single(xopt); % assumed by the MEX scripts p.fmag = single(p.fmag); % if flags(3) == 1, % xopt = [xopt;x;y]; % else % fixed.x = x; % fixed.y = y; % end if isempty(xopt), error('At least one element of flags must be 1'), end %%% Optimization error metric if isfield(p,'opt_errmetric'), switch lower(p.opt_errmetric) case 'l1' verbose(2, 'Using ML-L1 error metric'), case 'l2' verbose(2,'Using ML-L2 error metric'), case 'poisson' verbose(2,'Using ML-Poisson'), otherwise error([p.opt_errmetric ' is not defined']) return; end else p.opt_errmetric = 'poisson'; verbose(2, 'Using default Poisson error metric') end %%% Set specific variables needed for different metrics %%% switch lower(p.opt_errmetric) case 'poisson' fmag2 = p.fmag.^2; fmag2renorm = fmag2/p.renorm^2; initialerror = p.renorm^2*sum( p.fmask(:).*( (fmag2renorm(:)+0.5).*log(fmag2renorm(:)+1) ... - fmag2renorm(:) ... - 1 + 0.5*log(2*pi) + 1./(12*(fmag2renorm(:)+1)) ... - 1./(360*(fmag2renorm(:)+1).^3) + 1./(1260*(fmag2renorm(:)+1).^5) )) ... %% Approximation to log(n!) http://www.johndcook.com/blog/2010/08/16/how-to-compute-log-factorial/ + sum( fmag2(:)*log(renorm^2) ); clear fmag2renorm case 'l1' initialerror = 0; fmag2 = 0; case 'l2' initialerror = 0; fmag2 = p.fmag.^2; otherwise error(['Error metric ' p.opt_errmetric 'is not defined']) end %%% Regularization Npix = 0; if p. reg_mu > 0 for obnum = 1:p.numobjs Npix = Npix + p.object_size(obnum,1)*p.object_size(obnum,2); end Nm = prod(p.asize)*size(p.fmag,3); K = 8*Npix^2/(Nm*p.Nphot); creg = p.renorm^2*p.reg_mu/K; else creg = 0; end %%% Sieves preconditioning if any(p.smooth_gradient) ~= 0 if length(p.smooth_gradient) <= 1 % Hanning regularization auxi = fract_hanning_pad(512,512,0); auxi = fftshift(ifft2(auxi)); smooth_gradient = real(auxi(256:258,256:258)); % Regularization kernel ( = 0 to omit) end else smooth_gradient = 0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Main optimization loop %%% opt_time = tic; [tmp,p] = engines.ML.cgmin1('engines.ML.gradient_ptycho',xopt,p.opt_iter,p.opt_ftol,p.opt_xtol,p,fmag2,initialerror,fnorm,... creg, smooth_gradient); % ob and probes are passed to use as fixed variables when p.opt_flags is zero opt_time = toc(opt_time); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Arrange solution vector %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if p.opt_flags(1) == 1, for obnum = 1:p.numobjs objectelements = [p.object_size(obnum,1) p.object_size(obnum,2) p.object_modes]; p.object{obnum} = reshape(tmp(1:prod(objectelements)), objectelements) + ... 1i*reshape(tmp(prod(objectelements)+1:2*prod(objectelements)), objectelements); tmp = tmp(2*prod(objectelements)+1:end); end end if p.opt_flags(2) == 1, probeelements = [p.asize p.numprobs p.probe_modes]; p.probes = reshape(tmp(1:prod(probeelements)),probeelements) + ... 1i*reshape(tmp(prod(probeelements)+1:2*prod(probeelements)),probeelements); tmp = tmp(2*prod(probeelements)+1:end); end % if flags(3) == 1, % x = tmp(1:params.n); % y = tmp(params.n+1:2*params.n); % end if ~isempty(tmp) warning('Temporary vector is not empty, optimized values not assigned'); end verbose(3, 'Finished'); verbose(3, 'Time elapsed in optimization refinement: %f seconds', opt_time); %%%%%%%%%%%%%%%%% %%% Last plot %%% %%%%%%%%%%%%%%%%% if p.use_display||p.save.store_images p.plot.extratitlestring = sprintf(' (%dx%d) - ML', p.asize(2), p.asize(1)); core.analysis.plot_results(p, 'use_display', p.use_display); end core.errorplot; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% end optimization refinement %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%