% GET_IMG_INT_2D use FFT2 to integate the image along both axis -> can be used for phase
% unwrapping
%
%   integral = get_img_int_2D(dX,dY)
%
% Inputs:
%   **dX   - horizontal phase gradient
%   **dY   - vertical phase gradient
% *returns*
%   ++integral - 2D stack scalar rotation-free arrays that has vertical and horizontal gradients close to dX, dY


%*-----------------------------------------------------------------------*
%|                                                                       |
%|  Except where otherwise noted, this work is licensed under a          |
%|  Creative Commons Attribution-NonCommercial-ShareAlike 4.0            |
%|  International (CC BY-NC-SA 4.0) license.                             |
%|                                                                       |
%|  Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch)    |
%|                                                                       |
%|       Author: CXS group, PSI                                          |
%*-----------------------------------------------------------------------*
% You may use this code with the following provisions:
%
% If the code is fully or partially redistributed, or rewritten in another
%   computing language this notice should be included in the redistribution.
%
% If this code, or subfunctions or parts of it, is used for research in a 
%   publication or if it is fully or partially rewritten for another 
%   computing language the authors and institution should be acknowledged 
%   in written form in the publication: “Data processing was carried out 
%   using the “cSAXS matlab package” developed by the CXS group,
%   Paul Scherrer Institut, Switzerland.” 
%   Variations on the latter text can be incorporated upon discussion with 
%   the CXS group if needed to more specifically reflect the use of the package 
%   for the published work.
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% A publication that focuses on describing features, or parameters, that
%    are already existing in the code should be first discussed with the
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% This code and subroutines are part of a continuous development, they 
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% 

function integral = get_img_int_2D(dX,dY)
    
    Np = size(dX);

    fD = math.fft2_partial(dX + 1i*dY);

    xgrid = ifftshift(-fix(Np(2)/2):ceil(Np(2)/2)-1)/Np(2);
    ygrid = ifftshift(-fix(Np(1)/2):ceil(Np(1)/2)-1)/Np(1);

    % not sure why, but it seems to need also shift by 1 pixels to make it
    % consistent with gradient 
    X = exp((2i*pi)*(xgrid+ygrid'));
    
    % apply integration filter 
    X =  X./ (2i*pi*(xgrid+1i*ygrid'));
    X(1,1) = 0;
    integral = bsxfun(@times, fD,X);

    integral = math.ifft2_partial(integral);

end