Abstract

We present a technique for measuring the degree of coherence that is based on the self-imaging phenomenon. The technique is lensless, has multiplexing capabilities, and can work with high light throughput. Experimental verifications are given.

© 1993 Optical Society of America

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References

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  1. B. J. Thompson, E. Wolf, J. Opt. Soc. Am. 47, 895 (1957).
    [CrossRef]
  2. T. Asakura, H. Fujii, K. Murata, Opt. Acta 19, 273 (1972).
    [CrossRef]
  3. M. Michalski, E. E. Sicre, H. J. Rabal, Opt. Lett. 10, 585 (1985).
    [CrossRef] [PubMed]
  4. F. T. S. Yu, F. K. Hsu, T. H. Chao, Appl. Opt. 23, 333 (1984).
    [CrossRef] [PubMed]
  5. J. Ojeda-Castaneda, E. E. Sicre, Opt. Commun. 59, 87 (1986).
    [CrossRef]
  6. S. Chitraleka, K. V. Avudainayagam, S. V. Pappu, Appl. Opt. 29, 125 (1990).
    [CrossRef]
  7. J. Tu, L. Zhan, Opt. Commun. 82, 229 (1991).
    [CrossRef]
  8. G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977), p. 167.

1991 (1)

J. Tu, L. Zhan, Opt. Commun. 82, 229 (1991).
[CrossRef]

1990 (1)

1986 (1)

J. Ojeda-Castaneda, E. E. Sicre, Opt. Commun. 59, 87 (1986).
[CrossRef]

1985 (1)

1984 (1)

1972 (1)

T. Asakura, H. Fujii, K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

1957 (1)

Asakura, T.

T. Asakura, H. Fujii, K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Avudainayagam, K. V.

Chao, T. H.

Chitraleka, S.

Fujii, H.

T. Asakura, H. Fujii, K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Hsu, F. K.

Michalski, M.

Murata, K.

T. Asakura, H. Fujii, K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, E. E. Sicre, Opt. Commun. 59, 87 (1986).
[CrossRef]

Pappu, S. V.

Rabal, H. J.

Rogers, G. L.

G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977), p. 167.

Sicre, E. E.

Thompson, B. J.

Tu, J.

J. Tu, L. Zhan, Opt. Commun. 82, 229 (1991).
[CrossRef]

Wolf, E.

Yu, F. T. S.

Zhan, L.

J. Tu, L. Zhan, Opt. Commun. 82, 229 (1991).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

T. Asakura, H. Fujii, K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Opt. Commun. (2)

J. Ojeda-Castaneda, E. E. Sicre, Opt. Commun. 59, 87 (1986).
[CrossRef]

J. Tu, L. Zhan, Opt. Commun. 82, 229 (1991).
[CrossRef]

Opt. Lett. (1)

Other (1)

G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977), p. 167.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the proposed setup: (a) standard setup, (b) grating rotated by an angle θ.

Fig. 2
Fig. 2

(a) Graphical representation of sampling the complex degree of coherence; (b) sampling at intervals 2Qd cos θ along the x axis.

Fig. 3
Fig. 3

Irradiance distributions, measured in arbitrary units along a line, at the detection plane for (a) θ = 0°, (b) θ = 37.5°, and (c) θ = 90°.

Equations (18)

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t ( x , y ) = m = + n = + a m , n exp [ i 2 π ( x m + y n ) / d ] .
U ( x , y ) = m = + n = + c m , n exp ( i 2 π { m [ x + ( R / R 0 ) ξ ] + n [ y + ( R / R 0 ) η ] } / d ) ,
d = ( 1 + R / R 0 ) d
c m , n = a m , n exp [ i π λ ( 1 / R 0 + 1 / R ) 1 ( m 2 + n 2 ) / d 2 ] .
P ( x , y ; ξ , η ) = | U ( x , y ) | 2 = m = + n = + f m , n exp ( i 2 π { m [ x + ( R / R 0 ) ξ ] + n [ y + ( R / R 0 ) η ] } / d ) ,
f m , n = exp [ i π λ ( 1 / R 0 1 / R ) 1 ( m 2 + n 2 ) / d 2 ] × r = + s = + a m + r , n + s a r , s * × exp [ i π λ ( 1 / R 0 1 / R ) 1 ( 2 m r + 2 n s ) / d 2 ] .
I ( x , y ) = + I 0 ( ξ , n ) P ( x , y ; ξ , n ) d ξ d η = m = + n = + f m , n exp [ i 2 π ( m x + n y ) / d ] × + I 0 ( ξ , n ) exp [ i 2 π ( R / R 0 ) ( m ξ + n η ) / d ] d ξ d η = m = + n = + f m , n I ˜ 0 ( m R / R 0 d , n R / R 0 d ) × exp [ i 2 π ( m x + n y ) / d ] ,
I ˜ 0 ( u , υ ) = + I 0 ( ξ , n ) exp [ i 2 π ( u ξ + υ η ) ] d ξ d η .
Δ x = m λ R / d , Δ y = n λ R / d ,
Δ x = ( m λ / d ) ( 1 / R 0 + 1 / R ) 1 , Δ y = ( n λ / d ) ( 1 / R 0 + 1 / R ) 1 .
( 1 / R 0 + 1 / R ) 1 = 2 ( Q + q ) d 2 / λ , Q = 0 , ± 1 , ± 2 , , 0 q < 1 ,
Δ x = 2 m ( Q + q ) d , Δ y = 2 n ( Q + q ) d .
I ( x , y ) = m = + n = + f m , n exp { i 2 π [ ( m cos θ n sin θ ) x + ( n cos θ + m sin θ ) y ] / d } + I 0 ( ξ , n ) × exp { i 2 π ( R / R 0 ) [ ( m cos θ n sin θ ) ξ + ( n cos θ + m sin θ ) η ] / d } d ξ d η = m = + n = + f m , n Γ [ ( m cos θ n sin θ ) 2 ( Q + q ) d , ( n cos θ + m sin θ ) 2 ( Q + q ) d ] × exp { i 2 π [ ( m cos θ n sin θ ) x + ( n cos θ + m sin θ ) y ] / d } .
I 0 ( ξ , η ) = ( W 1 W 2 ) 1 rect ( ξ / W 1 ) rect ( η / W 2 ) ,
Γ ( Δ x , Δ y ) = sinc ( W 1 Δ x / λ R 0 ) sinc ( W 2 Δ y / λ R 0 ) ,
I ( x , y ) = τ { 1 + 2 m = 1 + sinc ( τ m ) sinc ( W 1 m 2 Q d cos θ / λ R 0 ) × sinc ( W 2 m 2 Q d sin θ / λ R 0 ) × cos [ 2 π m ( x cos θ + y sin θ ) / d ] } .
2 Q d L x ,
L x 2 M Q d .

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