Abstract

In order to confirm the theoretical results for the modulation transfer of an optical system with varying amounts of astigmatism it is first necessary to devise a method for introducing the required amount of astigmatism. This was very simply achieved using a low-power cylindrical spectacle lens. The modulation transfer for lines oriented parallel, perpendicular and at 45° to the tangential plane was measured using the interferometer described in a previous paper and good agreement was found between theory and experiment.

© 1964 Optical Society of America

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References

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  1. A. J. Montgomery, J. Opt. Soc. Am. 54, 191 (1964).
    [Crossref]
  2. M. De, Proc. Roy. Soc. (London) A233, 91 (1955); thesis, University of London, 1956.
  3. Max Herzberger, Opt. Acta 7, 239 (1960).

1964 (1)

1960 (1)

Max Herzberger, Opt. Acta 7, 239 (1960).

1955 (1)

M. De, Proc. Roy. Soc. (London) A233, 91 (1955); thesis, University of London, 1956.

De, M.

M. De, Proc. Roy. Soc. (London) A233, 91 (1955); thesis, University of London, 1956.

Herzberger, Max

Max Herzberger, Opt. Acta 7, 239 (1960).

Montgomery, A. J.

J. Opt. Soc. Am. (1)

Opt. Acta (1)

Max Herzberger, Opt. Acta 7, 239 (1960).

Proc. Roy. Soc. (London) (1)

M. De, Proc. Roy. Soc. (London) A233, 91 (1955); thesis, University of London, 1956.

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Figures (6)

Fig. 1
Fig. 1

Representation of astigmatism as a wavefront aberration.

Fig. 2
Fig. 2

Arrangement for the introduction of pure astigmatism.

Fig. 3
Fig. 3

Arrangement for the measurement of focal length.

Fig. 4
Fig. 4

Measurement of astigmatic foci. W22=nλ/π, ψ=90°. The actual focal shifts for the values of n from 1–4 are: (1) as measured from the relative response curves, 1.25, 2.60, 4.00, 5.50; (2) from fringe measurements, 1.23, 2.50, 3.86, 5.41; and (3) as calculated, 1.26, 2.60, 4.00, 5.50.

Fig. 5
Fig. 5

Modulation transfer in the presence of astigmatism—curves taken at midplane. W22=nλ/π, ψ=0° or 90°. The points marked are the theoretical results of De.

Fig. 6
Fig. 6

Modulation transfer in the presence of astigmatism—Curves taken at midplane. W22=nλ/π, ψ=45°. The points marked are the theoretical results of De.

Equations (7)

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W 22 σ 2 r 2 cos 2 ϕ ,
W ( r , ϕ ) = W 20 r 2 + W 22 r 2 cos 2 ϕ ,
W ( x , y ) = W 20 x 2 + ( W 20 + W 22 ) y 2 .
x = x cos ψ - y sin ψ , y = y cos ψ + x sin ψ .
W ( x , y ) = W 20 ( x 2 + y 2 ) + W 22 ( x 2 sin 2 ψ + y 2 cos 2 ψ + x y sin 2 ψ ) ,
δ = W ( x + s / 2 , y ) - W ( x - s / 2 , y ) , = s 2 ( W 20 + W 22 sin 2 ψ ) x + W 22 y sin 2 ψ ,
δ = s ( 2 W 20 + W 22 ) x + W 22 y .