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    MAXIMUM ATTAINABLE MTF FOR ROTATIONALLY SYMMETRIC LENS SYSTEMS

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    Author
    Frieden, B. Roy
    Issue Date
    1968-09-10
    Keywords
    Optics.
    
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    Publisher
    Optical Sciences Center, University of Arizona (Tucson, Arizona)
    Rights
    Copyright © Arizona Board of Regents
    Collection Information
    This title from the Optical Sciences Technical Reports collection is made available by the College of Optical Sciences and the University Libraries, The University of Arizona. If you have questions about titles in this collection, please contact repository@u.library.arizona.edu.
    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.
    Description
    QC 351 A7 no. 29
    Series/Report no.
    Optical Sciences Technical Report 29
    Collections
    Optical Sciences Technical Reports

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