In grazing incidence optics, COMA gets eliminated if optics has an even number of reflections and not for an odd number of reflection. I tried with ray tracing simulations from 1-4 reflections. Can anyone help to understand analytically?
Dear Panini, If your optical system is all mirror system, symmetric about center aperture, with unity magnification, even number of reflections can totally eliminate coma, because of asymmetry of the aberration. Center aperture could be mirror, in this case the number of reflection becomes odd. Therefore, numeber of reflections is not necessary condition for coma free but it is as a result of symmetric optics, I think. Regards, Shigeo
I agree with above mentioned condition of symmetry of the stop and balance magnification. For coma free condition independent of field position this needs to be considered. In addition; from a single lens point of you coma is lens shape dependent so one could design a lens for zero coma for a given field point.
I can't be absolutely sure of this answer but it may well be the answer. Coma is an aberration type that is asymmetric in the power of the field angle term (assuming wee approximate the total aberration by a Taylor sweries expansion in field angle and aperture). Reflection is equivalent to refraction in which the ratio of the optical index media either side of the boundary is -1. So a pair of reflections will result in a pair of oppositely-directed coma terms and hence cancellation.
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