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%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").
%
% Terms and Conditions of the LICENSE
% 1. LICENSOR grants to LICENSEE a royalty-free, non-exclusive license to use the PROGRAM for academic, non-commercial purposes, upon the terms and conditions
% hereinafter set out and until termination of this license as set forth below.
% 2. LICENSEE acknowledges that the PROGRAM is a research tool still in the development stage. The PROGRAM is provided without any related services, improvements
% or warranties from LICENSOR and that the LICENSE is entered into in order to enable others to utilize the PROGRAM in their academic activities. It is the
% LICENSEEs responsibility to ensure its proper use and the correctness of the results.
% 3. THE PROGRAM IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR
% A PARTICULAR PURPOSE AND NONINFRINGEMENT OF ANY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS. IN NO EVENT SHALL THE LICENSOR, THE AUTHORS OR THE COPYRIGHT
% HOLDERS BE LIABLE FOR ANY CLAIM, DIRECT, INDIRECT OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY ARISING FROM, OUT OF OR IN CONNECTION WITH THE PROGRAM OR THE USE
% OF THE PROGRAM OR OTHER DEALINGS IN THE PROGRAM.
% 4. LICENSEE agrees that it will use the PROGRAM and any modifications, improvements, or derivatives of PROGRAM that LICENSEE may create (collectively,
% "IMPROVEMENTS") solely for academic, non-commercial purposes and that any copy of PROGRAM or derivatives thereof shall be distributed only under the same
% license as PROGRAM. The terms "academic, non-commercial", as used in this Agreement, mean academic or other scholarly research which (a) is not undertaken for
% profit, or (b) is not intended to produce works, services, or data for commercial use, or (c) is neither conducted, nor funded, by a person or an entity engaged
% in the commercial use, application or exploitation of works similar to the PROGRAM.
% 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, 379382 (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, 6871 (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, 2908929108 (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
% names of any of its employees or laboratories, in any advertising, promotional or sales material without prior written consent obtained from LICENSOR in each case.
% 7. Ownership of all rights, including copyright in the PROGRAM and in any material associated therewith, shall at all times remain with LICENSOR, and LICENSEE
% agrees to preserve same. LICENSEE agrees not to use any portion of the PROGRAM or of any IMPROVEMENTS in any machine-readable form outside the PROGRAM, nor to
% 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.
% 8. The LICENSE shall not be construed to confer any rights upon LICENSEE by implication or otherwise except as specifically set forth herein.
% 9. DISCLAIMER: LICENSEE shall be aware that Phase Focus Limited of Sheffield, UK has an international portfolio of patents and pending applications which relate
% 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
% in case Phase Focus or any other third party will open a legal action against the LICENSEE due to the use of the program.
% 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
% the courts of Zürich, Switzerland.
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