Abstract

Laser Speckle is the optical phenomena resulting from the random interference of coherent light. This phenomenon can be utilized to measure the Modulation Transfer Function (MTF) of detector arrays. Common devices used for speckle generation, such as integrating spheres and ground glass, suffer from low efficiencies less than 20%. Microlens diffusers are shown to be more efficient alternatives for speckle generation. An analysis of the statistical behavior of microlens diffusers is presented with emphasis on their application to MTF testing of detector arrays in the visible spectrum.

© 2007 Optical Society of America

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References

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  1. RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com>.
  2. A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34, 860-868 (1995).
    [CrossRef]
  3. G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25, 148-150 (1986).
  4. A. M. Pozo and M. Rubiño, "Optical characterization of ophthalmic lenses by means of modulation transfer function determination from a laser speckle pattern," Appl. Opt. 44, 7744-7748 (2005).
    [CrossRef] [PubMed]
  5. M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32, 395-400 (1993).
    [CrossRef]
  6. A. M. Pozo and M. Rubiño, "Comparative analysis of techniques for measuring the modulation transfer functions of charge-coupled devices based on the generation of laser speckle," Appl. Opt. 44, 1543-1547 (2005).
    [CrossRef] [PubMed]
  7. G. Boreman, Y. Sun, and A. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29, 339-342 (1990).
    [CrossRef]
  8. J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 15-19.
  9. J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 46-54.
  10. J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, p. 40.
  11. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics, (John Wiley & Sons, 1978), Chap. 3.

2005 (2)

1995 (1)

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34, 860-868 (1995).
[CrossRef]

1993 (1)

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32, 395-400 (1993).
[CrossRef]

1990 (1)

G. Boreman, Y. Sun, and A. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29, 339-342 (1990).
[CrossRef]

1986 (1)

G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25, 148-150 (1986).

Appl. Opt. (2)

Opt. Eng. (4)

G. Boreman, Y. Sun, and A. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29, 339-342 (1990).
[CrossRef]

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32, 395-400 (1993).
[CrossRef]

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34, 860-868 (1995).
[CrossRef]

G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25, 148-150 (1986).

Other (5)

J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 15-19.

J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, pp. 46-54.

J. W. Goodman, Statistical Properties of Laser Speckle Patterns in Laser Speckle and Related Phenomena (Springer-Verlag, 1984), Chap. 2, p. 40.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics, (John Wiley & Sons, 1978), Chap. 3.

RPC Photonics, Engineered Diffusers and HiLAM diffusers, http://www.rpcphotonics.com>.

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Figures (7)

Fig. 1.
Fig. 1.

Magnified photograph of sample microlens array. (courtesy of RPC Photonics)

Fig. 2.
Fig. 2.

Experimental setup for polarization preservation measurement.

Fig. 3.
Fig. 3.

Experimental setup for measuring PDF of laser speckle intensity.

Fig. 4.
Fig. 4.

Comparison of measured to theoretical probability density functions for the intensity of the laser speckle generated with the microlens diffuser.

Fig. 5.
Fig. 5.

Measured output PSD shown as solid line and theoretical input PSD shown as dotted line.

Fig. 6.
Fig. 6.

Measured MTF of CCD detector array shown as solid line and theoretical MTF is shown as dotted line.

Fig. 7.
Fig. 7.

Measured PSD input is shown as a solid-line and theoretical PSD input is shown as a dashed-line.

Equations (8)

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p I ( I ) ( M I ) M 1 I M 1 ( M I I ) Γ ( M ) for I 0
M = [ 2 S m 0 S m ( 1 Δx S m ) sin c 2 ( Δx S c ) d Δ x ] 2 .
S c = 2 0 0 sin c 2 ( L Δ x λ z ) sin c 2 ( L Δ y λ z ) d Δ xd Δ y ,
PSD input , theo ( ξ , η ) = I 2 [ δ ( ξ , η ) + ( λz L ) 2 Λ ( λz L ξ ) Λ ( λz L η ) ]
PSD output , means ( ξ ) = 1 M i = 0 M 1 | { image ( 0 : N 1 , i ) } |
MTF means ( ξ ) = PSD output , means ( ξ ) PSD input , theo ( ξ ) .
MTF Theo , CCD ( ξ ) = Sinc 2 ( ξw )
PSD input , actual = PSD output , meas MTF Theo , CCD 2

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