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TestBench_Microlith_DIC.m
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%% Image of MBL/NNF Siemens target under differential interference contrast.
% This script simulates image of the Siemens test object from the MBL-NNF
% phase target for differential interference contrast (DIC) imaging.
% We simulate a small region 7umx7um near the center so that the
% computation can be carried out in reasonable time.
%
% Images for two models of DIC (as designed by Smith and Nomarski that uses
% prisms on both condenser and objective side) are compared.
% The diffraction model proposed in 1999 by Preza[1] failed to account for
% the coherence effects of the condenser-side prism and therefore predicts
% poor DIC contrast when imaging is done with large condenser aperture,
% which is actually the experimental advantage of DIC over other phase microscopy
% methods.
%
% Our model [2] correctly accounts for the coherence effects and predicts
% a contrast that matched well with experimental images.
%
% [1] C. Preza, D. L. Snyder, and J.-A. Conchello, “Theoretical development
% and experimental evaluation of imaging models for differential
% interference contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199
% (1999).
%
% [2] S. B. Mehta and C. J. R. Sheppard, “Partially coherent image
% formation in differential interference contrast (DIC) microscope,” Opt.
% Express 16, 19462–19479(2008).
%
% We also simulate an image assuming a PlasDIC system as designed by Zeiss
% that uses a slit on the illumination side and a prism on the objective
% side.
clear all;
%% Set parameters of the target.
% Following numbers are from Fig 8.2 of the book chapter on MBL/NNF
% target.
Rout=75/2;% Outer radius of siemens star.
Rin=0.6; %Inner radius of siemens star.
RISiO2=1.46;
ThickSiO2=0.09;
simRadius=7; % radius of simulated region.
%% Parameters of the DIC microscope.
% Parameters correspond to the experimental image that we use in the paper.
DICparams.wavelength=0.546;
DICparams.NAo=1.4;
DICparams.NAc=0.95; % Between the coverglass and coverslip airgap was present. Condenser was oiled though.
DICparams.nEmbb=1;
DICparams.nImm=1.515;
DICparams.shear=0.48/2; %Measured from fringe.
DICparams.bias=25;
DICparams.shearangle=45;
%% Compute specimen transmission.
xsim=-simRadius:0.02:simRadius;
%2nm sampling is required to properly sample slight over or under-etching of the target
usim=0;
%usim=-1:0.2:1; % To simulate defocus.
% Assume slight overetching and therefore non-square azimuthal phase
% grating.
OverEtchProfile=mblnnfSiemens(xsim,xsim,0.04);
oplOverEtch=(2*pi/DICparams.wavelength)*(DICparams.nEmbb-RISiO2)*OverEtchProfile*ThickSiO2;
specimenOverEtch=exp(1i*oplOverEtch);
DICMicroscope=microlith(xsim,usim); % Second argument is z.
% Compute system pupils and the image according to the model proposed by
% Mehta and Sheppard.
DICMicroscope.computesys('DIC',DICparams);
DICImage=DICMicroscope.computeimage(specimenOverEtch,'CPU');
% Compute system pupils and the image according to the model proposed by
% Preza et al.
DICMicroscope.computesys('DIC-Preza',DICparams);
DICPrezaImage=DICMicroscope.computeimage(specimenOverEtch,'CPU');
% Compute system pupils and the image for PlasDIC system.
DICparams.NAc=0.25;
DICMicroscope.computesys('PlasDIC',DICparams);
PlasDICImage=DICMicroscope.computeimage(specimenOverEtch,'CPU');
%% Compare the etch profile and images.
% Dark regions are etched and white regions are intact silica.
% Images are linked, so panning or zooming one will do the same for all
% images.
DICDisp=gray2norm(DICImage);
DICPrezaDisp=gray2norm(DICPrezaImage);
PlasDICDisp=gray2norm(PlasDICImage);
figure(1); clf;
set(1,'color','white','Position',[100 100 800 800],'defaultaxesfontsize',14);
colormap gray;
ha=imagecat(xsim,xsim,~OverEtchProfile,DICDisp,DICPrezaDisp,PlasDICDisp,'equal','link');
% All four images are linked, so zooming or panning one will do the same on
% all others.
axes(ha(1)); title('Etched pattern');
axes(ha(2)); title('DIC image (model: Mehta and Sheppard)');
set(gca,'Clim',[0 1]);
axes(ha(3)); title('DIC image (model: Preza et al)');
set(gca,'Clim',[0 1]);
axes(ha(4)); title('PlasDIC image');
set(gca,'Clim',[0 1]);
xlim([-6.5 6.5]); ylim([-6.5 6.5]);
% The features at the edges (about 200nm or the size of the image of a
% point) are affected by the edge artifacts.