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+math/get_img_int_2D.m

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+% 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.
+%
+% A publication that focuses on describing features, or parameters, that
+%    are already existing in the code should be first discussed with the
+%    authors.
+%   
+% This code and subroutines are part of a continuous development, they 
+%    are provided “as they are” without guarantees or liability on part
+%    of PSI or the authors. It is the user responsibility to ensure its 
+% 
+
+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
+