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2026-09-17 23:59:11 +09:00 · 2026-08-07 15:56:42 +09:00
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+% GET_PHASE_GRADIENT_1D get 1D gradient of phase of an image stack. 
+% Accept either complex image or just phase 
+%
+% [d_img] = get_phase_gradient_1D(img, ax=2, step=0)
+%
+% Inputs
+%     **img     - stack of complex valued input images 
+% *optional*
+%     **ax      - axis of derivative, default = 2
+%     **step    - step used to calculate the central difference, default=0 (analytic expression)
+%
+% *returns*
+%     ++d_img - phase gradient array
+    
+
+
+
+%*-----------------------------------------------------------------------*
+%|                                                                       |
+%|  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 
+%    proper use and the correctness of the results.
+
+function d_img = get_phase_gradient_1D(img, ax, step, shift)
+
+    import utils.*
+    import math.*
+
+    if isreal(img)
+        img = exp(1i*img);
+    end
+    if nargin < 2
+        ax = 2; 
+    end
+    if nargin < 3
+        step = 0.5;  % step of the difference (too small will amplify noise)
+    end
+    if nargin < 4
+        shift = 0;  % perform shift and gradient calculation in single step 
+    end
+    assert(step >= 0, 'Difference step has to be > 0')
+    
+    % suppress edge issues if phase ramp is not subtracted / there is no
+    % air around sample 
+    
+    pad_distance = 8; 
+    img = padarray(img,circshift([pad_distance,0,0], ax-1),'symmetric','both'); 
+    img = smooth_edges(img, pad_distance, ax);
+
+    if step == 0
+        % analytic formula (sensitive to noise) but faster 
+        img = img ./ (abs(img) + eps); 
+        d_img = get_img_grad(img, ax);  % img is assumed to be complex 
+        d_img = imag(conj(img).*d_img);
+    else
+        d_img = angle( imshift_fft_ax(img,-step+shift,ax) .* conj( imshift_fft_ax(img,step+shift,ax)))/(2*step);
+    end
+    % remove padding 
+    ind = circshift({pad_distance:size(d_img,ax)-pad_distance-1,':', ':'},ax-1);
+    d_img = d_img(ind{:}); 
+    
+
+end