Abstract

A new methodology for image sensor modulation transfer function measurement using band-limited laser speckle is presented. We use a circular opal milk glass diffuser illuminated by a 5mW He-Ne laser and a linear polarizer to generate band-limited speckle on the sensor. The power spectral density cut-off frequency of the speckle is chosen to be twice that of the sensor Nyquist frequency by placing the sensor at the specific Z location along the optical axis. For the speckle input, we calculate the power spectral density at the sensor using the Rayleigh-Sommerfeld integral and then measure the output power spectral density for the speckle pattern captured by the sensor. With these data, the two-dimensional image sensor modulation transfer function (MTF) is calculated.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. N. Sitter, Jr., J. S. Goddard, and R. K. Ferrell, "Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns," Appl. Opt. 34, 746-751 (1995).
    [CrossRef] [PubMed]
  2. M. Estribeau and P. Magnan, "Fast MTF measurement of CMOS imagers using ISO 12233 slanted edge methodology," Proc. SPIE 5251, 243-251 (2004).
    [CrossRef]
  3. B. T. Teipen and D. L. MacFarlane, "Liquid-crystal-display projector-based modulation transfer function measurements of charge-coupled-device video camera systems," Appl. Opt. 39, 515-525 (2000).
    [CrossRef]
  4. J. E. Greivenkamp and A. E. Lowman, "Modulation transfer function measurement of sparse-array sensors using a self-calibrating fringe pattern," Appl. Opt. 33, 5029-5036 (1994).
    [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. S. K. Park, R. Schowengerdt, and M. Kaczynski, "Modulation-transfer-function analysis for sampled image systems," Appl. Opt. 23, 2572-2582 (1984).
    [CrossRef] [PubMed]
  7. N. George, A. Jain, and R. D. S. Melville Jr., "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65-70 (1975).
    [CrossRef]
  8. N. George, A. Jain, and R. D. S. Melville Jr., "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157-169 (1975).
    [CrossRef]
  9. N. George, "Speckle at various planes in an optical system," Opt. Eng. 25, 754-764 (1986).
  10. P. Z. Peebles, Jr., Probability, random variables, and random signal principles, 3rd Ed. (McGraw-Hill, Inc., New York, 1993).
  11. A. Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst. 24, 652-654 (1977).
    [CrossRef]

2004 (1)

M. Estribeau and P. Magnan, "Fast MTF measurement of CMOS imagers using ISO 12233 slanted edge methodology," Proc. SPIE 5251, 243-251 (2004).
[CrossRef]

2000 (1)

1995 (1)

1994 (1)

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]

1986 (1)

N. George, "Speckle at various planes in an optical system," Opt. Eng. 25, 754-764 (1986).

1984 (1)

1977 (1)

A. Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst. 24, 652-654 (1977).
[CrossRef]

1975 (2)

N. George, A. Jain, and R. D. S. Melville Jr., "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65-70 (1975).
[CrossRef]

N. George, A. Jain, and R. D. S. Melville Jr., "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157-169 (1975).
[CrossRef]

Boreman, G. D.

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]

Ducharme, A. D.

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]

Estribeau, M.

M. Estribeau and P. Magnan, "Fast MTF measurement of CMOS imagers using ISO 12233 slanted edge methodology," Proc. SPIE 5251, 243-251 (2004).
[CrossRef]

Ferrell, R. K.

George, N.

N. George, "Speckle at various planes in an optical system," Opt. Eng. 25, 754-764 (1986).

N. George, A. Jain, and R. D. S. Melville Jr., "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65-70 (1975).
[CrossRef]

N. George, A. Jain, and R. D. S. Melville Jr., "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157-169 (1975).
[CrossRef]

Goddard, J. S.

Greivenkamp, J. E.

Jain, A.

N. George, A. Jain, and R. D. S. Melville Jr., "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157-169 (1975).
[CrossRef]

N. George, A. Jain, and R. D. S. Melville Jr., "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65-70 (1975).
[CrossRef]

Kaczynski, M.

Lowman, A. E.

MacFarlane, D. L.

Magnan, P.

M. Estribeau and P. Magnan, "Fast MTF measurement of CMOS imagers using ISO 12233 slanted edge methodology," Proc. SPIE 5251, 243-251 (2004).
[CrossRef]

Melville, R. D. S.

N. George, A. Jain, and R. D. S. Melville Jr., "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65-70 (1975).
[CrossRef]

N. George, A. Jain, and R. D. S. Melville Jr., "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157-169 (1975).
[CrossRef]

Papoulis, A.

A. Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst. 24, 652-654 (1977).
[CrossRef]

Park, S. K.

Schowengerdt, R.

Sensiper, M.

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]

Sitter, D. N.

Snyder, D. R.

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]

Teipen, B. T.

Appl. Opt. (4)

Appl. Phys. (2)

N. George, A. Jain, and R. D. S. Melville Jr., "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65-70 (1975).
[CrossRef]

N. George, A. Jain, and R. D. S. Melville Jr., "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157-169 (1975).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

A. Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst. 24, 652-654 (1977).
[CrossRef]

Opt. Eng. (2)

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]

N. George, "Speckle at various planes in an optical system," Opt. Eng. 25, 754-764 (1986).

Proc. SPIE (1)

M. Estribeau and P. Magnan, "Fast MTF measurement of CMOS imagers using ISO 12233 slanted edge methodology," Proc. SPIE 5251, 243-251 (2004).
[CrossRef]

Other (1)

P. Z. Peebles, Jr., Probability, random variables, and random signal principles, 3rd Ed. (McGraw-Hill, Inc., New York, 1993).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

Experimental setup

Fig. 2.
Fig. 2.

The input speckle pattern calculated for sensor located at Z=87mm away from the aperture plane.

Fig. 3.
Fig. 3.

The PSD of the speckle pattern shown in Fig. 2. The δ-function at zero frequency of the speckle PSD is excluded. The solid curve in black is the calculated PSD plot with ensemble averaging over 150 independent samples. The dashed curve in red is the polynomial fitting of the PSD curve. The x-axis is the spatial frequency in units of the Nyquist frequency. We use Ny to stand for the Nyquist frequency. Here Ny=227.3cys/mm for the 2.2µm pixel size. It is clear that the PSD is much higher than 0 at the Nyquist frequency of the sensor. The cut-off frequency of the PSD is 2Ny.

Fig. 4.(a)
Fig. 4.(a)

The cross-section of the measured speckle PSDs (fx ,0) shown in dash curve is aliased due to the sensor Nyquist frequency (Ny) is lower than the speckle PSD cut-off frequency which is twice the Nyquist frequency. The solid curves are the PSD(fx ,0) without aliasing. The repeating of the unaliased PSD with a period of 2Ny is due to the discrete sampling of 1/(2Ny) by the sensor in the space domain.

Fig. 4.(b)
Fig. 4.(b)

The cross-section of the sub-sampled speckle PSD. There is no aliasing artifacts because the sub-sampling has sampling size corresponding to twice the Nyquist frequency of the sensor.

Fig. 5.(a)
Fig. 5.(a)

The x-axis cross-section of the measured PSD the speckle pattern on the 6.0µm pixel size CMOS sensor. The spatial frequency range is from 0 to 2Ny.

Fig. 5.
Fig. 5.

(b) The y-axis cross-section of the measured PSD of the speckle pattern on the 6.0µm pixel size CMOS sensor. The x-axis in the plot is the spatial frequency. The range is from 0 to 2Ny.

Fig. 6.
Fig. 6.

The comparison between the theory and measurement of the input power spectral density, PSDI (fx,fy ). The average speckle size is 6µm. The theoretical calculation is shown in black dashed curve. The measured data is shown in black solid curve. The measured PSDI (fx,fy ) data is captured with a 2.2µm sensor. The product of the theoretical calculation of PSDI (fx,fy ) and the square of 2.2µm sensor MTF is shown as the dotted red curve. The theoretical calculation and experimental data agree with each other very well.

Fig. 7.
Fig. 7.

The 6.0µm monochrome CMOS sensor MTFs along the x-axis. The dotted blue curve is the measured sensor MTF using laser speckle method; the solid red curve is the polynomial fitting of the measured sensor MTF data using speckle method; the dash-dot green curve is the measured sensor MTF using the slanted edge method. The range of the spatial frequency is from 0 to the Nyquist frequency of the 6.0µm sensor.

Fig. 8.
Fig. 8.

The measured power spectral density, PSDS (fx,fy ), cross-section along the x-axis for a 2.2µm pixel size monochrome CMOS sensor. The range of the spatial frequency is from 0 to twice the Nyquist frequency.

Fig. 9.
Fig. 9.

The cross-section of MTF along the x-axis for a 2.2µm pixel-size monochrome CMOS sensor. The black solid curve is the measured sensor MTF using laser speckle technique. The red dash curve is the polynomial fitting of the measured MTF using speckle technique. The green dash-dot curve is the measured sensor MTF using the slanted edge technique with a F#3.5 lens. The range of the spatial frequency is from 0 to the Nyquist frequency of a 2.2µm sensor.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

S ( x , y ) = I ( x 1 , y 1 ) h ( x x 1 , y y 1 ) d x 1 d y 1 ,
R S ( Δ x , Δ y ) = R I ( Δ x , Δ y ) * h ( Δ x , Δ y ) * h * ( Δ x , Δ y ) ,
PSD S ( f x , f y ) = PSD I ( f x , f y ) MTF 2 ,
E 0 ( x 0 , y 0 ) = A ( x 0 , y 0 ) * e i θ ( x 0 , y 0 ) ,
A ( x 0 , y 0 ) = e ln 5 2 ( D 2 ) 2 ( x 0 2 + y 0 2 ) ,
P θ ( θ ) = { 1 10 π 0 θ < 10 π 0 otherwise .
E y ( x , y , z ) = i z λ d x 0 d y 0 E 0 ( x 0 , y 0 , 0 ) e i 2 π λ Z 2 + ( x x 0 ) 2 + ( y y 0 ) 2 Z 2 + ( x x 0 ) 2 + ( y y 0 ) 2 ,
d t = λ D Z .
Z = P λ D .
PSD ( f x , f y ) = lim X , Y E u XY ( f x , f y ) 2 X Y ,
I b ( x , y ) = i = 0 1 j = 0 1 [ h ( x , y ) I ( x , y ) n = m = δ ( x m P r i P ) δ ( y n P s j P ) ] ,
χ b ( f x , f y ) = i = 0 1 j = 0 1 [ H ( f x , f y ) n = m = χ ( f x m P , f y n P ) e i 2 π ( m r i P + n S j P ) ] ,
2 2 e i 2 π Δ x P 0.05 .

Metrics