Violation of Abbe's sine condition is well-known to cause coma in axisymmetric imaging systems, and generally any
offense against the sine condition (OSC) will cause aberrations that have linear dependence on the field angle. A well-corrected
imaging system must obey the Abbe sine condition. A misaligned optical system can have particular forms of
the OSC which are evaluated here. The lowest order non-trivial effects of misalignment have quadratic pupil
dependence which causes a combination of astigmatism and focus that have linear field dependence. Higher order terms
can arise from complex systems, but the effects of misalignment are nearly always dominated by the lowest order effects
which can be fully characterized by measuring images on axis and the on-axis offense against the sine condition. By
understanding the form of the on-axis images and the OSC, the state of alignment can be determined.
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