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References

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  1. J. W. Goodman, J. Opt. Soc. Am. 57, 493, (1967).
    [Crossref] [PubMed]
  2. E. T. Whittaker and G. N. Watson, Modern Analysis, 4th Edition (Cambridge University Press, London, 1927), p. 65.
  3. A. A. Friesem, A. Kozma, and G. Adams, Appl. Opt. 6, 861 (1967).
    [Crossref]
  4. The curve is normalized in such a way that a unit exposure, which in this case is taken to be the exposure produced by the reference beam, produces a transmittance which is centered on the linear portion of the Ta–E curve.
  5. W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw–Hill Book Company, New York, 1958), p. 183.
  6. This is analogous to electrical time signals, where the frequency bandwidth of the measurement filter must be much greater than the reciprocal of the measurement time to provide a good estimate of the power spectrum. See, for instance, R. B. Blackman and J. W. Tukey, Measurement of Power Spectra (Dover Publications, Inc., New York, 1958).
  7. E. N. Leith, Phot. Sci. Eng. 6, 75 (1962).
  8. C. B. Burckhardt, J. Opt. Soc. Am. 56, 1449A (1966).
    [Crossref]
  9. Burckhardt gives values for Φτ′τ′(f) from 200 l/mm to 750 l/mm. We assume that the experimental curve may be extrapolated to lower and higher spatial frequencies.

1967 (2)

1966 (1)

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1449A (1966).
[Crossref]

1962 (1)

E. N. Leith, Phot. Sci. Eng. 6, 75 (1962).

Adams, G.

Blackman, R. B.

This is analogous to electrical time signals, where the frequency bandwidth of the measurement filter must be much greater than the reciprocal of the measurement time to provide a good estimate of the power spectrum. See, for instance, R. B. Blackman and J. W. Tukey, Measurement of Power Spectra (Dover Publications, Inc., New York, 1958).

Burckhardt, C. B.

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1449A (1966).
[Crossref]

Davenport, W. B.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw–Hill Book Company, New York, 1958), p. 183.

Friesem, A. A.

Goodman, J. W.

Kozma, A.

Leith, E. N.

E. N. Leith, Phot. Sci. Eng. 6, 75 (1962).

Root, W. L.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw–Hill Book Company, New York, 1958), p. 183.

Tukey, J. W.

This is analogous to electrical time signals, where the frequency bandwidth of the measurement filter must be much greater than the reciprocal of the measurement time to provide a good estimate of the power spectrum. See, for instance, R. B. Blackman and J. W. Tukey, Measurement of Power Spectra (Dover Publications, Inc., New York, 1958).

Watson, G. N.

E. T. Whittaker and G. N. Watson, Modern Analysis, 4th Edition (Cambridge University Press, London, 1927), p. 65.

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, Modern Analysis, 4th Edition (Cambridge University Press, London, 1927), p. 65.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. W. Goodman, J. Opt. Soc. Am. 57, 493, (1967).
[Crossref] [PubMed]

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1449A (1966).
[Crossref]

Phot. Sci. Eng. (1)

E. N. Leith, Phot. Sci. Eng. 6, 75 (1962).

Other (5)

Burckhardt gives values for Φτ′τ′(f) from 200 l/mm to 750 l/mm. We assume that the experimental curve may be extrapolated to lower and higher spatial frequencies.

E. T. Whittaker and G. N. Watson, Modern Analysis, 4th Edition (Cambridge University Press, London, 1927), p. 65.

The curve is normalized in such a way that a unit exposure, which in this case is taken to be the exposure produced by the reference beam, produces a transmittance which is centered on the linear portion of the Ta–E curve.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw–Hill Book Company, New York, 1958), p. 183.

This is analogous to electrical time signals, where the frequency bandwidth of the measurement filter must be much greater than the reciprocal of the measurement time to provide a good estimate of the power spectrum. See, for instance, R. B. Blackman and J. W. Tukey, Measurement of Power Spectra (Dover Publications, Inc., New York, 1958).

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Figures (2)

Fig. 1
Fig. 1

Reconstruction of the real image. The hologram is assumed to be square with sides of length L. W is the reconstruction wave and C is its center of curvature. R is the reconstructed real image.

Fig. 2
Fig. 2

Optical system for measuring Φττ(p,q). I0 is the intensity of the monochromatic plane wave incident on P1;P1 contains the random complex amplitude-transmittance function τ′(x,y); P2 contains the filter; and P3 contains the random complex amplitude distribution function f(x,y). (PC)1 and (PC)2 are photocells. L is a lens.

Equations (28)

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I n ( α , β ) = I p λ 2 2 d i 2 - d Δ x d Δ y - d x 1 d y 1 rect x 1 L rect y 1 L rect ( x 1 - Δ x ) L rect ( y 1 - Δ y ) L φ τ τ ( Δ x , Δ y ) exp j π λ 2 ( 1 d i - 1 d p ) ( Δ x 2 + Δ y 2 ) exp j 2 π λ 2 [ ( 1 d i - 1 d p ) ( x 1 Δ x + y 1 Δ y ) - 1 d i ( α Δ x + β Δ y ) ] .
φ τ τ ( Δ x , Δ y ) = τ ( x + Δ x , y + Δ y ) τ * ( x , y ) ,
I n ( α , β ) = I p λ 2 2 d i 2 - d x 1 d y 1 rect x 1 L rect y 1 L × Φ τ τ [ α λ 2 d i - 1 λ 2 d i ( 1 - d i d p ) x 1 , β λ 2 d i - 1 λ 2 d i ( 1 - d i d p ) y 1 ] ,
Φ τ τ ( p , q ) = - φ τ τ ( x , y ) exp [ - j 2 π ( p x + q y ) ] d x d y ,
p = α λ 2 d i - 1 λ 2 d i ( 1 - d i d p ) x 1 ; q = β λ 2 d i - 1 λ 2 d i ( 1 - d i d p ) y 1 ,
I n ( α , β ) = [ I p / ( 1 - d i d p ) 2 ] a 1 a 2 b 1 b 2 Φ τ τ ( p , q ) d p d q ,
( a 1 a 2 ) = α λ 2 d i ± L 2 λ 2 d i ( 1 - d i d p ) ;             ( b 1 b 2 ) = β λ 2 d i ± L 2 λ 2 d i ( 1 - d i d p ) .
I n ( α , β ) = [ I p / ( 1 - d i d p ) 2 ] Φ τ τ ( p 0 , q 0 ) a 1 a 2 b 1 b 2 d p d q ,
I n ( α , β ) = I p A t λ 2 2 d i 2 Φ τ τ ( p 0 , q 0 ) ,
I i / I n = K 2 χ 2 E r E σ A t / Φ τ τ ( p 0 , q 0 ) .
K = 1 A t A t K [ x λ 2 d i ( 1 - d i d p ) - α λ 2 d i , y λ 2 d i ( 1 - d i d p ) - β λ 2 d i ] d x d y ,
I i I n = K 2 η 2 m 2 A t Φ τ τ ( p 0 , q 0 ) ,
I n ( α , β ) = I p λ 2 2 d i 2 Φ τ τ ( α λ 2 d i , β λ 2 d i ) - rect x 1 L rect y 1 L d x 1 d y 1 = I p A t λ 2 2 d i 2 Φ τ τ ( α λ 2 d i , β λ 2 d i )
I i I n = K 2 η 2 m 2 A t / Φ τ τ ( α λ 2 d i , β λ 2 d i ) .
f ( x , y ) = τ ( x , y ) * h ( x , y ) ,
φ f f ( Δ x , Δ y ) = f ( x + Δ x , y + Δ y ) f * ( x , y ) ,
φ f f ( Δ x , Δ y ) = - d p d q Φ τ τ ( p , q ) H ( p , q ) 2 × exp j 2 π ( p Δ x + q Δ y ) .
H ( p , q ) 2 = 1             for             p 0 - ( δ / 2 ) p p 0 + ( δ / 2 )
q 0 - ( δ / 2 ) q q 0 + ( δ / 2 ) H ( p , q ) 2 = 0             otherwise
φ f f ( 0 , 0 ) = Φ τ τ ( p 0 , q 0 ) δ 2
Φ τ τ ( p 0 , q 0 ) = φ f f ( 0 , 0 ) / ( l / mm ) 2 .
φ f f ( 0 , 0 ) 1 A A f ( x , y ) 2 d x d y = B 1 B 2 ,
Φ τ τ ( f ) = [ exp ( - 0.00248 f ) ] × 10 - 8 ,
I i / σ = [ I i / 2 I n ] 1 2 .
m 2 min = 50 Φ τ τ ( 300 ) K 2 η 2 A t .
I i / I n = [ K 2 η 2 m 2 A t / Φ τ τ ( p 0 , q 0 ) ] ( A s / A t ) 2 .
I i / I n = [ K 2 η 2 ( E s / E r ) / Φ τ τ ( p 0 , q 0 ) ] ( A t / N ) .
I i I n = K 2 η 2 λ 2 2 ( E s / E r ) Φ τ τ ( p 0 , q 0 ) ( L 0 / d i ) 2 .