Abstract

A measurement technique for the noise performance of a white-light optical signal processor is presented. The technique utilizes a scanning photometer to trace out the output noise intensity fluctuation of the optical system. The effect of noise performance due to noise perturbation at the input and Fourier planes is measured. The experimental results, except for amplitude noise at the input plane, show the claims for better noise immunity, if the optical system is operating in the partially coherent regime. We have also measured the noise performance due to perturbation along the optical axis of the system. The experimental results show that the resulting output SNR improves considerably by increasing the bandwidth and source size of the illuminator. The optimum noise immunity occurs for phase noise at the input and output planes. For amplitude noise, the optimum SNR occurs at the Fourier plane. In brief, the experimental results confirm the analytical results that we recently evaluated.

© 1985 Optical Society of America

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References

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  1. P. Chavel, S. Lowenthal, “Noise and Coherence in Optical Image Processing. II. Noise Fluctuations,” J. Opt. Soc. Am. 68, 721 (1978).
    [CrossRef]
  2. P. Chavel, “Optical Noise and Temporal Coherence,” J. Opt. Soc. Am. 70, 935 (1980).
    [CrossRef]
  3. E. N. Leith, J. A. Roth, “Noise Performance of an Achromatic Coherent Optical System,” Appl. Opt. 18, 2803 (1979).
    [CrossRef] [PubMed]
  4. F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. I: Temporally Partially Coherent Illumination,” J. Opt. Soc. Am. A 1, 489 (1984).
    [CrossRef]
  5. F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. II: Spatially Partially Coherent Illumination,” Appl. Phys. B36, 1 (1985).
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).
  7. B. J. Chang, K. Winick, “Silver-Halide Gelatin Holograms” Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

1985 (1)

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. II: Spatially Partially Coherent Illumination,” Appl. Phys. B36, 1 (1985).

1984 (1)

1980 (2)

P. Chavel, “Optical Noise and Temporal Coherence,” J. Opt. Soc. Am. 70, 935 (1980).
[CrossRef]

B. J. Chang, K. Winick, “Silver-Halide Gelatin Holograms” Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

1979 (1)

1978 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Chang, B. J.

B. J. Chang, K. Winick, “Silver-Halide Gelatin Holograms” Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

Chavel, P.

Leith, E. N.

Lowenthal, S.

Roth, J. A.

Shaik, K. S.

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. II: Spatially Partially Coherent Illumination,” Appl. Phys. B36, 1 (1985).

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. I: Temporally Partially Coherent Illumination,” J. Opt. Soc. Am. A 1, 489 (1984).
[CrossRef]

Winick, K.

B. J. Chang, K. Winick, “Silver-Halide Gelatin Holograms” Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Yu, F. T. S.

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. II: Spatially Partially Coherent Illumination,” Appl. Phys. B36, 1 (1985).

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. I: Temporally Partially Coherent Illumination,” J. Opt. Soc. Am. A 1, 489 (1984).
[CrossRef]

Zhuang, S. L.

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. II: Spatially Partially Coherent Illumination,” Appl. Phys. B36, 1 (1985).

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. I: Temporally Partially Coherent Illumination,” J. Opt. Soc. Am. A 1, 489 (1984).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

F. T. S. Yu, K. S. Shaik, S. L. Zhuang, “Noise Performance of a White-Light Optical Signal Processor. II: Spatially Partially Coherent Illumination,” Appl. Phys. B36, 1 (1985).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

B. J. Chang, K. Winick, “Silver-Halide Gelatin Holograms” Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964).

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Figures (9)

Fig. 1
Fig. 1

Grating-based white-light optical processor: γ(x0,y0), source intensity distributions; P0, source plane; P1, input plane; P2, Fourier plane; P3, output plane; s(x,y), object transparency; Hn(α,β), slit filter; PM, photometer; OSC, oscilloscope; L, achromatic transform lenses.

Fig. 2
Fig. 2

Effect on output image (with a section of photometer traces) due to phase noise at the input plane for different spectral bandwidths. The source size used is 0.7 mm square (i.e., a = 0.7 mm): (a) Δλn = 1500 Å; (b) Δλn = 1000 Å; (c) Δλn = 500 Å.

Fig. 3
Fig. 3

Output SNR for phase noise at the input plane as a function of spectral bandwidth of the slit filter for various values of source sizes.

Fig. 4
Fig. 4

Output SNR for phase noise at the input plane as a function of source size for various values of spectral bandwidths.

Fig. 5
Fig. 5

Effect of output image due to strong phase perturbation at the input plane (a = 0.7 mm): (a) Δλn = 3000 Å; (b) Δλn = 1500 Å; (c) Δλn = 500 Å; (d) obtained with a He–Ne laser.

Fig. 6
Fig. 6

Output SNR for amplitude noise at the Fourier plane as a function of spectral bandwidth for various source sizes.

Fig. 7
Fig. 7

Output SNR for phase noise at the Fourier plane as a function of source size for various values of spectral bandwidths.

Fig. 8
Fig. 8

Variation of the output SNR due to thin phase noise as a function of the Z direction for various source sizes.

Fig. 9
Fig. 9

Variation of the output SNR due to thin amplitude noise as a function of the Z direction for various source sizes.

Equations (8)

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I ( x , y ) = λ l n λ h n γ ( x 0 , y 0 ) | S ( x 0 + α λ f ν 0 , y 0 + β ) H n ( α , β ) exp [ i 2 π λ f ( x α + y β ) ] d α d β | 2 d x 0 d y 0 d λ ,
T ( x ) = exp ( i 2 π ν 0 x ) .
γ ( x 0 , y 0 ) = rect ( x 0 a ) rect ( y 0 a ) ,
rect ( x 0 a ) { 1 , | x 0 | a 2 , 0 , | x 0 | > a 2 .
Δ λ n = λ h n λ l n Δ α n ν 0 f .
N Δ λ Δ λ n Δ λ ν 0 f Δ α n ,
SNR n ( y ) E [ I n ( y ) ] / σ n ( y ) ,
σ n 2 ( y ) E [ I n 2 ( y ) ] { E [ I n ( y ) ] } 2 .

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