Abstract

The Strehl ratio, in the form of McCutchen’s theorem, is employed to design a spatial filter that increases the depth of focus. Computer-simulated images show the increment in focal depth.

© 1985 Optical Society of America

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References

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  1. Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981).
    [CrossRef]
  2. Y. Li, J. Opt. Soc. Am. 72, 770 (1982).
    [CrossRef]
  3. G. Häusler, E. Körner, Appl. Opt. 23, 2468 (1984).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, J. Ojeda-Castaneda, N. Streibl, Opt. Acta 30, 399 (1983).
    [CrossRef]
  5. A. W. Lohmann, Optik 51, 105 (1978).
  6. N. Streibl, Opt. Commun. 49, 6 (1984).
    [CrossRef]
  7. J. Ojeda-Castaneda, J. Opt. Soc. Am. 73, 1042 (1983).
    [CrossRef]
  8. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, Opt. Lett. 8, 458 (1983).
    [CrossRef] [PubMed]
  9. G. Indebetouw, H. Bai, Appl. Opt. 23, 4299 (1984).
    [CrossRef] [PubMed]
  10. C. Varamit, G. Indebetouw, J. Opt. Soc. Am. A 2, 799 (1985).
    [CrossRef]
  11. K. Strehl, Z. Instrumentenkd. 22, 213 (1903).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 462.
  13. C. W. McCutchen, J. Opt. Soc. Am. 54, 240 (1964).
    [CrossRef]

1985 (1)

1984 (3)

1983 (3)

1982 (1)

1981 (1)

Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

1978 (1)

A. W. Lohmann, Optik 51, 105 (1978).

1964 (1)

1903 (1)

K. Strehl, Z. Instrumentenkd. 22, 213 (1903).

Bai, H.

Berriel-Valdos, L. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 462.

Häusler, G.

Indebetouw, G.

Körner, E.

Li, Y.

Y. Li, J. Opt. Soc. Am. 72, 770 (1982).
[CrossRef]

Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castaneda, N. Streibl, Opt. Acta 30, 399 (1983).
[CrossRef]

A. W. Lohmann, Optik 51, 105 (1978).

McCutchen, C. W.

Montes, E.

Ojeda-Castaneda, J.

Strehl, K.

K. Strehl, Z. Instrumentenkd. 22, 213 (1903).

Streibl, N.

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

A. W. Lohmann, J. Ojeda-Castaneda, N. Streibl, Opt. Acta 30, 399 (1983).
[CrossRef]

Varamit, C.

Wolf, E.

Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 462.

Appl. Opt. (2)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

A. W. Lohmann, J. Ojeda-Castaneda, N. Streibl, Opt. Acta 30, 399 (1983).
[CrossRef]

Opt. Commun. (2)

Y. Li, E. Wolf, Opt. Commun. 39, 211 (1981).
[CrossRef]

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Opt. Lett. (1)

Optik (1)

A. W. Lohmann, Optik 51, 105 (1978).

Z. Instrumentenkd. (1)

K. Strehl, Z. Instrumentenkd. 22, 213 (1903).

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 462.

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Figures (3)

Fig. 1
Fig. 1

Generalized pupil function and Strehl ratio for (a) a clear pupil, (b) the spatial filter in Ref. 8, (c) the spatial filter in expression (10).

Fig. 2
Fig. 2

Out-of-focus images, w20 = λ/4, of a wheel target for (a) a clear pupil, (b) the spatial filter in Ref. 8, (c) the spatial filter in expression (10).

Fig. 3
Fig. 3

Same as Fig. 2, but with w20 = λ.

Equations (15)

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p ( r , z ) = 2 π 0 p ˜ ( ρ ) exp ( i π λ z ρ 2 ) J 0 ( 2 π ρ r ) ρ d ρ ,
S ( z ) = p ( r = 0 , z ) 2 / p ( r = 0 , z = 0 ) 2 .
S ( z ) = | - q ˜ ( ζ ) exp ( i 2 π z ζ ) d ζ | 2 ,
ζ = λ ρ 2 / 2 ,             q ˜ ( ζ ) = p ˜ ( ρ ) / p ( 0 , 0 ) .
q ( z ) = - q ˜ ( ζ ) exp ( i 2 π z ζ ) d ζ ,
q ˜ ( ζ ) = - q ( z ) exp ( - 2 π z ζ ) d z .
q ˜ ( ζ ) = rect [ ( ζ - ζ 0 / 2 ) / ζ 0 ] ,             s ( z ) = sinc ( π ζ 0 z ) 2 ,
q ˜ ( ζ ) = sinc ( π z 0 ζ ) ,             s ( z ) = rect ( z / z 0 ) .
q ˜ ( ζ ) = sinc ( π z 0 ζ ) rect [ ( ζ - ζ 0 / 2 ) / ζ 0 ]
q ( z ) ~ rect ( z / z 0 )             if z 0 = 1 / ζ 0 .
p ˜ ( ρ ) = sinc ( π ρ 2 / ρ 0 2 ) s ( z ) ~ rect [ z / ( λ ρ 0 2 / 2 ) - 1 ] ,
z = 1 / ( 2 λ ρ 0 2 ) , 2 / ( λ ρ 0 2 ) ,
w 20 = λ / 4 , λ
exp ( i π λ z ρ 2 ) = exp ( i k w 20 ρ 2 / ρ 0 2 ) ,
w 20 = ( λ 2 ρ 0 2 ) z / 2 ,

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