Download 2017-OPTI-518-HW-7

OPTI518
Introduction to aberrations
Each problem is worth 10 points.
HW #7
1) Prove the identity between vectors A , B , and C :


 


2 A  B A  C  A  A B  C  A2  BC


2
2) Assume that a system has 4 waves of quadratic astigmatism: W222 H   and 2
waves of uniform astigmatism: W02002  i    . Determine where in the field the
2
nodes are located. Provide a figure that illustrates the field.
3) What should be the condition in a two-mirror system that is plane symmetric so
that there is no anamorphic distortion or uniform astigmatism? Give a physical
interpretation.
4) Is it true that if in a plane symmetric system made out of reflective surfaces is
corrected for field tilt, then there is no linear astigmatism?
5) A yolo telescope has a concave primary mirror and a concave secondary mirror.
Both are tilted as to avoid obscuration in the beam of light. Spherical aberration is
corrected with the conic constant of the primary, uniform astigmatism with a
cylindrical deformation on the secondary, and uniform coma by the tilt of the
secondary. If Rp and Rs are the radii of curvature of the mirrors, t is the mirror
spacing, and alpha and beta are the mirror tilts with respect to the optical axis ray
(ORA), then determine, beta given alpha so that there is no uniform coma.
Optional: provide Rs and Rt of the secondary mirror so that there is no uniform
astigmatism, and provide the conic constant of the primary so that there is no
spherical aberration.
6) A Cassegrain type system is designed so that when the secondary mirror is
laterally displaced no uniform-coma is created. The system is also corrected for
spherical aberration. Determine what the conic constants for the primary and the
secondary mirrors are.
See for example: Two-mirror telescope design with third-order coma insensitive
to decenter misalignment, Optics Express, Vol. 21, Issue 6, pp. 6851-6865 (2013).