Abstract

The intensity distribution in the Fraunhofer diffraction patterns of slit and circular apertures illuminated with partially coherent light is examined both theoretically and experimentally. It is shown that a detailed knowledge of the mutual coherence function across the diffracting aperture is required to describe fully the diffraction phenomena.

© 1966 Optical Society of America

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References

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  1. G. B. Parrent and T. J. Skinner, Opt. Acta8, 93 (1961).
    [Crossref]
  2. E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).
  3. R. A. Shore, Proceedings of Symposium on Electromagnetic Theory and Antennas, Copenhagen, Denmark (Pergamon Press, London, June, 1962), p. 787.
  4. J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).
    [Crossref]
  5. W. T. Cathey, J. Opt. Soc. Am. 54, 1406A (1964).
  6. B. J. Thompson, International Commission for Optics Meeting on Interference and Coherence, Sydney, Australia (August 1964).
  7. B. J. Thompson, J. Opt. Soc. Am. 54, 1406A (1964).
  8. The equation is written out in full here since Eq. (42) of Ref. 1 contains some typographical errors.
  9. A. C. Schell, Ph.D. thesis, MIT (1961).
  10. This quantity is defined more exactly later in terms of the experimental parameters.

1964 (2)

W. T. Cathey, J. Opt. Soc. Am. 54, 1406A (1964).

B. J. Thompson, J. Opt. Soc. Am. 54, 1406A (1964).

1961 (1)

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).
[Crossref]

1954 (1)

E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).

Bakos, J.

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).
[Crossref]

Cathey, W. T.

W. T. Cathey, J. Opt. Soc. Am. 54, 1406A (1964).

Kantor, K.

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).
[Crossref]

Parrent, G. B.

G. B. Parrent and T. J. Skinner, Opt. Acta8, 93 (1961).
[Crossref]

Schell, A. C.

A. C. Schell, Ph.D. thesis, MIT (1961).

Shore, R. A.

R. A. Shore, Proceedings of Symposium on Electromagnetic Theory and Antennas, Copenhagen, Denmark (Pergamon Press, London, June, 1962), p. 787.

Skinner, T. J.

G. B. Parrent and T. J. Skinner, Opt. Acta8, 93 (1961).
[Crossref]

Thompson, B. J.

B. J. Thompson, J. Opt. Soc. Am. 54, 1406A (1964).

B. J. Thompson, International Commission for Optics Meeting on Interference and Coherence, Sydney, Australia (August 1964).

Wolf, E.

E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).

J. Opt. Soc. Am. (2)

B. J. Thompson, J. Opt. Soc. Am. 54, 1406A (1964).

W. T. Cathey, J. Opt. Soc. Am. 54, 1406A (1964).

Nuovo Cimento (1)

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).
[Crossref]

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

E. Wolf, Proc. Roy. Soc. (London) A225, 96 (1954).

Other (6)

R. A. Shore, Proceedings of Symposium on Electromagnetic Theory and Antennas, Copenhagen, Denmark (Pergamon Press, London, June, 1962), p. 787.

G. B. Parrent and T. J. Skinner, Opt. Acta8, 93 (1961).
[Crossref]

The equation is written out in full here since Eq. (42) of Ref. 1 contains some typographical errors.

A. C. Schell, Ph.D. thesis, MIT (1961).

This quantity is defined more exactly later in terms of the experimental parameters.

B. J. Thompson, International Commission for Optics Meeting on Interference and Coherence, Sydney, Australia (August 1964).

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Figures (11)

F. 1
F. 1

Coordinate system.

F. 2
F. 2

Theoretical Fraunhofer intensity distribution of a circular aperture illuminated by a circular source for various values of c. c = 0.25 (— · —); c = 1.0 (– – – –); c = 2.0 (— · · —); c = 5.0 (——); c = 10.0 (— ⋯ —).

F. 3
F. 3

Comparison between the theoretical intensity distributions for exponential and Besinc correlation for a circular aperture; (a) c = 0.25, (b) c = 1.0, (c) c = 2.0.

F. 4
F. 4

Theoretical Fraunhofer intensity distribution of a slit aperture illuminated by a circular source for various values of c. c = 0.5 (— · —), c = 0.75 (— · · —), c = 2.0 (– – – –), c = 4.0 (——), c = 10.0 (— ⋯ —), c = 20.0 (— · — · —).

F. 5
F. 5

Theoretical Fraunhofer intensity distribution for a slit aperture illuminated by a slit source for various values of c. = 0 (— · —), c = 0.5 (— · · —), c = 1.0 (– – – –), c = 2.0 (——), =4.0 (— ⋯ —), c = 10.0 (— · — · —), c = 20.0 (— · – – · —).

F. 6
F. 6

Experimental arrangement.

F. 7
F. 7

Experimental Fraunhofer intensity distribution for a circular aperture illuminated by a circular source for various values of c. c = 0.29 (— · —), c = 0.96 (– – – –), c = 1.53 (— · · —), c = 2.83 (——),c = 4.62(— ⋯ —).

F. 8
F. 8

Comparison between theoretical and experimental curves for a circular aperture illuminated by a circular source for c = 1.0. Experimental (– – – –), Theoretical (——).

F. 9
F. 9

Comparison between theoretical and experimental curves for a circular aperture illuminated by a circular source. Theoretical curve c = 5.0 (——), Experimental curve c = 4.62 (– – – –).

F. 10
F. 10

Experimental Fraunhofer intensity distribution for a slit aperture illuminated by a circular source for various values of c. c = 0.74 (— · —), c = 2.18 (– – – –), c = 3.58 (— · · —), c = 5.70 (——).

F. 11
F. 11

Theoretical Fraunhofer intensity distribution for comparison with Fig. 10. The key is identical to Fig. 10.

Tables (1)

Tables Icon

Table I Intensity values (showing the central minimum) near c = 4.5 for a circular aperture illuminated by a circular source.

Equations (6)

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I ( x ) = 1 ( a 2 / α 2 + x 2 ) 2 [ ( 1 + exp ( 2 a / α ) 2 ) × ( x 2 a 2 α 2 ) x 2 ( sin x x ) 2 + a α ( a 2 α 2 + x 2 ) + a 2 α ( a 2 α 2 x 2 ) cos 2 x exp ( 2 a α 1 ) 2 a α x 2 sin 2 x 2 x exp ( 2 a α ) ] ,
I p = | u 1 | 2 + | u 2 | 2 + 2 γ 12 ( 0 ) Re ( u 1 u 2 * ) .
I ( P ) = ( A cos 2 θ / λ ¯ 2 R 2 ) × γ ( S , 0 ) C ( S ) exp ( i k sin θ p ̂ S ) d S ,
I ( U , V ) = 1 V { Si ( V + U ) + Si ( V U ) 1 cos ( V U ) ( V U ) 1 cos ( V + U ) ( V + U ) } .
I ( U , 0 ) = [ sin ( U / 2 ) / U / 2 ] 2 ,
circular aperture , c = d / α = 2 π d r / λ f 1 slit aperture , c = a / α = 2 π a r / λ f 1 .