Lens Design, OPTI 517
Homework #3
Spherical aberration, cont.
In this homework we will get hands-on experience in designing a Dall and an Offner null
corrector. Note that in the Offner corrector we have effective variables to control both
third-order and higher-order spherical aberration. We will also design a Schmidt, a
Maksutov, and a Houghton camera. These designs involve the correction of spherical
aberration and should reinforce the class discussions.
1) The Hubble space telescope has a primary mirror that is 2400 mm in diameter and has
a vertex radius of curvature of -11040 mm. The conic constant is about -1.003. Evaluate
the amount of spherical aberration that the primary mirror generates when it is
illuminated from its center of curvature with a point source at 633 nm. Make a drawing of
the ray caustic near the center of curvature. 4 points
2) Use the aberration coefficients for spherical aberration and coma to derive conditions
(the conic constants) for the absence of spherical aberration and coma in a Cassegrain
type telescope. Use the magnification of the secondary m to express your results.
The answer is:
K primary  1  
2s
4mm  1  2m  s 
and K sec ondary  1  
3
m
m  13
where s is the ratio of the back focal distance to the mirror vertex separation. (10 points)
3) Design now a Dall null compensator for the Hubble primary mirror using a single
plano-convex lens with a 150 mm maximum clear aperture. Set this lens in front of the
mirror at the appropriate distance so that the clear aperture used is 150 mm. This should
be set in double pass to actually simulate a test configuration. The stop should be set at
the mirror. Why? Light should be focused after passing through the lens. Then, increase
the power of the lens till you minimize spherical aberration. Note the magnitude of the
residual spherical aberration. Compare the two solutions; i.e. flat or convex side facing
the mirror. Use BK7 glass which can be very homogeneous, inexpensive, and melt in
large chunks. 4 points
4) Design an Offner null corrector for the Hubble primary mirror using a single planoconvex relay lens with a 150 mm maximum clear aperture. Set this lens in front of the
mirror at the appropriate distance so that the clear aperture used is 150 mm. This should
be set in double pass to actually simulate a test configuration. The stop should be set at
the mirror. Light should focus between the mirror and the relay lens and then again after
the relay lens. Have the convex side of the lens facing the mirror. Increase the relay lens
power till you minimize spherical aberration and note the magnitude. If you do not have a
real focus after the relay lens decrease the size of the relay lens so that its power will
increase and thus create a real focus. Then insert a field lens at the mirror center of
curvature with its convex surface facing the mirror; the other surface is flat. Use BK7
glass. Adjust by hand the field lens optical power so that it images the mirror onto the
relay lens approximately. Then use the default merit function to optimize. Design
variables are the curvatures of the lenses and the spacing to the observation plane (almost
or the paraxial focal plane). Make sure that the zonal spherical aberration has been
controlled; compare with the Dall null lens. 8 points
5) Use the lens scaling option to scale down the lens of point 3) by a factor of 1/10. 1
point
6) Set a concave spherical mirror with a 800 mm radius of curvature. The stop is located
at the center of curvature and the entrance pupil diameter is 100 mm. The object is at
infinite. Note the amount of spherical aberration. 1 point
7) Set a system as in 6). Insert a plano parallel plate (BK7 glass) at the stop and aspherize
the front surface to correct spherical aberration (use the fourth order coefficient of
asphericity). Now add curvature to the front surface until the slope of the aspheric plate at
the 7/10 aperture radius is perpendicular to the optical axis. Maintain the correction for
spherical aberration. At this point you have a Schmidt camera. 5 points
8) Same as in 6) but now use a negative meniscus lens to correct spherical aberration.
This lens should have little negative power and a strong bending. Some thickness is
necessary. This will almost get a Maksutov system. The difference is that this system is
not corrected for axial color. Make sure the beam is not divergent too much after the
meniscus lens. 5 points
9) Same as in 6) but now use an afocal lens doublet made out of the same glass to correct
for spherical aberration. Except for color correction this would be a Houghton camera. 6
points.