Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems

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.