trace chief ray
Contents
% load lens clear load kidger
trial axial ray
pos_in = [0 pya(1,1) 0]; dir_in = [0 0 1]; raytrace(pos_in,dir_in,cv,th,rn);
n X Y Z kx ky kz OPL 0 0.000 6.250 0.000 0.0000 0.0000 1.0000 1 0.000 6.250 1.081 0.0000 -0.2161 1.6059 1.08095444 2 0.000 6.054 0.040 0.0000 -0.2078 0.9782 2.38514582 3 0.000 5.058 -0.430 0.0000 -0.0955 1.6336 4.79142914 4 0.000 4.935 0.667 0.0000 0.0797 0.9968 3.43728438 5 0.000 4.979 0.000 0.0000 0.0797 0.9968 0.54215402 6 0.000 5.316 0.209 0.0000 0.0306 1.6201 4.22983074 7 0.000 5.347 -0.655 0.0000 -0.1256 0.9921 2.65142083 8 0.000 -0.002 0.000 0.0000 -0.1256 0.9921
trial chief-ray
pos_in = [0 pyc(1,1) 0]; theta = 22*pi/180; dir_in = [0 sin(theta) cos(theta)]; raytrace(pos_in,dir_in,cv,th,rn);
n X Y Z kx ky kz OPL 0 0.000 -4.670 0.000 0.0000 0.3746 0.9272 1 0.000 -4.451 0.540 0.0000 0.5239 1.5334 0.58267803 2 0.000 -3.776 0.015 0.0000 0.5184 0.8551 3.38235467 3 0.000 -0.664 -0.007 0.0000 0.5028 1.5572 6.00384731 4 0.000 -0.338 0.003 0.0000 0.4904 0.8715 1.73749257 5 0.000 0.339 0.000 0.0000 0.4904 0.8715 1.38140915 6 0.000 2.623 0.051 0.0000 0.4639 1.5526 4.65609292 7 0.000 3.281 -0.244 0.0000 0.3705 0.9288 3.72879815 8 0.000 19.976 0.000 0.0000 0.3705 0.9288
exercise 1
'differential' trace and Newton-Raphson to trace ray through center of pupil
aim = pyc(1,1); theta = 22*pi/180; dir_in = [0 sin(theta) cos(theta)]; pos_in = [0 aim 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th(1:ast),rn); fz = pos(2); fprintf('%2s %10s %10s\n','#','Y','aim'); delta = 1e-3 * pya(1,1); fprintf('%2d %10.6f %10.6f\n',0,fz,aim); for k=1:20 pos_in = [0 aim+delta 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th(1:ast),rn); diff = (pos(2) - fz)/delta; aim = aim - fz/diff; pos_in = [0 aim 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th(1:ast),rn); fz = pos(2); fprintf('%2d %10.6f %10.6f\n',k,fz,aim); if abs(fz)<1e-7 break; end end
# Y aim 0 0.339474 -4.669695 1 -0.001397 -5.129706 2 0.000000 -5.127829
fprintf('\n chief ray (through center of pupil)\n\n');
raytrace(pos_in,dir_in,cv,th,rn);
chief ray (through center of pupil) n X Y Z kx ky kz OPL 0 0.000 -5.128 0.000 0.0000 0.3746 0.9272 1 0.000 -4.866 0.648 0.0000 0.5376 1.5286 0.69837066 2 0.000 -4.208 0.019 0.0000 0.5313 0.8472 3.21496309 3 0.000 -0.996 -0.017 0.0000 0.5078 1.5556 6.04515152 4 0.000 -0.660 0.012 0.0000 0.4836 0.8753 1.77002922 5 0.000 0.000 0.000 0.0000 0.4836 0.8753 1.36556977 6 0.000 2.234 0.037 0.0000 0.4612 1.5534 4.62008157 7 0.000 2.909 -0.192 0.0000 0.3781 0.9258 3.83932725 8 0.000 19.978 0.000 0.0000 0.3781 0.9258
Uin = theta; Qin = aim*cos(Uin); trig_ray(Qin,Uin,cv,th,rn);
n Y n sin(U) 1 -4.86621 0.53756 2 -4.20802 0.53134 3 -0.99602 0.50775 4 -0.66037 0.48359 5 0.00000 0.48359 6 2.23422 0.46116 7 2.90853 0.37808 8 19.97790 0.37808
exercise 2
% Coddington trace N = 20; fields = zeros(N+1,4); for n=0:N h = n/N; u = h*22; fields(n+1,1:2) = [h u]; theta = u*pi/180; Y = h*pyc(1,1); % Y = aim_ray(h*aim,theta,cv,th(1:ast),rn); fields(n+1,3:4) = codd_ray(Y*cos(theta),theta,cv,th,rn); end fprintf('%10s%10s%10s%10s\n','h','U','tan shift','sag shift'); disp(fields)
h U tan shift sag shift
0 0 0.2299 0.2299
0.0500 1.1000 0.2294 0.2270
0.1000 2.2000 0.2277 0.2184
0.1500 3.3000 0.2250 0.2042
0.2000 4.4000 0.2214 0.1845
0.2500 5.5000 0.2172 0.1598
0.3000 6.6000 0.2126 0.1303
0.3500 7.7000 0.2078 0.0965
0.4000 8.8000 0.2030 0.0590
0.4500 9.9000 0.1983 0.0185
0.5000 11.0000 0.1938 -0.0243
0.5500 12.1000 0.1893 -0.0684
0.6000 13.2000 0.1840 -0.1128
0.6500 14.3000 0.1772 -0.1563
0.7000 15.4000 0.1669 -0.1976
0.7500 16.5000 0.1507 -0.2351
0.8000 17.6000 0.1248 -0.2670
0.8500 18.7000 0.0836 -0.2912
0.9000 19.8000 0.0195 -0.3055
0.9500 20.9000 -0.0784 -0.3070
1.0000 22.0000 -0.2248 -0.2925
Results from ZEMAX
Y Angle (deg) Tan Shift Sag Shift Real Height Ref. Height Distortion
0.00000000 0.22999260 0.22999260 0.00000000 0.00000000 0.00000000 %
1.10000000 0.22950749 0.22712745 0.95548619 0.95549421 -0.00083993 %
2.20000000 0.22804559 0.21857114 1.91162863 1.91169323 -0.00337909 %
3.30000000 0.22569174 0.20444154 2.86908367 2.86930392 -0.00767585 %
4.40000000 0.22258058 0.18493664 3.82850786 3.82903734 -0.01382811 %
5.50000000 0.21888554 0.16033694 4.79055792 4.79161085 -0.02197425 %
6.60000000 0.21480221 0.13100882 5.75589080 5.75775024 -0.03229458 %
8.80000000 0.20621464 0.06009117 7.69903249 7.70368556 -0.06040058 %
9.90000000 0.20195541 0.01971176 8.67815390 8.68499565 -0.07877663 %
11.00000000 0.19769643 -0.02295929 9.66318208 9.67290481 -0.10051506 %
11.22000000 0.19682630 -0.03169217 9.86095395 9.87134879 -0.10530321 %
11.44000000 0.19594327 -0.04047361 10.05899336 10.07009531 -0.11024673 %
11.66000000 0.19504339 -0.04929561 10.25730552 10.26915093 -0.11534949 %
11.88000000 0.19412219 -0.05814993 10.45589560 10.46852225 -0.12061548 %
12.10000000 0.19317453 -0.06702809 10.65476877 10.66821593 -0.12604879 %
13.20000000 0.18781099 -0.11146279 11.65356137 11.67175498 -0.15587725 %
14.30000000 0.18057413 -0.15507654 12.66020048 12.68437389 -0.19057631 %
15.40000000 0.16979637 -0.19650638 13.67531632 13.70695362 -0.23081203 %
16.50000000 0.15293022 -0.23418702 14.69952333 14.74040736 -0.27736026 %
18.70000000 0.08428453 -0.29082195 16.77753721 16.84377218 -0.39323122 %
19.80000000 0.01950904 -0.30529168 17.83239776 17.91570366 -0.46498814 %
20.90000000 -0.07868639 -0.30692140 18.89840730 19.00255835 -0.54808961 %
22.00000000 -0.22486754 -0.29241758 19.97584459 20.10546871 -0.64472067 %plot(fields(:,3),fields(:,1),'k',fields(:,4),fields(:,1),'k--','LineWidth',2); ylabel('fractional field'); xlabel('shift');
exercise 3
del = 0.1;
h = 1;
theta = h*22*pi/180;
dir_in = [0 sin(theta) cos(theta)];
pos_in = [0 h*pyc(1,1) 0];
[pos dir] = raytrace(pos_in,dir_in,cv,th,rn);
yh = pos(2);
tanuh = dir(2)/dir(3);
fprintf('image height %g fractional height %g\n',yh,h);
image height 19.9758 fractional height 1
% tangential focus pos_in = [0 h*pyc(1,1)+del 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th,rn); fprintf('\ntangential focus\n'); dy = pos(2)-yh; du = dir(2)/dir(3) - tanuh; fprintf('dy %g du %g\n',dy,du); fprintf('solve %g\n',-dy/du);
tangential focus dy -0.000464773 du -0.00205744 solve -0.225898
% sagittal focus pos_in = [del h*pyc(1,1) 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th,rn); fprintf('\nsagittal focus\n'); tanv = dir(1)/dir(3); fprintf('dx %g dv %g\n',pos(1),tanv); fprintf('solve %g\n',-pos(1)/tanv); clear dy du tanuh tanv
sagittal focus dx -0.000594109 dv -0.00203087 solve -0.292539
exercise 4
% tangential fan ya = linspace(-1,1,41); fprintf('%10s %10s %10s\n','rel ap','y','x'); for k=1:length(ya) pos_in = [0 pyc(1,1)+ya(k)*pya(1,1) 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th,rn); yr(k) = pos(2) - yh; xr(k) = pos(1); fprintf('%10.2f %10.4f %10.4f\n',ya(k),yr(k)*1e3,xr(k)*1e3); end
rel ap y x
-1.00 -132.6919 0.0000
-0.95 -103.6311 0.0000
-0.90 -79.8058 0.0000
-0.85 -60.3453 0.0000
-0.80 -44.5339 0.0000
-0.75 -31.7797 0.0000
-0.70 -21.5901 0.0000
-0.65 -13.5528 0.0000
-0.60 -7.3212 0.0000
-0.55 -2.6029 0.0000
-0.50 0.8498 0.0000
-0.45 3.2473 0.0000
-0.40 4.7689 0.0000
-0.35 5.5678 0.0000
-0.30 5.7754 0.0000
-0.25 5.5048 0.0000
-0.20 4.8537 0.0000
-0.15 3.9072 0.0000
-0.10 2.7397 0.0000
-0.05 1.4176 0.0000
0.00 0.0000 0.0000
0.05 -1.4586 0.0000
0.10 -2.9075 0.0000
0.15 -4.2980 0.0000
0.20 -5.5823 0.0000
0.25 -6.7119 0.0000
0.30 -7.6364 0.0000
0.35 -8.3019 0.0000
0.40 -8.6494 0.0000
0.45 -8.6137 0.0000
0.50 -8.1208 0.0000
0.55 -7.0866 0.0000
0.60 -5.4143 0.0000
0.65 -2.9921 0.0000
0.70 0.3100 0.0000
0.75 4.6437 0.0000
0.80 10.1860 0.0000
0.85 17.1441 0.0000
0.90 25.7615 0.0000
0.95 36.3239 0.0000
1.00 49.1680 0.0000
idx = find(ya>-0.55); plot(ya(idx),yr(idx)*1e3,'k','LineWidth',2); grid(); xlabel('relative aperture'); ylabel('ray error (\mum)');
% sagittal fan ya = linspace(-1,1,41); yr = zeros(size(ya)); xr = yr; fprintf('%10s %10s %10s\n','rel ap','y','x'); for k=1:length(ya) pos_in = [ ya(k)*pya(1,1) pyc(1,1) 0]; [pos dir] = raytrace(pos_in,dir_in,cv,th,rn); yr(k) = pos(2) - yh; xr(k) = pos(1); fprintf('%10.2f %10.4f %10.4f\n',ya(k),yr(k)*1e3,xr(k)*1e3); end
rel ap y x
-1.00 -4.7092 13.8208
-0.95 -3.6217 20.7816
-0.90 -2.7551 25.2615
-0.85 -2.0686 27.8251
-0.80 -1.5288 28.9255
-0.75 -1.1083 28.9263
-0.70 -0.7845 28.1174
-0.65 -0.5389 26.7294
-0.60 -0.3559 24.9437
-0.55 -0.2229 22.9018
-0.50 -0.1291 20.7118
-0.45 -0.0656 18.4549
-0.40 -0.0253 16.1894
-0.35 -0.0019 13.9553
-0.30 0.0094 11.7773
-0.25 0.0127 9.6681
-0.20 0.0113 7.6299
-0.15 0.0077 5.6574
-0.10 0.0039 3.7392
-0.05 0.0010 1.8596
0.00 0.0000 0.0000
0.05 0.0010 -1.8596
0.10 0.0039 -3.7392
0.15 0.0077 -5.6574
0.20 0.0113 -7.6299
0.25 0.0127 -9.6681
0.30 0.0094 -11.7773
0.35 -0.0019 -13.9553
0.40 -0.0253 -16.1894
0.45 -0.0656 -18.4549
0.50 -0.1291 -20.7118
0.55 -0.2229 -22.9018
0.60 -0.3559 -24.9437
0.65 -0.5389 -26.7294
0.70 -0.7845 -28.1174
0.75 -1.1083 -28.9263
0.80 -1.5288 -28.9255
0.85 -2.0686 -27.8251
0.90 -2.7551 -25.2615
0.95 -3.6217 -20.7816
1.00 -4.7092 -13.8208
plot(ya,yr,'b--',ya,xr,'k','LineWidth',2); grid xlabel('relative aperture'); ylabel('ray error (\mum)');
