MAXIMUM ATTAINABLE MTF FOR ROTATIONALLY SYMMETRIC LENS SYSTEMS

Abstract

Most optical systems have rotational symmetry. For such systems, we establish a method of finding (a) the maximum attainable modulation transfer function (MTF) at arbitrary frequency wo; and (b) the required pupil function U(wo;p). Physically, the latter comprises absorbing films in the pupil of diffraction -limited optics. The method of solution is numerical and iterative, based on the Newton -Raphson algorithm. Solutions (a) and (b) are established at frequencies wo = 0.1, 0.2, ..., 0.9 (x optical cutoff). The computed (a) are correct to ±0.0001 over all wo indicated. Quantities (b) have an average error over each pupil of ±0.002 for frequencies wo <- 0.5. With 0.6 s wo <- 0.9, the error is 0.01. The curve of maximum MTF(wo) seems smooth enough to allow for accurate interpolation. Solutions (a) and (b) were also found over the finer subdivision wo = 0.05, 0.1, 0.15, ..., 0.8 with slightly less accuracy than above, in order to allow for interpolation of pupils U(wo;p) over values wo. This seems possible for 0.05 < wo < 0.40. The maximum MTF(wo) shows appreciable gain (e.g., 8% at wo = 0.2) over the MTF for uncoated, diffraction -limited optics at all wo except in the inter- mediate region 0.4 <- wo <- 0.6. In the high - frequency band 0.5 <- wo <- 1.0, however, the maximum MTF(wo) shows little gain over the MTF due to an uncoated, diffraction -limited pupil with the proper central obscuration. The light loss due to each U(wo;p) may be measured by the total energy transmission and the Strehl flux ratio. These are plotted against wo, .and indicate moderate light loss.