dx2

add spherical aberration as a defect - now no ideal solution exists

Contents

system definition

global cv th rn;
cv = [ 0 0.25 -0.15 0];
th = [ 0  0    0 0];
rn = [ 1 1.5 1  1];

find contours

n=128;
u1 = linspace(-0.3,0.3,n);
u2 = linspace(-0.4,0.2,n);
map = zeros(n,n);
for r=1:n
    v(2)=u2(r);
    for c=1:n
        v(1)=u1(c);
        f = sing2(v);
        map(r,c)=f'*f;
    end
end
cmax = max(max(map));
fprintf('contour map max %g min %g\n',cmax,min(min(map)));
map = map/cmax;

save sing2 cv th rn u1 u2 map

contour map max 1.16758 min 2.82131e-006

contours

[c2 hc2] = contour(u1,u2,map,logspace(1,-4,16));
nc = get(hc2,'Children');
for i = 1:4:length(nc)
   set(nc(i),'LineWidth',1.5);
end
axis square;
legend;
xlabel('cv1');
ylabel('cv2');

% resize plot window
pos = get(gcf,'Position');
pos(3)=480;
pos(4)=480;
set(gcf,'Position',pos);

optimization

x = [ 0.25 -0.15]';
for (k=1:5)
   fprintf('step %d\n\n',k);
   fprintf('starting point: %.6f  %.6f\n',x); % display starting point
   [A fz] = calculate_derivatives(@sing2,x);
   x = SVD_diagram(A,fz,x,0.05);
end

step 1

starting point: 0.250000  -0.150000
step 2

starting point: -0.155673  -0.283581
step 3

starting point: -0.074541  -0.173431
step 4

starting point: 0.016005  -0.083650
step 5

starting point: 0.071000  -0.029008

Published with MATLAB® 7.6