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%DM Difference-Map algorithm
%
% Publications most relevant to the Difference-Map implementation
% + P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer,
% "High-Resolution Scanning X-ray Diffraction Microscopy," Science 321, 379-382 (2008)
% + P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer,
% "Probe retrieval in ptychographic coherent diffractive imaging,"
% Ultramicroscopy 109, 338343 (2009)
% 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
% LICENSEEs 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, 379382 (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, 6871 (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, 2908929108 (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 ] = DM( p )
import math.*
import utils.verbose
import utils.pshift
global proj1_time objproj_time probeproj_time elsewheretime proj2_time plot_time
fdb.status = core.engine_status;
% mex or matlab - object_update / probe_update / Fourier_loop
if ~isfield(p, 'use_mex')
p.use_mex = zeros(1,3);
elseif numel(p.use_mex) == 1
if any(p.use_mex)
verbose(3, 'Using mex files for DM.')
end
p.use_mex = repmat(p.use_mex,1,3);
end
% Starting iterate
% iter is a large array and is only needed for Matlab Difference map
iter = cell(p.numscans,1);
fmag = cell(p.numscans,1);
for ii = 1:p.numscans
iter{ii} = complex(zeros([p.asize, length(p.scanidxs{ii}), p.probe_modes, p.object_modes]));
fmag{ii} = double(p.fmag(:,:,p.scanidxs{ii})); % can cause memory duplication if it was not double, migrate to single in future !!!
end
if p.object_modes == 1 && p.numprobs == 1
obj_proj = complex(zeros([p.asize, length(p.scanidxs{1})]));
end
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
p.probe_mask = to_threshold < quantile(to_threshold(:), p.probe_mask_area );
else
p.probe_mask = 1;
end
% check what is the actual size of the object
for i = 1:p.numobjs
p.object_size(i,:) = size(p.object{i});
ob{i} = double(p.object{i});
end
% move to doubles (not needed)
p.probes = double(p.probes);
p.fmag = double(p.fmag);
for obnum = 1:p.numobjs
avob{obnum} = zeros([p.object_size(obnum,:) p.object_modes]);
end
% get views from probes and objects
for ii = 1:p.numscans
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
if p.object_modes == 1 && p.numprobs == 1
% faster version without extra memory allocation
obj_proj = core.get_projections(p, ob{obnum}, ii,obj_proj);
iter{ii} = bsxfun(@times, p.probes, obj_proj);
else
% general version
for obmode = 1:p.object_modes
obj_proj = core.get_projections(p, ob{obnum}(:,:,obmode), ii);
iter{ii}(:,:,:,:,obmode) = bsxfun(@times, p.probes(:,:,prnum,:), obj_proj);
end
end
end
% A power bound (relaxed Fourier) that scales with number of photons per diffraction pattern
p.power_bound = p.count_bound*p.renorm^2;
% Set indices for user supplied flat mask p.object_flat_region
if ~isempty(p.object_flat_region)
p.userflatregion = true;
if (p.numscans>1)&&(~p.share_object)
error('Object flat region not yet implemented for multiple objects. Set object_flat_region = []')
end
if any(p.object_size ~= size(p.object_flat_region))
error('Mask p.object_flat_region does not match size of object');
else
p.userflatind = (p.object_flat_region == 1);% Find indices of flat region
end
else
p.userflatregion = false;
end
for obnum = 1:p.numobjs
avob{obnum} = zeros([p.object_size(obnum,:) p.object_modes]);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Main Difference map loop %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% A power bound (relaxed Fourier) that scales with number of photons per diffraction pattern
p.power_bound = p.count_bound*p.renorm^2;
% Prepare statistics
proj1_time = 0;
proj2_time = 0;
plot_time = 0;
objproj_time = 0;
probeproj_time = 0;
elsewheretime = 0;
cfact_temp = p.probe_regularization *p.numpts;
if p.share_probe
cfact = zeros(1,p.numprobs);
for ii=1:p.numscans
cfact(p.share_probe_ID(ii)) = cfact(p.share_probe_ID(ii)) + cfact_temp(ii);
end
else
cfact = cfact_temp;
end
err = 0;
rfact = 0;
numav = 0;
for it=1:p.number_iterations
verbose(2, 'Iteration # %d of %d',it, p.number_iterations);
% 1. Overlap projection - a large loop where probe and object are refined.
verbose(3, ' - projection 1: overlap constraint - ');
proj1tic = tic;
% Check once each iteration to see whether the named file exists,
% signalling a user break.
fid = fopen(p.io.break_check_name);
if (fid ~= -1)
fprintf('The file %s exists.',p.io.break_check_name);
fprintf('It will be deleted now and then the program terminates.\n');
delete(p.io.break_check_name);
sprintf('Terminating program upon user request.\n');
break
end
% The simple iterative scheme
prch0 = 0;
breakprobeloop = 0;
for inner=1:10
if ~breakprobeloop
cprobes = conj(p.probes);
for obnum = 1:p.numobjs
pr_nrm{obnum} = 1e-8 * ones(p.object_size(obnum,:));
% % This could be zero, but better make it a very small number instead to avoid eventual divisions by 0.
ob{obnum} = 1e-8*(1+1i)*ones([p.object_size(obnum,:) p.object_modes]);
%pr_nrm{obnum} = 1e-0*ob{obnum};
% This could be zero, but better make it a very small number instead to avoid eventual divisions by 0.
%ob{obnum} = 1e-0*ob{obnum};
end
for ii = 1:p.numscans
objtic = tic;
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
% Decide which matlab code to use
if (p.probe_modes == 1)&&(p.object_modes == 1)&&p.use_mex(1)
% Mex code object loop
engines.DM.object_update_norm(iter{ii},...
cprobes(:,:,prnum),ob{obnum},pr_nrm{obnum},int32(p.positions(p.scanidxs{ii},:)),...
int32(p.numpts(ii)));
else
% Pure matlab version
if p.object_modes == 1 && p.numprobs == 1
% faster version without memory allocation
cprobe = cprobes;
obj_update = sum(bsxfun(@times, cprobe, iter{ii}),4);
ob{obnum} = core.set_projections(p, ob{obnum}, obj_update , ii);
else
cprobe = cprobes(:,:,prnum,:);
for obmode = 1:p.object_modes
obj_update = sum(bsxfun(@times, cprobe, iter{ii}(:,:,:,:,obmode)),4);
ob{obnum}(:,:,obmode) = core.set_projections(p, ob{obnum}(:,:,obmode), obj_update , ii);
end
end
pr_nrm{obnum} = core.set_projections(p, pr_nrm{obnum}, sum(abs(cprobe).^2,4) , ii);
end
objproj_time = objproj_time + toc(objtic);
end
for obnum = 1:p.numobjs
ob{obnum} = bsxfun(@rdivide, ob{obnum}, pr_nrm{obnum});
if p.userflatregion % Not supported with modes
ob{obnum}(userflatind) = mean(ob{obnum}(userflatind));
end
elsewheretic = tic;
if p.clip_object
aob = abs(ob{obnum});
too_high = (aob > p.clip_max);
too_low = (aob < p.clip_min);
ob{obnum} = (1-too_high).*(1-too_low).*ob{obnum} + (too_high.*p.clip_max + too_low*p.clip_min).*ob{obnum}./aob;
end
elsewheretime = elsewheretime + toc(elsewheretic);
end
if p.probe_change_start >= it
breakprobeloop = 1;
else
% Defining the new probes (regularization)
nprobes = bsxfun(@times,p.probes, reshape(cfact,1,1,[]));
pr_denoms = bsxfun(@times,ones(p.asize), reshape(cfact,1,1,[]));
for ii = 1:p.numscans
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
probetic = tic;
nprobe = nprobes(:,:,prnum,:); % Current scan probe, third index is modes
pr_denom = pr_denoms(:,:,prnum); % Current scan denominator, no mode index
% Decide which code to use
if (p.probe_modes == 1)&&(p.object_modes == 1)&&p.use_mex(2)
% Mex code
engines.DM.probe_update_norm(iter{ii},...
squeeze(nprobe),ob{obnum},pr_denom,...
int32(p.positions(p.scanidxs{ii},:)),int32(p.numpts(ii)));
else
% Pure matlab code
if p.object_modes == 1 && p.numprobs == 1
% faster version without memory allocation
obj_proj = core.get_projections(p, ob{obnum}, ii, obj_proj);
nprobe = nprobe + sum(bsxfun(@times,iter{ii}, conj(obj_proj)), 3);% sum over positions
pr_denom = pr_denom + sum(abs(obj_proj).^2,3);% sum over positions
else
for obmode = 1:p.object_modes
obj_proj = core.get_projections(p, ob{obnum}(:,:,obmode), ii);
nprobe = nprobe + sum(bsxfun(@times,iter{ii}(:,:,:,:,obmode), conj(obj_proj)),3); % sum over positions
pr_denom = pr_denom + sum(abs(obj_proj).^2,3); % sum over positions
end
end
end
probeproj_time = probeproj_time + toc(probetic);
nprobes(:,:,prnum,:) = nprobe;
pr_denoms(:,:,prnum) = pr_denom;
end
probe_new = bsxfun(@rdivide, nprobes, pr_denoms);
probe_new = bsxfun(@times, p.probe_mask , probe_new);
% get relative residuum
prch = squeeze(sqrt(sum(sum(sum(abs(p.probes - probe_new).^2,1),2),4) ./ sum(sum(sum(abs(p.probes).^2,1),2),4)));
for prnum = 1:p.numprobs
verbose(3, 'Change in probe %d: %3.2g%%',prnum,prch(prnum)*100);
end
p.probes = probe_new;
if all(prch < 0.01)
breakprobeloop = 1;
end
end
end
end
proj1_time = proj1_time + toc(proj1tic);
er2 = 0;
% 2. Fourier projection + complete difmap loop
verbose(3, ' - projection 2: Fourier modulus constraint - ');
% perform normalization of probe (avoid probe - object scaling ambiguity)
if (it < p.average_start && p.remove_scaling_ambiguity)
pnorm = math.norm2(p.probes);
if length(unique(p.share_probe_ID)) == p.numscans && ...
length(unique(p.share_object_ID)) == p.numscans
p.probes = p.probes ./ pnorm;
for ii = 1:p.numscans
ob{ii} = ob{ii} .* pnorm(ii);
end
else
pnorm = mean(pnorm);
p.probes = p.probes / pnorm;
for ii = 1:p.numscans
ob{ii} = ob{ii} * pnorm;
end
end
end
tic;
if (p.probe_modes == 1)&&(p.object_modes == 1)&&p.use_mex(3)
for ii = 1:p.numscans
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
p1 = zeros(p.asize)+eps*(1+1i);
p2 = zeros(p.asize)+eps*(1+1i);
f = zeros(p.asize)+eps*(1+1i);
ph = zeros(p.asize)+eps*(1+1i);
df = zeros(p.asize)+eps*(1+1i);
af = zeros(p.asize);
fdev = zeros(p.asize);
fdev2 = zeros(p.asize);
fmaski = zeros(p.asize);
rf = 0;
rf_nrm = 0;
fmask_per_scan = ndims(p.fmask) == 3;
% Mex code
% Fourier_DM_loop_par2(iter,probe,ob{obnum},p1,p2,f,ph,df,double(fmask),fmag,double(p.power_bound),er2,rf,rf_nrm,af, fdev, fdev2, fmaski,int32(positions),int32(sum(p.numpts)),int32(fmask_per_scan),int32(compute_rfact));
engines.DM.Fourier_DM_loop_par2(iter{ii},...
(p.probes(:,:,prnum)),(ob{obnum}),p1,p2,f,ph,df,...
double(p.fmask(:,:,p.scanidxs{ii})),...
fmag{ii},double(p.power_bound),...
er2,rf,rf_nrm,af, fdev, fdev2, fmaski,int32(p.positions(p.scanidxs{ii},:)),...
int32(p.numpts(ii)),int32(fmask_per_scan),int32(p.compute_rfact));
% What the Mex function does:
% fnorm = sqrt(a2);
% rf = 0;
% rf_nrm = 0;
% if ~p.fmask_per_scan
% fmaski = fmask;
% end
% for jj=p.scanidxs{ii}
% if fmask_per_scan
% fmaski = fmask(:,:,jj);
% end
% Indy = p.positions(jj,1) + (1:p.asize(1));
% Indx = p.positions(jj,2) + (1:p.asize(2));
% p1 = p.probes(:,:,prnum) .* ob{obnum}(Indy, Indx);
%
% f = fft2( 2*p1 - iter(:,:,jj) )/fnorm;
% af = abs(f);
% ph = f ./ (af+1e-10);
% fdev = af - fmag(:,:,jj);
% fdev2 = fmaski.*fdev.^2;
% power = sum(sum(fdev2))/a2;
% if power > p.power_bound
% renorm = sqrt(p.power_bound / power);
% af = af.*(1-fmaski) + fmaski.*(fmag(:,:,jj) + fdev * renorm);
% end
% p2 = fnorm*ifft2(af .* ph);
%
% df = p2 - p1;
% iter(:,:,jj) = iter(:,:,jj) + df;
%
% er2 = er2 + sum(sum(abs(df).^2));
%
% if p.compute_rfact
% rf = rf + sum(sum(abs(abs(fft2(p1))/fnorm - fmag(:,:,jj))));
% rf_nrm = rf_nrm + sum(sum(fmag(:,:,jj)));
% end
% end
end
else
% Pure Matlab version
% verbose(2,'Matlab Fourier loop')
% The solution seems equivalent down to the displayable
% digits, but when starting optimization the error metric
% of the current guess is slightly different
for ii = 1:p.numscans
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
fnorm = sqrt(prod(p.asize));
rf = 0;
rf_nrm = 0;
p1 = zeros([p.asize,length(p.scanidxs{ii}),p.probe_modes,p.object_modes]);
if p.object_modes == 1 && p.numprobs == 1
% faster version without memory allocation
obj_proj = core.get_projections(p, ob{obnum}, ii,obj_proj);
p1 = bsxfun(@times,p.probes,obj_proj);
else
for obmode = 1:p.object_modes
obj_proj = core.get_projections(p, ob{obnum}(:,:,obmode), ii);
p1(:,:,:,:,obmode) = bsxfun(@times,p.probes(:,:,prnum,:),obj_proj);
end
end
f = fft2( 2*p1 - iter{ii} )/fnorm;
af = abs(f); % Amplitude of f before projection
ph = f ./ (af+1e-3);
fmag_target = bsxfun(@times, af, fmag{ii}./sqrt(sum(af.^2,4)));
fdev = af - fmag_target;
if size(p.fmask,3)==p.numpos
fmaski = p.fmask(:,:,p.scanidxs{ii});
else
fmaski = p.fmask;
end
af = bsxfun(@times, af, 1-fmaski) + bsxfun(@times, fmaski, fmag_target + fdev * p.pfft_relaxation);
p2 = fnorm*ifft2(af .* ph);
clear ph af
df = p2 - p1;
clear p1 p2
iter{ii} = iter{ii} + df;
er2 = sum2(squeeze(sum2(abs(df).^2))); % faster than (:)
clear df
end
end
if p.center_probe
% Find probe centroid
for ii = 1:p.numscans
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
Iprobe = abs(p.probes(:,:,prnum,:)).^2;
[probe_c2, probe_c1]=center(Iprobe);
% shift all arrays accordingly
if (probe_c1 ~= 1) || (probe_c2 ~= 1)
verbose(3,'Shifting all arrays by (%d, %d)', probe_c1,probe_c2);
p.probes(:,:,prnum) = pshift(p.probes(:,:,prnum,:),[probe_c1 probe_c2]);
ob{obnum} = pshift(ob{obnum},[probe_c1 probe_c2]);
avob{obnum} = pshift(avob{obnum},[probe_c1 probe_c2]);
for i=p.scanidxs{ii}
iter(:,:,i,:) = pshift(iter(:,:,i,:), [probe_c1 probe_c2]);
end
end
end
end
proj2_time = proj2_time + toc();
err(it) = 2*sqrt(er2/(prod(p.asize)*sum(p.numpts)));
if p.compute_rfact
rfact(it) = rf/rf_nrm;
verbose(3, 'Error: %12.3f \t R-factor: %12.3f %%',err(it),100*rfact(it));
else
verbose(3,'Error: %12.3f',err(it));
end
if (it >= p.average_start) && mod(it, p.average_interval)==0
for obnum = 1:p.numobjs
avob{obnum} = avob{obnum} + ob{obnum};
end
numav = numav + 1;
end
p.error_metric.iteration = 1:it ;
p.error_metric.value = err(1:it);
p.error_metric.err_metric = 'RMS';
p.error_metric.method = p.name;
p.object = ob;
tic;
if (round(mod(it,p.plot.interval))==0)||(it==1) && p.use_display
p.plot.extratitlestring = sprintf(' (%dx%d) - iter %d', p.asize(2), p.asize(1), it);
core.analysis.plot_results(p);
end
plot_time = plot_time + toc();
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% end main difference map loop %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
verbose(3, 'Finished difference map');
verbose(3, 'Time elapsed in projection 1: %f seconds', proj1_time);
verbose(3, ' in object projection: %f seconds', objproj_time);
verbose(3, ' in probe projection: %f seconds', probeproj_time);
verbose(3, 'Time elapsed in projection 2: %f seconds', proj2_time);
verbose(3, 'Time spent plotting: %f seconds', plot_time);
% Average
for obnum = 1:p.numobjs
if numav > 0
avob{obnum} = avob{obnum}/ numav;
else
avob{obnum} = ob{obnum};
end
end
% R-factor
av_rfact = 0;
av_rfact_nrm = 0;
for ii = 1:p.numscans
prnum = p.share_probe_ID(ii);
obnum = p.share_object_ID(ii);
for i=p.scanidxs{ii}
Indy = round(p.positions(i,1)) + (1:p.asize(1));
Indx = round(p.positions(i,2)) + (1:p.asize(2));
fcalc = abs(fftn(avob{obnum}(Indy,Indx).*p.probes(:,:,prnum)))/sqrt(prod(p.asize));
av_rfact = av_rfact + sum(sum(abs(fcalc - p.fmag(:,:,i))));
av_rfact_nrm = av_rfact_nrm + sum(sum(p.fmag(:,:,i)));
end
end
av_rfact = av_rfact / av_rfact_nrm;
p.object = avob;
% save additional feedback into engine's fdb variable
fdb.rfact = rfact;
fdb.av_rfact = av_rfact;
end