Abstract

Apodizations with decreasing transmissions and with central obstructions transmute the point spread functions in image size and in the distribution of image irradiance. The distributions are characterized by the envelope functions which are exponential functions descending with variable exponents. At high apodization levels and lower central obstruction (<0.1) new extended radial zones in the outer part of the central ring groups are formed. Such transmutations of the image functions are of more than theoretical interest, particularly if the irradiance levels in the outer ring zones are to be compared to background irradiance levels.

© 1983 Optical Society of America

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References

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  1. H. F. A. Tschunko, Appl. Opt. 18, 3770 (1979).
    [CrossRef] [PubMed]
  2. H. F. A. Tschunko, Appl. Opt. 18, 955 (1979).
    [CrossRef] [PubMed]

1979 (2)

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Figures (6)

Fig. 1
Fig. 1

Aperture parameters N1 = 2/(1 − a) and N2 = 1/a vs a, the central obstruction ratio.

Fig. 2
Fig. 2

Point spread functions I vs image radius for obstruction ratios a = 0.1 and 0.8 with normalized central irradiances.

Fig. 3
Fig. 3

Point-spread functions vs the image radius for various apodizations for the unobstructed aperture.

Fig. 4
Fig. 4

Point-spread functions for various apodization exponents n and central obstruction ratios a, I from 1 to 10−6 and x from 1 to 100 (log–log) in optical units. An optical unit is equal to λ ·FN/π, where λ = wave lengths, focal number FN = focal length/aperture diameter.

Fig. 5
Fig. 5

Radius of the image center spot x0 for various apodizations n vs central obstruction a.

Fig. 6
Fig. 6

Point-spread functions for apodization exponent n = 2 and extended central obstructions a.

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