Hi ,
Can Some one please help with optimization.
Here when I run the program and I get MF1 as 36. Ideally I must have 1 but near to it is also fine.
Inoder to achieve this we have to set the value of V1 to V9 variables in a way that we MF1 = 1 or near to 1.
Please help. Or suggest me the ways how can I do it.
tic
clear
Nsample = 600; % Number of sample points in x and in y direction
Windowsample =60; % Size of samling window [µm], sampling points to be distributed evenly across
FFbins =60; % Number of bins in histogram of FF
x = linspace( 1/2*Windowsample/Nsample, Windowsample-1/2*Windowsample/Nsample, Nsample);
y = linspace( 1/2*Windowsample/Nsample, Windowsample-1/2*Windowsample/Nsample, Nsample);
[X,Y] = meshgrid(x,y);
z= zeros(Nsample,Nsample);
R2x = zeros(Nsample,Nsample);
R2y = zeros(Nsample,Nsample);
R2z = zeros(Nsample,Nsample);
R1x = zeros(Nsample,Nsample);
R1y = zeros(Nsample,Nsample);
R1z = zeros(Nsample,Nsample);
Theta2x = zeros(Nsample,Nsample);
Theta2y = zeros(Nsample,Nsample);
%Angle2z = zeros(Nsample,Nsample); Not needed
Theta3x = zeros(Nsample,Nsample);
Theta3y = zeros(Nsample,Nsample);
%Angle4z = zeros(Nsample,Nsample); Not needed
% 0.030208
Target_Value = ones(FFbins,FFbins)*(Nsample/FFbins)^2;
% z = V1*sin(2*pi/20*1*X) + V2* sin(2*pi/20*1*Y)...
% + -V3*sin(2*pi/20*1*X).*sin(2*pi/20*1*Y) + V4*sin(2*pi/20*3*X) + V5*sin(2*pi/20*3*Y)...
% + V6*sin(2*pi/20*5*X) + V7*sin(2*pi/20*5*Y) + -V8*sin(2*pi/20*3*X).*sin(2*pi/20*1*Y)...
% + -V9*sin(2*pi/20*1*X).* sin(2*pi/20*3*Y); % z in [µm]
% I have taken few manual values of V1 to V9 to Optmize MF1 (at the bottom) as much I can.
z = 3.7019*sin(2*pi/20*1*X) + 3.700191* sin(2*pi/20*1*Y)...
+ -0.015*sin(2*pi/20*1*X).*sin(2*pi/20*1*Y) + 0.2000*sin(2*pi/20*3*X) + 0.200*sin(2*pi/20*3*Y)...
+ 0.042016*sin(2*pi/20*5*X) + 0.0553*sin(2*pi/20*5*Y) + -0.10001*sin(2*pi/20*3*X).*sin(2*pi/20*1*Y)...
+ -0.200005*sin(2*pi/20*1*X).* sin(2*pi/20*3*Y); % z in [µm]
nx1 = zeros(Nsample,Nsample); % Normal vector of first surface
ny1 = zeros(Nsample,Nsample);
nz1 = zeros(Nsample,Nsample);
[nx1, ny1, nz1] = surfnorm(X,Y,z);
S1 = [0 0 1]; % Incident light being collimated
NX2= 0; % Normal vector of second surface
NY2= 0;
NZ2= -1;
for c = 1:600
for r = 1:600
%%%%%%%%%%%%% Normal of First surface surface %%%%%%%%%%%%%%%%%%
NX1= -nx1(r,c);
NY1= -ny1(r,c);
NZ1= -nz1(r,c);
Nsurf1 = [NX1 NY1 NZ1];
%%%%%%%%%%%%%%%%%%% Light vector S2 after first surface %%%%%%%%%%%%%%%%%%%%%
Fa = (1/1.5*(cross(Nsurf1,cross(-Nsurf1,S1))));
Fb = (Nsurf1*sqrt(1-(dot(1/2.25,(dot(cross(Nsurf1,S1),cross(Nsurf1,S1)))))));
S2 = (Fa-Fb);
R1x(r,c) = S2(1);
R1y(r,c) = S2(2);
R1z(r,c) = S2(3);
%%%%%%%%%%%%%%%%%%% Angle of S2 after first surface %%%%%%%%%%%%%%%%%%%%
% Theta2 = asind(S2/norm(S2)); Not needed
Theta2x(r,c) = asind(S2(1)/norm(S2));
Theta2y(r,c) = asind(S2(2)/norm(S2));
%Angle2z(r,c) = Theta2(3); Not needed
%%%%%%%%%%%%% Normal of Second surface surface %%%%%%%%%%%%%%%%%%
Nsurf2 = [NX2 NY2 NZ2];
%%%%%%%%%%%%%%%%%%% Light S3 after 2nd surface %%%%%%%%%%%%%%%%%%%
Fa2 = (1.5*(cross(Nsurf2,cross(-Nsurf2,S2))));
Fb2 = (Nsurf2*sqrt(1-(dot(2.25,(dot(cross(Nsurf2,S2),cross(Nsurf2,S2)))))));
S3 = (Fa2-Fb2);
% S3(S3~=real(S3)) = 0; not needed
R2x(r,c) = S3(1);
R2y(r,c) = S3(2);
R2z(r,c) = S3(3);
%%%%%%%%%%%%%%%%%%% Angle of S3 after 2nd surface %%%%%%%%%%%%%%%%
%Theta4 = asind(S3/norm(S3)); not needed
Theta3x(r,c) = asind(S3(1)/norm(S3));
Theta3y(r,c) = asind(S3(2)/norm(S3));
%Angle4z(r,c) = Theta4(3); Not needed
end
end
toc
f = figure(1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% First surface Plot %%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(1,3,1)
Xedges = [-30:1:30];
Yedges = [-30:1:30];
W1 = histogram2(Theta2x,Theta2y,Xedges,Yedges,'DisplayStyle','tile','ShowEmptyBins','on');%,'DisplayStyle','tile','ShowEmptyBins','on'
counts_First_surface = W1.Values ;%%%%%%%%%%%%%% Data in each Bin %%%%%%%%%%%%%%%%%%
Bincounts_First_surface = W1.BinCounts;
xlabel('x Angle with yz plane [°]');
ylabel('y Angle with xz plane [°]');
colormap(jet(256));
colorbar;
axis equal
xlim([-35 35]);
ylim([-35 35]);
title('FF after first surface')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Second surface Plot %%%%%%%%%%%%%%%%%%%%%%
subplot(1,3,2)
Xedges = [-30:1:30];
Yedges = [-30:1:30];
W2 = histogram2(Theta3x,Theta3y,Xedges ,Yedges,'DisplayStyle','tile','ShowEmptyBins','on'); %,'DisplayStyle','tile','ShowEmptyBins','on'
counts_Second_surface = W2.Values; %%%%%%%%%%%%%% Data in each Bin %%%%%%%%%%%%%%%%%%
Bincounts_Second_surface = W2.BinCounts;
MAX_Second_surface =max(W2.Values,[],'all');%max(h.Values)
MIN_Second_surface= min(W2.Values,[],'all');
Ratio = MIN_Second_surface/MAX_Second_surface; %%%%%%%%%%%%%%%%%%%% Ratio of Max and Min %%%%%%%%%%%%%%%%%%
Real_Value = (W2.Values); %%%%%%%%%%%%%% Merit Function rms of differences %%%%%%%%%%%%%%%%%%
SamplesinFF = sum(Real_Value,'all') % Test if all rays are getting into FF
Merit_Function = Real_Value - Target_Value;
MF1 = sqrt( sum(Merit_Function.*Merit_Function,'all')/FFbins/FFbins)
xlabel('x Angle with yz plane [°]');
ylabel('y Angle with xz plane [°]');
colormap(jet(256));
colorbar;
axis equal
xlim([-35 35]);
ylim([-35 35]);
title('FF after second surface')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Contour surface Plot %%%%%%%%%%%%%%%%%%%%
subplot(1,3,3)
contourf(X,Y,z)
xlabel('x [µm]');
ylabel('y [µm]');
title('Contour of first surface')
colorbar;
axis equal
xlim([-5 65]);
ylim([-5 65]);
toc
