Abstract

We present a new technique for measuring the modulation transfer function (MTF) of a focal plane array (FPA). The main idea is to project a periodic pattern of thin lines that are canted with respect to the sensor’s columns. Practically, one aims the projection by using the self-imaging property of a periodic target. The technique, called the canted periodic target test, has been validated experimentally on a specific infrared FPA, leading to MTF evaluation to as great as five times the Nyquist frequency.

© 1999 Optical Society of America

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References

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  1. G. C. Holst, “Infrared imaging system testing,” in Infrared and Electro-optical Systems Handbook, M. C. Dudzik, ed. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), Vol. 4, pp. 223–232.
  2. J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
    [CrossRef]
  3. M. Chambon, J. Primot, M. Girard, “Modulation transfer function assessment for sampled imaging systems: application of the generalized line spread function to a standard infrared camera,” Infrared Phys. Technol. 37, 619–626 (1996).
    [CrossRef]
  4. S. E. Reichenbach, S. K. Park, R. Rarayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
    [CrossRef]
  5. M. A. Chambliss, J. A. Dawson, E. J. Borg, “Measuring the MTF of undersampled staring IRFPA sensors using a 2D discrete Fourier transform,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, G. C. Holst, ed., Proc. SPIE2470, 312–324 (1995).
  6. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol 27, pp. 1–108.
    [CrossRef]
  7. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967).
    [CrossRef]
  8. J. J. Winthrop, C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373–381 (1965).
    [CrossRef]
  9. Y. Cohen-Sabban, D. Joyeux, “Aberration-free nonparaxial self-imaging,” J. Opt. Soc. Am. 73, 707–719 (1983).
    [CrossRef]

1996

J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
[CrossRef]

M. Chambon, J. Primot, M. Girard, “Modulation transfer function assessment for sampled imaging systems: application of the generalized line spread function to a standard infrared camera,” Infrared Phys. Technol. 37, 619–626 (1996).
[CrossRef]

1991

S. E. Reichenbach, S. K. Park, R. Rarayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

1983

1967

1965

Borg, E. J.

M. A. Chambliss, J. A. Dawson, E. J. Borg, “Measuring the MTF of undersampled staring IRFPA sensors using a 2D discrete Fourier transform,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, G. C. Holst, ed., Proc. SPIE2470, 312–324 (1995).

Caes, M.

J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
[CrossRef]

Chambliss, M. A.

M. A. Chambliss, J. A. Dawson, E. J. Borg, “Measuring the MTF of undersampled staring IRFPA sensors using a 2D discrete Fourier transform,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, G. C. Holst, ed., Proc. SPIE2470, 312–324 (1995).

Chambon, M.

M. Chambon, J. Primot, M. Girard, “Modulation transfer function assessment for sampled imaging systems: application of the generalized line spread function to a standard infrared camera,” Infrared Phys. Technol. 37, 619–626 (1996).
[CrossRef]

J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
[CrossRef]

Cohen-Sabban, Y.

Dawson, J. A.

M. A. Chambliss, J. A. Dawson, E. J. Borg, “Measuring the MTF of undersampled staring IRFPA sensors using a 2D discrete Fourier transform,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, G. C. Holst, ed., Proc. SPIE2470, 312–324 (1995).

Deschamps, J.

J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
[CrossRef]

Girard, M.

M. Chambon, J. Primot, M. Girard, “Modulation transfer function assessment for sampled imaging systems: application of the generalized line spread function to a standard infrared camera,” Infrared Phys. Technol. 37, 619–626 (1996).
[CrossRef]

Holst, G. C.

G. C. Holst, “Infrared imaging system testing,” in Infrared and Electro-optical Systems Handbook, M. C. Dudzik, ed. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), Vol. 4, pp. 223–232.

Joyeux, D.

Montgomery, W. D.

Park, S. K.

S. E. Reichenbach, S. K. Park, R. Rarayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol 27, pp. 1–108.
[CrossRef]

Primot, J.

J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
[CrossRef]

M. Chambon, J. Primot, M. Girard, “Modulation transfer function assessment for sampled imaging systems: application of the generalized line spread function to a standard infrared camera,” Infrared Phys. Technol. 37, 619–626 (1996).
[CrossRef]

Rarayanswamy, R.

S. E. Reichenbach, S. K. Park, R. Rarayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Reichenbach, S. E.

S. E. Reichenbach, S. K. Park, R. Rarayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Winthrop, J. J.

Worthington, C. R.

Infrared Phys. Technol.

M. Chambon, J. Primot, M. Girard, “Modulation transfer function assessment for sampled imaging systems: application of the generalized line spread function to a standard infrared camera,” Infrared Phys. Technol. 37, 619–626 (1996).
[CrossRef]

J. Mod. Opt.

J. Primot, M. Chambon, M. Caes, J. Deschamps, “Evaluation of the modulation transfer function of an infrared focal plane array using the Talbot effect,” J. Mod. Opt. 43, 347–354 (1996).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

S. E. Reichenbach, S. K. Park, R. Rarayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Other

M. A. Chambliss, J. A. Dawson, E. J. Borg, “Measuring the MTF of undersampled staring IRFPA sensors using a 2D discrete Fourier transform,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing, G. C. Holst, ed., Proc. SPIE2470, 312–324 (1995).

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol 27, pp. 1–108.
[CrossRef]

G. C. Holst, “Infrared imaging system testing,” in Infrared and Electro-optical Systems Handbook, M. C. Dudzik, ed. (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), Vol. 4, pp. 223–232.

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Figures (11)

Fig. 1
Fig. 1

Classical GLSF method: (a) Ideal target spatial-frequency spectrum. (b) Effects of filtering and sampling on the input spatial-frequency spectrum.

Fig. 2
Fig. 2

CPTT: (a) Ideal target spatial-frequency spectrum. (b) Effects of filtering and sampling on the input spatial-frequency spectrum.

Fig. 3
Fig. 3

Ray-tracing approach, geometry of the problem.

Fig. 4
Fig. 4

Evolution of the Fourier coefficients D p versus z from p = 1 (top curve) to p = 5 (bottom curve).

Fig. 5
Fig. 5

Experimental setup: 1, sensor tested; 2, canted periodic target; 3, cold filter; 4, cold shield; 5, window; 6, rotating interference filter; 7, canted slit (parallel to the target lines).

Fig. 6
Fig. 6

Transmission T γ(λ) of the interference filter used for three orientations γ (from right to left: γ = 0°, γ = 20°, γ = 40°).

Fig. 7
Fig. 7

Image of the target for two tilt angles of the interference filter: (a) γ = 20°; (b) γ = 40°. 50 × 50 pixels are represented.

Fig. 8
Fig. 8

DFT of an image recorded for a filter tilt angle of γ = 20°.

Fig. 9
Fig. 9

Variation of the measured output frequencies D p OUT/D 0 OUT versus filter tilt angle γ.

Fig. 10
Fig. 10

(a) Variation of the predicted input frequencies D p IN/D 0 IN versus filter tilt angle γ. (b) D p OUT/D p IN ratio curves versus γ.

Fig. 11
Fig. 11

Measured MTF (dotted line, predicted MTF).

Equations (17)

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Inν=p=-+ DpINδν-p/d,
OTFp/d=DpOUT/DpIN.
tx=p=-+ Cp exp2iπpx/d,
Cp=1d0a txexp-2iπpx/ddx.
uR=-pminpmax Cp exp2iπλx sin θp+z cos θp,
sin θp=λp/d+sin α,
|sin θp|1,
|x-z tan θp|D/2,
uR=exp2iπλ x sin α-pminpmax Cpz, α, λ×exp2iπpx/d,
Cpz, α, λ=Cp exp2iπλ z1-λp/d+sin α21/2.
Φpparz, α, λ=-πλ zλp/d+sin α2.
Φpaberrz, α, λ=πz4λλp/d+sin α4.
Iphx, z=λhc |ux, z|2,
Iphx, z=-pmin+pmax+pmax+pmin Dpz, α, λexp2iπpx/d,
Dpz, α, λ=λhcqCp×Cp-q¯
DpINz, T, Δα=-Δλ/2Δλ/2-Δα/2Δα/2 TλDpz, α, λdαdλ.
MTFν=sinπνlflatπνlflat11+4π2ν2ldiff.

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