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97 lines
4.2 KiB
Matlab
97 lines
4.2 KiB
Matlab
% PROP_FREE_NF Near field propagation
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%
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% wout = prop_free_nf(win, lambda, z, pixsize) returns the propagated wavefield
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% WIN by a distance Z, using wavelength LAMBDA. PIXSIZE is the dimension
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% of one pixel.
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%
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% wout = prop_free_nf(win, lambda, z) is the same as above, assuming PIXSIZE=1
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% (that is, Z and LAMBDA are expressed in pixel units).
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%
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% [~,H] = prop_free_nf(win, lambda, z, pixsize) Does not compute propagation only
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% computes and returns H, the Fourier domain propagation function
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%*-----------------------------------------------------------------------*
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%| |
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%| Except where otherwise noted, this work is licensed under a |
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%| Creative Commons Attribution-NonCommercial-ShareAlike 4.0 |
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%| International (CC BY-NC-SA 4.0) license. |
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%| |
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%| Copyright (c) 2017 by Paul Scherrer Institute (http://www.psi.ch) |
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%| |
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%| Author: CXS group, PSI |
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%*-----------------------------------------------------------------------*
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% You may use this code with the following provisions:
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%
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% If the code is fully or partially redistributed, or rewritten in another
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% computing language this notice should be included in the redistribution.
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%
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% If this code, or subfunctions or parts of it, is used for research in a
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% publication or if it is fully or partially rewritten for another
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% computing language the authors and institution should be acknowledged
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% in written form in the publication: “Data processing was carried out
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% using the “cSAXS matlab package” developed by the CXS group,
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% Paul Scherrer Institut, Switzerland.”
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% Variations on the latter text can be incorporated upon discussion with
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% the CXS group if needed to more specifically reflect the use of the package
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% for the published work.
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%
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% A publication that focuses on describing features, or parameters, that
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% are already existing in the code should be first discussed with the
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% authors.
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%
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% This code and subroutines are part of a continuous development, they
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% are provided “as they are” without guarantees or liability on part
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% of PSI or the authors. It is the user responsibility to ensure its
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% proper use and the correctness of the results.
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function [wout, H] = prop_free_nf(win, lambda, z, dx)
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if ndims(win) < 2
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error('Input wavefield should be at least 2-dimensional array!')
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end
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sz = size(win);
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if all(z==0)
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wout = win;
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H = ones(sz(1),sz(2),'like',win);
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return
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end
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if nargin < 4
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dx = [1. 1.];
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end
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% Evaluate if aliasing could be a problem
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if any(sqrt(sum(1./dx.^2) * sum(1./(sz(1:2).*dx).^2)) * abs(z) * lambda > 1)
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utils.verbose(0,'Warning: there could be some aliasing issues...');
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utils.verbose(0,'(you could enlarge your array, or try a far field method)');
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end
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type = ones(1,'like',win);
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xgrid = type*[-sz(1)/2:floor((sz(1)-1)/2)]/sz(1)*lambda/dx(1);
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ygrid = type*[-sz(2)/2:floor((sz(2)-1)/2)]/sz(2)*lambda/dx(min(end,2));
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[x1,x2] = ndgrid(xgrid, ygrid);
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q2 = math.fftshift_2D(x1.^2 + x2.^2); % prevents numerical errors by keeping q2 unitless
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z = reshape(z,1,1, []); % if more than one "z" is used, propagate each layer differenly
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if isa(win,'double')
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H = exp(2i * pi * (z / lambda) .* (sqrt(1 - q2) - 1));
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else
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% for single precision use approximation to avoid numerical issues,
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% precise with relative error less than 1e-7 for common use
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H = exp((2i * pi * (z / lambda)) .* (-q2/2));
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end
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if nargout < 2
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wout = ifft2(fft2(win) .* H );
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else
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wout = []; % do not calculate the wout and return only H factor
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end
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end
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