Lens Design
Homework 5
Chromatic Aberration
In this homework we will exercise the correction of chromatic aberrations. Many lens systems required to
be achromatized and a lens designer needs to be able to handle this correction. We can achromatize lens
systems mainly because different glasses have different dispersive powers. Newton might not have been
aware of this fact and therefore did not pursue the fabrication of achromatic doublets. Instead, he worked in
reflecting telescopes. For a historical note on the development of the achromatic doublet see the History of
the Telescope by King.
1) Set a plano-convex lens (BK7 glass) working at f/12 and with a focal length of 2400 mm. Consider the
colors corresponding to the F, D, and C lines. The object is at infinite. Quantify the longitudinal axial
color. Compare it with the value f/. (3 points)
2) Design an achromatic (cemented) doublet corrected for spherical aberration (all spherical surfaces)
working at f/12 and a focal length of 2400 mm. Use BK7 and F4 glass or other glass pair you prefer.
Compare the longitudinal secondary spectrum with f/2400 (this is not an f/# is the focal length divided over
2400). (6 points)
3) Find the four solutions possible for problem 2; i.e. two crown in front and two flint in front. Compare
their performance on axis. Make sure the lenses are not too thick or too thin. (7 points)
4) Achromatize the Maksutov telescope that you designed in HK 3 by proper selection of the meniscus lens
thickness. Maintain the correction for spherical aberration. (5 points) . Make sure the meniscus optical
power is maintained I slow as not to have an oversized mirror..
5) Achromatize the Houghton telescope you designed in HK 3 by the proper choice of the doublet optical
power (near zero). Use only BK7 glass. Maintain the correction for spherical aberration. (5 points)
6) Design a Schupmann medial telescope. Use only spherical surfaces. Correct axial color by the proper
design of the Mangin mirror and lateral color by the proper choice of the field lens optical power. Reduce
the spherical aberration (less than ¼ wave at 550 nm) by increasing the F/# (decrease the aperture and then
scale the whole telescope to restore the proper aperture size). The aperture should be 100 mm in diameter
and the final f/# should be F/12 to F/16. Use only BK7 glass and a field of view of ¼ of a degree. The
shape of the first lens can be used to minimize coma but in this exercise use it to minimize spherical
aberration. The Mangin lens should be about half the first lens diameter. The final focus should be near the
focal point of the first lens. You need to plan carefully your design approach to actually find the thirdorder solution which we know exists. Design this telescope as if it were axially symmetric (not with tilted
components as it is actually used) (10 points).