Contents

chromatic.m shows an example of chromatic aberrations

requires CODDINGTON

See Also: COMA, ASTIG, ABDEMO

by Chuck DiMarzio Northeastern University 2011

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!! CRC Press, Boca Raton, FL, 2011.
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Index data from http://refractiveindex.info/

C1 = 1.03961212;
C2 = 0.00600069867;
C3 = 0.231792344;
C4 = 0.0200179144;
C5 = 1.01046945;
C6 = 103.560653;
lambda=(0.3:0.01:2.5); % lambda in microns for the equation
n2m1 = C1*lambda.^2./(lambda.^2-C2) +...
       C3*lambda.^2./(lambda.^2-C4) + ...
       C5*lambda.^2./(lambda.^2-C6);
n=sqrt(n2m1+1);
fig1=figure;plot(lambda*1000,n);grid on;
xlabel('\lambda, Wavelength, nm.');
ylabel('n, Index of Refraction');
%
%
p =
    -1
q =
   -0.7467

Set nominal focal length.

$$\frac{1}{f} = (n-1)(\frac{1}{r_1}-\frac{1}{r_2})$$

The lensmakers equation for a thin lens is
Let's optimize for spherical aberration assuming object at infinity

$$p = f \frac{s'-s}{s'+s}$$, \ \
$$s \rightarrow \infty $$

lambdanom=0.500;
nnom=1.52141;
fnom=4000; % Keep everything in microns now.  This could be a 40x microscope
           % objective with a 160-mm tube length.
p=-1
q=2*(nnom^2-1)*p/(nnom+2)
[ls,qmin]=coddington(p,[],fnom,1,nnom);

compute radii using

$$q=\frac{r_2-r_1}{r_2+r_1}$$
and
$$\frac{1}{f} = (n-1)(\frac{1}{r_1}-\frac{1}{r_2}) $$

r1=2*fnom*q/(q+1)*(nnom-1);
r2=-2*fnom*q/(q-1)*(nnom-1);
%
%

Find actual focal length vs. wavelength.

$$\frac{1}{f} = (n-1)(\frac{1}{r_1}-\frac{1}{r_2}) $$

fchrom=1./((n-1)*(1/r1-1/r2));
fig2=figure;plot(lambda*1000,fchrom/1000);grid on;
xlabel('\lambda, Wavelength, nm.');
ylabel('f, Focal Length, mm');
moose=axis;
Chromatic aberration is severe, causing focal shifts of close to 100
micrometers over the visible spectrum.

Compare focal change caused by spherical aberration.

Remember...

$$ ls = \frac{1}{s'} - \frac{1}{s'(0)} $$

h=(10:10:600);
na=sin(atan(h/fnom));  % Plot vs. NA
[ls,qmin]=coddington(p,q,fnom,h,nnom);
fspher=1./(ls+1/fnom);
fig3=figure;plot(na,fspher/1000);grid on;
xlabel('NA');
ylabel('f_h, Focal Length, mm');
axis([0,0.2,moose([3,4])]);

Spherical aberration is worse than chromatic, even for these very small numerical apertures.