Abstract

Purcell and Koomen have shown [ J. D. Purcell and M. J. Koomen, Coronagraph with Improved Scattered-Light Properties, Report of NRL Progress, 1962 ( U.S. GPO, Washington, D.C., 1962)] that a toothed occulting disk greatly reduces diffraction problems in coronagraphy. In the present paper, the use of toothed apertures to reduce diffraction errors in radiometry is studied in detail. Simple formulas are derived which allow the design of toothed apertures for given applications. Experimental measurements are presented which demonstrate the usefulness of toothed apertures to reduce diffraction errors by at least an order of magnitude. This technique is shown to be particularly useful for radiometric measurements involving a series of apertures; in such cases, the diffraction errors of the individual apertures can simply add up, resulting in important over-all errors if ordinary circular apertures are used.

© 1978 Optical Society of America

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References

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  1. W. R. Blevin, Metrologia 6, 39 (1970).
    [Crossref]
  2. W. H. Steel, M. De, J. A. Bell, J. Opt. Soc. Am. 62, 1099 (1972).
    [Crossref]
  3. L. P. Boivin, Appl. Opt. 14, 2002 (1975).
    [Crossref] [PubMed]
  4. L. P. Boivin, Appl. Opt. 15, 1204 (1976).
    [Crossref] [PubMed]
  5. J. D. Purcell, M. J. Koomen, Coronagraph with Improved Scattered-Light Properties, Report of NRL Progresss, 1962 (U.S. GPO, Washington, D.C., 1962).
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), Sec. 8.9.
  7. L. P. Boivin, Appl. Opt. 16, 377 (1977).
    [Crossref] [PubMed]

1977 (1)

1976 (1)

1975 (1)

1972 (1)

1970 (1)

W. R. Blevin, Metrologia 6, 39 (1970).
[Crossref]

Bell, J. A.

Blevin, W. R.

W. R. Blevin, Metrologia 6, 39 (1970).
[Crossref]

Boivin, L. P.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), Sec. 8.9.

De, M.

Koomen, M. J.

J. D. Purcell, M. J. Koomen, Coronagraph with Improved Scattered-Light Properties, Report of NRL Progresss, 1962 (U.S. GPO, Washington, D.C., 1962).

Purcell, J. D.

J. D. Purcell, M. J. Koomen, Coronagraph with Improved Scattered-Light Properties, Report of NRL Progresss, 1962 (U.S. GPO, Washington, D.C., 1962).

Steel, W. H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), Sec. 8.9.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Metrologia (1)

W. R. Blevin, Metrologia 6, 39 (1970).
[Crossref]

Other (2)

J. D. Purcell, M. J. Koomen, Coronagraph with Improved Scattered-Light Properties, Report of NRL Progresss, 1962 (U.S. GPO, Washington, D.C., 1962).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964), Sec. 8.9.

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Figures (8)

Fig. 1
Fig. 1

Configuration of the toothed apertures.

Fig. 2
Fig. 2

Schematic diagram of a typical radiometric system.

Fig. 3
Fig. 3

Measured diffraction errors as a function of tooth depth for 7-mm and 15-mm diam apertures. Zero tooth depth corresponds to a smooth circular aperture; otherwise the apertures have sixty teeth of the indicated tooth depth.

Fig. 4
Fig. 4

7-mm diam toothed apertures all having approximately the same tooth depth (0.1 mm) and having 120 (A), 90 (B), 60 (C), 36 (D), and 20 (E) teeth. Left: photographs of the edges of the apertures (magnification is about 26×). Center: configurations of the apertures, including ray tracings showing the diffracted rays and their envelopes. Right: photographs of the corresponding diffraction patterns.

Fig. 5
Fig. 5

Diffraction pattern corresponding to a smooth circular 7-mm diam aperture.

Fig. 6
Fig. 6

Measured diffraction errors for the apertures of Figs. 4 and 5. The theoretical diameter of the diffraction-free region is calculated using Eqs. (1) and (2).

Fig. 7
Fig. 7

Photograph of the edge of the 4-mm diam aperture having 120 teeth. The magnification is about 75×.

Fig. 8
Fig. 8

Measured diffraction errors for a series of apertures. The squares and circles give the values for the smooth edged and toothed apertures, respectively. The apertures have a diameter of 7 mm. The solid curve is the theoretical prediction. The measurement uncertainty is about ±0.05% in all cases.

Equations (7)

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X = R cos ( θ + ϕ ) ,
tan θ = ( R sin ϕ ) / [ R ( 1 cos ϕ ) + Δ ] .
D = 2 [ ( a + b ) / a ] X ,
= ( λ e b ) / ( π 2 R r ) ,
U d edge exp [ i K ( r + s ) ] d l ,
δ = 2 π λ R Δ ( a + b ) a b ,
Δ π = ( λ a b ) / [ 2 R ( a + b ) ] .

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