QC 351 A7 no. 29 / 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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/621623 |
| Date | 10 September 1968 |
| Creators | Frieden, B. Roy |
| Publisher | Optical Sciences Center, University of Arizona (Tucson, Arizona) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | Technical Report |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Optical Sciences Technical Report 29 |
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