dx7
Contents
triplet setup
clear; global cv th rn dn; cv = [ 0 0 0 0 0 0 0 0]; %th = [ 0 0 0 0 0 0 0 0]; th = [ 0 2 0 1 0 3 0 0]; sk16 = [1.617271 1.622861 1.627559]; f4 = [1.611644 1.620578 1.628484]; bk7 = [1.514322 1.51680 1.522376]; rn = [ 1 sk16(2) 1 f4(2) 1 bk7(2) 1 1]; dn = [ 0 sk16(3)-sk16(1) 0 f4(3)-f4(1) 0 bk7(3)-bk7(1) 0 0]; sa = [0 6.5 6.5 6.5 0 6.5 6.5 6.5 0]; lp = find(rn>1); as = 5; v = [1/50 -2/50]';
trip1 code
cv(2:3)=lens_shape(v(1),1,rn(2)); % shape 1 (convex-plano) cv(4:5)=lens_shape(v(2),0,rn(4)); % shape 2 (equi-concave) cv(6)=0; yap = 50/8; uco = tan(2.0*pi/180); scl = yap^2/2; ya = parax([yap 0],cv,th,rn); usolve = -0.125; yn=ya(7,1); % paraxial height solve for image distance th(7) = -yn/usolve; ya(8,1) = 0; % paraxial angle solve for power if (abs(yn)>1e-6) cv(7)= -(rn(7)*usolve-rn(6)*ya(6,2))/((rn(7)-rn(6))*yn); end ya(7,2)=usolve; show_lens drawsys
system prescription
sn rd th rn
0 0.00000 0.00000 1.00000
1 31.14305 2.00000 1.62286
2 0.00000 0.00000 1.00000
3 -31.02890 1.00000 1.62058
as 31.02890 0.00000 1.00000
5 0.00000 3.00000 1.51680
6 -13.41606 50.63215 1.00000
7 0.00000 0.00000 1.00000
paraxial raytrace
sn ya ua yc uc clap
0 6.25000 0.00000 -0.06678 0.03492 6.31678
1 6.25000 -0.07702 -0.06678 0.02234 6.31678
2 6.09595 -0.12500 -0.02210 0.03626 6.11805
3 6.09595 -0.00190 -0.02210 0.02210 6.11805
4 6.09405 0.11880 0.00000 0.03581 6.09405
5 6.09405 0.07832 0.00000 0.02361 6.09405
6 6.32902 -0.12500 0.07084 0.03309 6.39985
7 0.00000 -0.12500 1.74604 0.03309 1.74604
W040 W131 W222 W220 W311 W220P
57.99 -13.86 0.31 0.42 0.04 -0.25
Chromatic Aberrations
axial lateral
-3.10 0.33
th(3)=5; th(5)=7; trip1(v); show_lens drawsys
system prescription
sn rd th rn
0 0.00000 0.00000 1.00000
1 31.14305 2.00000 1.62286
2 0.00000 5.00000 1.00000
3 -31.02890 1.00000 1.62058
as 31.02890 7.00000 1.00000
5 0.00000 3.00000 1.51680
6 -14.89584 50.63215 1.00000
7 0.00000 0.00000 1.00000
paraxial raytrace
sn ya ua yc uc clap
0 6.25000 0.00000 -0.27680 0.03492 6.52680
1 6.25000 -0.07702 -0.27680 0.02493 6.52680
2 6.09595 -0.12500 -0.22694 0.04046 6.32290
3 5.47095 -0.00961 -0.02466 0.02466 5.49561
4 5.46134 0.09365 0.00000 0.03996 5.46134
5 6.11686 0.06174 0.27975 0.02635 6.39660
6 6.30207 -0.12500 0.35879 0.02752 6.66086
7 -0.02694 -0.12500 1.75197 0.02752 1.77891
W040 W131 W222 W220 W311 W220P
50.46 0.55 -0.40 0.01 0.07 -0.21
Chromatic Aberrations
axial lateral
1.47 1.24
[f v]=trip3; %[xo vout hp]=cycle(v,@trip3); %[A fz] = calculate_derivatives(@trip3,xo); [A fz] = calculate_derivatives(@trip3,v); [U W V] = svd(A,0); d = diag(W); n = length(d); sing = 1e-8; semilogy(1:n,d,'ko',0,1); %semilogy(1:n,d,'ko',[0 n],sing*max(d)*[1 1],'b--'); ylabel('eigenvalues'); fprintf('eigenvalues: min %g max %g\n',min(d),max(d));
eigenvalues: min 0.00985783 max 34518
Va = abs(V); totals = sum(Va); size(Va) size(totals) Vn = Va./(ones(size(totals))'*totals); % variable names vname = cellstr(['cv2'; 'cv3'; 'cv4'; 'cv5'; 'cv6'; 'cv7'; 'th3'; 'th5']); for k=1:8 str = char(vname(k)); fprintf('%3s %6.1f %6.1f %6.1f %6.1f %6.1f %6.1f %6.1f %6.1f\n',str,100*Vn(:,k)); end imwrite(imresize(Vn,16,'nearest'),'html/dx7.jpg');
ans =
8 8
ans =
1 8
cv2 15.5 15.3 14.6 14.9 18.8 21.0 0.0 0.0
cv3 29.3 26.7 0.1 1.4 1.5 40.8 0.1 0.1
cv4 21.7 11.8 36.2 17.7 3.7 8.6 0.0 0.3
cv5 0.5 17.0 21.1 33.4 17.9 9.6 0.2 0.2
cv6 14.8 10.2 7.2 13.1 36.0 18.2 0.1 0.4
cv7 25.0 29.6 13.9 18.7 10.2 2.4 0.1 0.2
th3 0.2 0.8 0.2 0.5 0.6 0.2 1.9 95.6
th5 0.0 0.0 0.2 0.3 0.3 0.1 97.1 1.9
This image shows the above array
optimize
[xo vout hp] = cycle(v,@trip3);
1 41.56 0.24 44.2 8 2 32.14 0.716 75.7 8 3 3.006 0.683 27.1 8 4 1.818 0.504 6.51 8 5 0.674 0.933 5.37 8 6 0.0003815 1 0.29 8 7 2.654e-008 1 0.000552 8 8 1.158e-012 1 3.77e-008 8
show_lens
system prescription
sn rd th rn
0 0.00000 0.00000 1.00000
1 18.74934 2.00000 1.62286
2 -200.66262 7.38428 1.00000
3 -13.83423 1.00000 1.62058
as 10.58907 4.35964 1.00000
5 36.40854 3.00000 1.51680
6 -10.61340 44.39750 1.00000
7 0.00000 0.00000 1.00000
paraxial raytrace
sn ya ua yc uc clap
0 6.25000 0.00000 -0.47878 0.03492 6.72878
1 6.25000 -0.12794 -0.47878 0.03132 6.72878
2 5.99412 -0.22623 -0.41615 0.05212 6.41027
3 4.32355 -0.01992 -0.03129 0.03129 4.35484
4 4.30363 0.21993 0.00000 0.05071 4.30363
5 5.26244 0.09575 0.22110 0.03137 5.48354
6 5.54969 -0.12500 0.31519 0.03223 5.86488
7 0.00000 -0.12500 1.74604 0.03223 1.74604
W040 W131 W222 W220 W311 W220P
-0.00 -0.00 0.00 0.00 -0.00 0.00
Chromatic Aberrations
axial lateral
-0.00 -0.00
optimization progress plot
sigma = hp(:,1); damp = hp(:,2); n = length(sigma); k = (1:n)-1; subplot(2,1,1); if n<20 %plot(k,log10(sigma),'ko-','LineWidth',2); semilogy(k,sigma,'ko-','LineWidth',2); else semilogy(k,sigma,'k','LineWidth',2); end grid; xlabel('iteration'); ylabel('merit value'); subplot(2,1,2); if n<20 plot(k(2:n),damp(2:n),'ko-',0,1.1,'LineWidth',2); else plot(k(2:n),damp(2:n),'k',0,1.1,'LineWidth',2); end grid; xlabel('iteration'); ylabel('damping');
final design
subplot(1,1,1) drawsys
show steps
sz = size(vout); disp(sz) for k=1:8 str = sprintf('iteration %d',k); v = vout(k,:); trip3(v); subplot(2,4,k); drawsys; axis([0 25 -8 8]); title(str); end
9 8
