%FWD_PROJ get complex projections for multilayer ptychography from the provided 3D volume generate 
%
% projData = fwd_proj(volData,  theta,Nlayers, type)
% 
%  Inputs: 
%   **volData      - 3D array, linearized tomographic volume (ie tranmission == exp(sum(volData,1)) == prod(exp(volData))  )
%   **theta        - scalar, angle of the provided projection  
%   **Nlayers      - int, number of layers to split the projected volume 
%   **type         - either @real or @imag, each part is processed separatelly to avoid mixing during iterpolation in the rotation 
%  *returns*
%   ++projData     - multilayer object for ptychography 


% 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 PtychoShelves 
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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 
%       another computing language:
%       "Data processing was carried out using the PtychoShelves 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 
% 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 
% high-level framework for high-performance analysis of ptychographic data, J. Appl. Cryst. 53(2) (2020). (doi: 10.1107/S1600576720001776)
% and 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 LSQ-ML:
% M. Odstrčil, A. Menzel, and M. Guizar-Sicairos, Iterative least-squares solver for generalized maximum-likelihood ptychography, Opt. Express 26(3), 3108 (2018). 
%   (doi: 10.1364/OE.26.003108),
% 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),
% and/or for OPRP:
% 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. 
% Opt. Express 24.8 (8360-8369) 2016. (doi: 10.1364/OE.24.008360).
% 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.
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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 
%       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 projData = fwd_proj(volData,  theta,Nlayers, type)
    import utils.crop_pad 
   
    
    % pick real or imaginary 
    fun = str2func(type); 
    volData = fun(volData); 
    
     if ~isreal(volData)
         error('Process real and imaginary part separatelly')
     end
    
    % rotate volume to the given angle
    projData = utils.imrotate_ax(volData,  theta, 3, 0, 'bicubic');

    
    Nw = size(projData,2); 
   
    
    % permute to see it from the beam direction 
    if Nlayers == 1
        % fast option for single layer 
        projData = mean(projData,2)*Nw/Nlayers;
    else
        % slower option for multilayer 
       
        
        %% periodic boundary interpolate real and imaginary part separatelly 
        % first decimate the data quickly by binning 
        binning = ceil(Nw/Nlayers/4); 
        projData = utils.binning_2D(projData, [1, binning]);    % in order to reduce computational requirements, use a combination of interpolation FFT and simple and fast upsampling
        Nw = size(projData,2); 
        % now do more precise downsampling by centered FFT interpolation 
        
        %% %%% centered FFT interpolation %%%

        % pre-fft tranform 
        projData = fft(projData,[], 2);
        % interpolate + 0.5 px shift 
        projData = utils.interpolateFT_ax(projData,Nlayers,2, false);
        projData = utils.imshift_fft_ax(projData,-0.5,2, false); 
        % post-ifft transform
        projData = real(ifft(projData,[], 2));
        projData = projData * (binning*Nw/Nlayers);

        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        
    end
    
    
    % permute the axis so the the projection is seen along the beam 
    projData = permute(projData, [3,1,2]);
 

end