Abstract

Photon-correlation experiments have verified the theoretical prediction of Baltes et al. that a phase grating hidden by a diffuser can be detected by correlation measurements. We have additionally demonstrated that a simpler method of detecting the presence of the grating, valid for arbitrarily fine diffusers, is to measure the temporal autocorrelation of the intensity of the scattered field at a single point.

© 1983 Optical Society of America

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References

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  1. H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
    [Crossref]
  2. H. P. Baltes, H. A. Ferwerda, IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
    [Crossref]
  3. H. P. Baltes, A. S. Glass, K. M. Jauch, Opt. Acta 28, 873–876 (1981).
    [Crossref]
  4. H. P. Baltes, K. M. Jauch, J. Opt. Soc. Am. 71, 1434–1439 (1981).
    [Crossref]
  5. A. S. Glass, H. P. Baltes, Opt. Acta 29, 169–185 (1982).
    [Crossref]
  6. A. S. Glass, H. P. Baltes, K. M. Jauch, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).
  7. K. M. Jauch, H. P. Baltes, Opt. Acta 28, 1013–1015 (1981).
    [Crossref]
  8. A. S. Glass, Opt. Acta 29, 575–583 (1982).
    [Crossref]
  9. K. M. Jauch, H. P. Baltes, Opt. Lett. 7, 127–129 (1982).
    [Crossref] [PubMed]
  10. K. M. Jauch, H. P. Baltes, A. S. Glass, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).
  11. P. F. Gray, Opt. Acta 25, 765–775 (1978).
    [Crossref]
  12. B. M. Levine, J. C. Dainty, Opt. Commun. 45, 252–257 (1983).
    [Crossref]
  13. J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Heidelberg, 1975), p. 63.
  14. H. Z. Cummins, E. R. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, London, 1974), p. 75.
  15. J. C. Dainty, in Progress in Optics XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1976), p. 1.
  16. K. A. O’Donnell, J. Opt. Soc. Am. 72, 191–197 (1982).
    [Crossref]
  17. T. Asakura, N. Takai, Appl. Phys. 25, 179–194 (1981).
    [Crossref]

1983 (1)

B. M. Levine, J. C. Dainty, Opt. Commun. 45, 252–257 (1983).
[Crossref]

1982 (6)

K. A. O’Donnell, J. Opt. Soc. Am. 72, 191–197 (1982).
[Crossref]

A. S. Glass, H. P. Baltes, Opt. Acta 29, 169–185 (1982).
[Crossref]

A. S. Glass, H. P. Baltes, K. M. Jauch, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

A. S. Glass, Opt. Acta 29, 575–583 (1982).
[Crossref]

K. M. Jauch, H. P. Baltes, Opt. Lett. 7, 127–129 (1982).
[Crossref] [PubMed]

K. M. Jauch, H. P. Baltes, A. S. Glass, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

1981 (6)

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
[Crossref]

H. P. Baltes, H. A. Ferwerda, IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[Crossref]

H. P. Baltes, A. S. Glass, K. M. Jauch, Opt. Acta 28, 873–876 (1981).
[Crossref]

H. P. Baltes, K. M. Jauch, J. Opt. Soc. Am. 71, 1434–1439 (1981).
[Crossref]

K. M. Jauch, H. P. Baltes, Opt. Acta 28, 1013–1015 (1981).
[Crossref]

T. Asakura, N. Takai, Appl. Phys. 25, 179–194 (1981).
[Crossref]

1978 (1)

P. F. Gray, Opt. Acta 25, 765–775 (1978).
[Crossref]

Asakura, T.

T. Asakura, N. Takai, Appl. Phys. 25, 179–194 (1981).
[Crossref]

Baltes, H. P.

K. M. Jauch, H. P. Baltes, A. S. Glass, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

K. M. Jauch, H. P. Baltes, Opt. Lett. 7, 127–129 (1982).
[Crossref] [PubMed]

A. S. Glass, H. P. Baltes, Opt. Acta 29, 169–185 (1982).
[Crossref]

A. S. Glass, H. P. Baltes, K. M. Jauch, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

K. M. Jauch, H. P. Baltes, Opt. Acta 28, 1013–1015 (1981).
[Crossref]

H. P. Baltes, K. M. Jauch, J. Opt. Soc. Am. 71, 1434–1439 (1981).
[Crossref]

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
[Crossref]

H. P. Baltes, H. A. Ferwerda, IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[Crossref]

H. P. Baltes, A. S. Glass, K. M. Jauch, Opt. Acta 28, 873–876 (1981).
[Crossref]

Dainty, J. C.

B. M. Levine, J. C. Dainty, Opt. Commun. 45, 252–257 (1983).
[Crossref]

J. C. Dainty, in Progress in Optics XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1976), p. 1.

Ferwerda, H. A.

H. P. Baltes, H. A. Ferwerda, IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[Crossref]

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
[Crossref]

Glass, A. S.

A. S. Glass, H. P. Baltes, K. M. Jauch, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

A. S. Glass, Opt. Acta 29, 575–583 (1982).
[Crossref]

A. S. Glass, H. P. Baltes, Opt. Acta 29, 169–185 (1982).
[Crossref]

K. M. Jauch, H. P. Baltes, A. S. Glass, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
[Crossref]

H. P. Baltes, A. S. Glass, K. M. Jauch, Opt. Acta 28, 873–876 (1981).
[Crossref]

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Heidelberg, 1975), p. 63.

Gray, P. F.

P. F. Gray, Opt. Acta 25, 765–775 (1978).
[Crossref]

Jauch, K. M.

K. M. Jauch, H. P. Baltes, A. S. Glass, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

K. M. Jauch, H. P. Baltes, Opt. Lett. 7, 127–129 (1982).
[Crossref] [PubMed]

A. S. Glass, H. P. Baltes, K. M. Jauch, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

K. M. Jauch, H. P. Baltes, Opt. Acta 28, 1013–1015 (1981).
[Crossref]

H. P. Baltes, K. M. Jauch, J. Opt. Soc. Am. 71, 1434–1439 (1981).
[Crossref]

H. P. Baltes, A. S. Glass, K. M. Jauch, Opt. Acta 28, 873–876 (1981).
[Crossref]

Levine, B. M.

B. M. Levine, J. C. Dainty, Opt. Commun. 45, 252–257 (1983).
[Crossref]

O’Donnell, K. A.

K. A. O’Donnell, J. Opt. Soc. Am. 72, 191–197 (1982).
[Crossref]

Steinle, B.

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
[Crossref]

Takai, N.

T. Asakura, N. Takai, Appl. Phys. 25, 179–194 (1981).
[Crossref]

Appl. Phys. (1)

T. Asakura, N. Takai, Appl. Phys. 25, 179–194 (1981).
[Crossref]

IEEE Trans. Antennas Propag. (1)

H. P. Baltes, H. A. Ferwerda, IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[Crossref]

J. Opt. Soc. Am. (2)

H. P. Baltes, K. M. Jauch, J. Opt. Soc. Am. 71, 1434–1439 (1981).
[Crossref]

K. A. O’Donnell, J. Opt. Soc. Am. 72, 191–197 (1982).
[Crossref]

Opt. Acta (6)

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, Opt. Acta 28, 11–28 (1981).
[Crossref]

P. F. Gray, Opt. Acta 25, 765–775 (1978).
[Crossref]

A. S. Glass, H. P. Baltes, Opt. Acta 29, 169–185 (1982).
[Crossref]

H. P. Baltes, A. S. Glass, K. M. Jauch, Opt. Acta 28, 873–876 (1981).
[Crossref]

K. M. Jauch, H. P. Baltes, Opt. Acta 28, 1013–1015 (1981).
[Crossref]

A. S. Glass, Opt. Acta 29, 575–583 (1982).
[Crossref]

Opt. Commun. (1)

B. M. Levine, J. C. Dainty, Opt. Commun. 45, 252–257 (1983).
[Crossref]

Opt. Lett. (1)

K. M. Jauch, H. P. Baltes, Opt. Lett. 7, 127–129 (1982).
[Crossref] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

K. M. Jauch, H. P. Baltes, A. S. Glass, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

A. S. Glass, H. P. Baltes, K. M. Jauch, Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

Other (3)

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Heidelberg, 1975), p. 63.

H. Z. Cummins, E. R. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, London, 1974), p. 75.

J. C. Dainty, in Progress in Optics XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1976), p. 1.

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Figures (4)

Fig. 1
Fig. 1

Experimental arrangement.

Fig. 2
Fig. 2

Theoretical average intensity in the far field of phase grating–diffuser combinations: (a) L/b = 1.0, (b) L/b = 0.50, and (c) L/b = 0.33. (L is the 1/e correlation length of the complex amplitude transmittance of the diffuser and b is the period of the sinusoidal phase grating).

Fig. 3
Fig. 3

Peak values of the intensity cross-correlation measured at angles (−θ0, θ0) as a function of L/b.

Fig. 4
Fig. 4

The temporal-intensity autocorrelation function measured at the center of the far field with parameters L ≈ 1 μm, b = 9.2 μm, a = 0.33 mm, υξ ≈ 50 mm sec−1, and υη ≈ 560 mm sec−1. Note that the period of the modulation is b/υξ.

Equations (15)

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U ( ξ ) = P ( ξ ) e i φ ( ξ ) T ( ξ ) ,
P ( ξ ) = I 0 1 / 2 exp ( ξ 2 / 4 a 2 ) ,
T ( ξ ) = exp [ i α sin ( 2 π ξ / b ) ] ,
exp { i [ φ ( ξ 1 ) φ ( ξ 2 ) ] } exp ( | ξ 1 ξ 2 | 2 / 2 L 2 ) ,
L = l h / [ 2 π ( n 1 ) σ h λ ] ,
T ( ξ ) = exp [ i α sin ( 2 π ξ / b ) ] = n = g n exp ( i 2 π n ξ / b ) ,
Γ ( x 1 , x 2 ) = U ( ξ 1 ) U * ( ξ 2 ) × exp [ i 2 π λ R ( x 1 ξ 1 x 2 ξ 2 ) ] d ξ 1 d ξ 2 ,
γ ( x 1 , x 2 ) = Γ ( x 1 , x 2 ) [ Γ ( x 1 , x 1 ) Γ ( x 2 , x 2 ) ] 1 / 2 .
γ ( s , σ ) = n , m = g m g n exp { 1 2 k 2 a 2 [ σ ( m n ) λ b ] 2 } exp { 1 2 k 2 L 2 [ s 1 2 ( m + n ) λ b ] 2 } { n | g n | 2 exp [ 2 π 2 L 2 b 2 ( s + σ 2 n λ b ) 2 ] } 1 / 2 { n | g n | 2 exp [ 2 π 2 L 2 b 2 ( s σ 2 n λ b ) 2 ] } 1 / 2 ,
C I ( x 1 , x 2 ) = I ( x 1 ) I ( x 2 ) I ( x 1 ) I ( x 2 ) 1 .
C I ( x 1 , x 2 ) = | γ ( x 1 , x 2 ) | 2 .
φ [ ξ ( t ) , η ( t ) ] = φ ( ξ υ ξ t , η υ η t ) .
exp ( i { φ [ ξ 1 ( t ) , η 1 ( t ) ] φ [ ξ 2 ( t + τ ) , η 2 ( t + τ ) ] } ) exp [ ( | ξ 1 ξ 2 υ ξ τ | 2 + | η 1 η 2 υ η τ | 2 ) / 2 L 2 ] ,
Re [ γ ( s x , 0 , σ x , 0 , τ ) ] exp ( | v | 2 τ 2 / 8 a 2 ) × n , m ( cos [ 2 π υ ξ τ b ( s x sin θ 0 n + m 2 ) ] g n g m × exp { 1 2 k 2 a 2 [ σ x ( n m ) λ b ] 2 } × exp { 1 2 k 2 L 2 [ s x 1 2 ( n + m ) λ b ] 2 } ) ,
C I ( 0 , 0 , 0 , 0 , τ ) exp ( | v | 2 τ 2 / 4 a 2 ) [ | g 0 | 2 + 4 | g 1 | 2 exp ( 2 π 2 L 2 b 2 ) cos ( 2 π υ ξ τ b ) ] | g 0 | 2 + 4 | g 1 | 2 exp ( 2 π 2 L 2 b 2 ) .

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