%HERMITE_LIKE
% Receives a probe and maximum x and y order M N. Based on the given probe
% and multiplying by a Hermitian function new modes are computed. The modes
% are then orthonormalized.
%

% 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 cSAXS 
%   ptychography MATLAB package computer software program and associated documentation furnished hereunder (hereafter "PROGRAM").
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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 cSAXS ptychography MATLAB 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 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 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).
% 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 
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%       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. 
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%       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 
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% 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 
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function H = hermite_like(fundam,X,Y,M,N)
import plotting.c2image

% corresponding to this. Returns all 

m = [0:M];
n = [0:N];

% fundam = abs(probe);

cenx = sum(sum(X.*abs(fundam).^2))/sum(sum(abs(fundam).^2));
ceny = sum(sum(Y.*abs(fundam).^2))/sum(sum(abs(fundam).^2));
varx = sum(sum((X-cenx).^2.*abs(fundam).^2))/sum(sum(abs(fundam).^2));
vary = sum(sum((Y-ceny).^2.*abs(fundam).^2))/sum(sum(abs(fundam).^2));

counter = 1;

% Create basis
for nii = n
    for mii = m
        auxfunc = ((X-cenx).^mii).*((Y-ceny).^nii).*fundam;
        if counter == 1
            auxfunc = auxfunc/sqrt(sum(abs(auxfunc(:)).^2));
        else
            auxfunc = auxfunc.*exp(-((X-cenx).^2/(2*varx))-((Y-ceny).^2/(2*vary)));
            auxfunc = auxfunc/sqrt(sum(abs(auxfunc(:)).^2));
        end
        
        % Now make it orthogonal to the previous ones
        for ii = 1:counter-1 % The other ones
            auxfunc = auxfunc - H(:,:,ii)*sum(sum(H(:,:,ii).*conj(auxfunc),1),2);
        end
        auxfunc = auxfunc/sqrt(sum(abs(auxfunc(:)).^2));
        H(:,:,counter) = auxfunc;
        index(counter,:) = [mii nii];
        
%         figure(1)
%         subplot(3,3,counter)
%         imagesc(c2image(H(:,:,counter)));
%         title(num2str(index(counter,:)))
%         axis xy equal tight
        
        counter = counter+1;
    end
end

% hermite_gauss - Recieves X, Y and gaussian waist (w) and computes the 
% Hermite Gauss beam
end