Abstract

It is known that the diffraction of coherent light can be used for various spatial-noise measurements including the power-spectrum estimation of photographic emulsions. A number of such measurements are presented. The power spectrum of grain noise is compared with several theoretical models. The spectra of grain and phase noise for overexposed film are obtained. A simple procedure for obtaining the variance of the phase noise of photographic film, assuming gaussian statistics and statistical independence between grain and phase noise, is furnished.

© 1971 Optical Society of America

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References

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  1. H. Stark, W. Bennett, M. Arm, Appl. Opt. 8, 11 (1969).
    [CrossRef]
  2. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).
  3. M. Savelli, Compt. Rend. 246, 3605 (1958).
  4. L. Silberstein, Phil. Mag. 44, 257(1922).

1969 (1)

H. Stark, W. Bennett, M. Arm, Appl. Opt. 8, 11 (1969).
[CrossRef]

1958 (1)

M. Savelli, Compt. Rend. 246, 3605 (1958).

1922 (1)

L. Silberstein, Phil. Mag. 44, 257(1922).

Arm, M.

H. Stark, W. Bennett, M. Arm, Appl. Opt. 8, 11 (1969).
[CrossRef]

Bennett, W.

H. Stark, W. Bennett, M. Arm, Appl. Opt. 8, 11 (1969).
[CrossRef]

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

Savelli, M.

M. Savelli, Compt. Rend. 246, 3605 (1958).

Silberstein, L.

L. Silberstein, Phil. Mag. 44, 257(1922).

Stark, H.

H. Stark, W. Bennett, M. Arm, Appl. Opt. 8, 11 (1969).
[CrossRef]

Appl. Opt. (1)

H. Stark, W. Bennett, M. Arm, Appl. Opt. 8, 11 (1969).
[CrossRef]

Compt. Rend. (1)

M. Savelli, Compt. Rend. 246, 3605 (1958).

Phil. Mag. (1)

L. Silberstein, Phil. Mag. 44, 257(1922).

Other (1)

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

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Figures (9)

Fig. 1
Fig. 1

Power spectrum of grain noise of Kodak 2479 film compare with theoretical models. — modified OCG; ⋯ random checkerboard; – – – overlapping circular grain (OCG); 〰 measured spectrum; average amplitude transmittance, t0 = 0.58; dev. = D-19, 10 min, 20°C.

Fig. 2
Fig. 2

Power spectrum of grain noise of Kodak 2475, developed in D-19, compared with theoretical models. — modified OCG; ⋯ random checkerboard; – – – overlapping circular grain (OCG); 〰 measured spectrum; average amplitude transmittance, t0 = 0.58; dev. = D-19, 10 min, 20°C.

Fig. 3
Fig. 3

Power spectrum of grain noise of Kodak 2475, developed in Dektol, compared with theoretical models. — modified OCG; ⋯ random checkerboard; – – – overlapping circular grain (OCG); 〰 measured spectrum; average amplitude transmittance, t0 = 0.58; dev. = Dektol, 3 min, 22°C.

Fig. 4
Fig. 4

Variation of grain noise with amplitude transmittance for Kodak 2475. Dev. = Dektol, 3 min, 22° C.

Fig. 5
Fig. 5

Variation of grain sizes with amplitude transmittance for Kodak 2475. ○, modified overlapping circular grain; □, overlapping circular grain; △, random checkerboard.

Fig. 6
Fig. 6

Power spectrum of total film noise at peak grain noise (Kodak 2475). Average amplitude transmittance, t0 = 0.58; average complex transmittance, |R0| = 0.34; dev. = Dektol, 3 min, 22°C.

Fig. 7
Fig. 7

Anomalous behavior of dense film (Kodak 2475). Average amplitude transmittance, t0 = 0.17; average complex transmittance, |R0| = 0.07; dev. = Dektol, 3 min, 22°C.

Fig. 8
Fig. 8

Experimental relationship between the real and complex transmittance of film (Kodak 2496). Film type: Kodak 2496; dev. = D-19, 10 min, 20°C.

Fig. 9
Fig. 9

Experimental relationship between the real and complex transmittance of film (Kodak 2475). Film type: Kodak 2475; dev. = Dektol, 3 min, 22°C.

Equations (7)

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R ( x , y ) = t ( x , y ) e j ψ ( x , y ) ,
r ( x , y ) = R ( x , y ) - R 0 , where R 0 = R ( x , y ) , τ ( x , y ) = t ( x , y ) - t 0 , where t 0 = t ( x , y ) .
ϕ R ( α , β ) = ϕ R ( ρ ) , where ρ = ( α 2 + β 2 ) 1 2 .
W R ( u , v ) = W R ( w ) , where w = ( u 2 + v 2 ) 1 2 .
W r ( u , v ) = e - σ 2 W τ ( u , v ) + t 0 2 W θ ( u , v ) + W τ ( u , v ) * W θ ( u , v ) ,
P ( t = 0 ) = 1 - exp [ - ( E T A g / ω ) ] ,
R 0 = t 0 e - σ 2 / 2 = R 0 .

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