Axially symmetric telescopes produce well known "Seidel" off-axis third-order
aberration patterns: coma, astigmatism, curvature of field and distortion. When
axial symmetry is broken by the small misalignments of optical elements,
additional third-order aberration patterns arise: one each for coma,
astigmatism and curvature of field and two for distortion. Each of these
misalignment patterns is characterized by an associated two-dimensional vector,
each of which in turn is a linear combination of the tilt and decenter vectors
of the individual optical elements. For an N-mirror telescope, 2(N-1) patterns
must be measured to keep the telescope aligned. Alignment of the focal plane
may require two additional patterns. For N = 3, as in a three mirror
anastigmat, there is a two-dimensional "subspace of benign misalignment" over
which the misalignment patterns for third-order coma, astigmatism and curvature
of field are identically zero. One would need to measure at least one of the
two distortion patterns to keep the telescope aligned. Alternatively, one might
measure one of the fifth-order misalignment patterns, which are derived herein.
But the fifth-order patterns are rather insensitive to misalignments, even with
moderately wide fields, rendering them of relatively little use in telescope
alignment. Another alternative would be to use telescope pointing as part of
the alignment solution.Comment: 50 pages, 13 figures, Accepted for Publication in PAS