Lens Design, OPTI 517
Homework #2
Spherical aberration.
As a lens designer one must understand in detail what spherical aberration is, how it is generated, and how
it is controlled. Spherical aberration has a quadratic dependence as a function of the shape factor of a thin
lens. A positive single lens introduces positive spherical aberration. Since spherical aberration depends on
the cube of the lens optical power, a way to reduce it, is by splitting the lens into two components of about
the same optical power. This will reduce spherical aberration to about 1/4 the original amount. One can
further split a component and increase the index of refraction to nullify spherical aberration. Another way
to deal with spherical aberration is by the use of an aspheric surface but this may not be welcome by the
fabricator. Another way is by combining a positive and a negative lens and then bending both to cancel
spherical aberration.
In canceling spherical aberration it may occur that some residual, high-order, may be present. Sometimes
this residual is called zonal spherical aberration. There are several ways to deal with higher order spherical
aberration, for example the thin airspace, the Merte surface, the field lens, the meniscus lens, and of course
an aspheric surface.
Having a good understanding of all these tools will be a firm step in learning about the control of spherical
aberration and later on to control other aberrations, in particular distortion.
a) Set a plano convex lens made from BK7 glass, f = 100 mm, @ 633 nm, stop at lens. Central thickness 10
mm. Light is from infinite and the convex side faces the incoming beam. Calculate third-order spherical
aberration, the total spherical aberration, for speeds f/2, f/4, and f/8. Compare the total aberration and the
third-order. The total spherical aberration is giving by the OPD of a real marginal ray. The third-order and
higher orders are components of the total aberration.
b) Bend the f/4 lens and plot spherical aberration as a function of bending. Select an appropriate range of
shape factors.
c) Split the f/4 lens into two plano convex lenses and calculate W040 and the total spherical aberration.
Compare. The split lenses should have the same shape factor.
d) Increase the index to 1.8 of the lenses in part a) and calculate W040 and the total spherical aberration.
Compare for the f/2, f/4, and f/8 cases.
e) Bend the split f/4 lens (both lenses to have the same shape) and plot total spherical aberration vs. shape
factor.
f) Aspherize the front surface of lens @ f/4 in part a) to cancel (correct) spherical aberration of all orders.
g) Aspherize the rear surface of lens @ f/4 in part a) to cancel (correct) spherical aberration of all orders.
h) Design a f/4, f=100, @ 633 nm cemented doublet made of BK7 and F4 glasses. Correct for spherical
aberration by choosing appropriate shape factors for the positive and negative lenses. See note below.
i) Break the cemented interface and find the appropriate thickness that reduces zonal spherical aberration.
Every part is worth 4 points.
Note that since we have more variables than needed, there is an infinite number of solutions for parts h and
i. Select a solution where the positive lens has about 2.6 times the total power and the negative lens 1.6
times.