Effects of corrugation of aspherical mirrors on the optical performance of imaging optics with the mirror near an image plane

Abstract

We discuss an estimation method of production tolerance of an aspherical mirror located near an image plane of imaging optics. Local corrugation error having a period smaller than the footprint width of the illuminated area is considered. A simple periodic corrugation model using a radial trigonometric function is made. Related equations for ray-tracing calculations are derived. Also, analytical equations for calculating ray aberrations on the image plane are derived for the verification of ray tracing. Ray tracing simulations are made using optical parameters of example projection optics, which have a large aspherical mirror near the image plane and attain extraordinary large projection angles of 136 deg. The simulation result teaches that an increase of the rms spot radius on the image plane, as well as MTF degradation, depend on the maximum tilt angle of corrugation. This result is valid at the corrugation frequency higher than the reciprocal of half the meridional footprint width on the aspherical mirror as long as the scattering effect is ignored. In addition, minimum MTF against the maximum tilt angle of corrugation is calculated using the projection optics. If an admissible MTF degradation is assumed to be 10% at the Nyquist frequency (0.42 lp/mm) of the projected pixels having a pitch of 1.2 mm, the tolerance of the maximum tilt angle of corrugation is found to be 0.035 mrad at a relative field of 1.0, and the tolerance is increased to be 0.075 mrad at a relative field of 0.75.