Abstract

Any finite-sized photodetector has an effect on the spatial frequency content of the detected image. An expression for the modulation transfer function (MTF) of a nonrectangular detector in the along-scan direction is obtained. A comparison of our theoretical prediction is made with published experimental and numerical values for the MTF of a photosite having an exponentially tapered shape. Structures of this form are used as the readout region in SPRITE (signal processing in the element) detectors.

© 1989 Optical Society of America

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References

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  1. C. T. Elliott, “New Detector for Thermal Imaging Systems,” Electron. Lett. 17, 312 (1981).
    [CrossRef]
  2. C. T. Elliott, D. Day, D. J. Wilson, “An Integrating Detector for Serial Scan Thermal Imaging,” Infrared Phys. 22, 31 (1982).
    [CrossRef]
  3. A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
    [CrossRef]
  4. D. J. Day, T. J. Shepherd, “Transport in Photo-Conductors—I,” Solid State Electron. 25, 707 (1982).
    [CrossRef]
  5. G. Boreman, A. Plogstedt, “Modulation Transfer Function and Number of Equivalent Elements for SPRITE Detectors,” Appl. Opt. 27, 4331 (1988).
    [CrossRef] [PubMed]
  6. T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
    [CrossRef]
  7. J. M. Lloyd, Thermal Imaging Systems (Plenum, New York, 1975), Chap. 9.
  8. L. G. Callahan, W. M. Brown, “One- and Two-Dimensional Processing in Line Scanning Systems,” Appl. Opt. 2, 401 (1963).
    [CrossRef]
  9. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 95–96.
  10. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 311–312.
  11. S. P. Braim, A. P. Campbell, “TED (SPRITE) Detector MTF,” in Proceedings of the Conference on Advanced IR Detectors and Systems (IEE, London, 1983), Vol. 228, p. 63.

1988 (1)

1984 (1)

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

1982 (3)

C. T. Elliott, D. Day, D. J. Wilson, “An Integrating Detector for Serial Scan Thermal Imaging,” Infrared Phys. 22, 31 (1982).
[CrossRef]

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

D. J. Day, T. J. Shepherd, “Transport in Photo-Conductors—I,” Solid State Electron. 25, 707 (1982).
[CrossRef]

1981 (1)

C. T. Elliott, “New Detector for Thermal Imaging Systems,” Electron. Lett. 17, 312 (1981).
[CrossRef]

1963 (1)

Ashley, T.

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

Blackburn, A.

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Blackman, M. V.

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Boreman, G.

Braim, S. P.

S. P. Braim, A. P. Campbell, “TED (SPRITE) Detector MTF,” in Proceedings of the Conference on Advanced IR Detectors and Systems (IEE, London, 1983), Vol. 228, p. 63.

Brown, W. M.

Callahan, L. G.

Campbell, A. P.

S. P. Braim, A. P. Campbell, “TED (SPRITE) Detector MTF,” in Proceedings of the Conference on Advanced IR Detectors and Systems (IEE, London, 1983), Vol. 228, p. 63.

Charlton, D. E.

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Day, D.

C. T. Elliott, D. Day, D. J. Wilson, “An Integrating Detector for Serial Scan Thermal Imaging,” Infrared Phys. 22, 31 (1982).
[CrossRef]

Day, D. J.

D. J. Day, T. J. Shepherd, “Transport in Photo-Conductors—I,” Solid State Electron. 25, 707 (1982).
[CrossRef]

Dunn, W. A. E.

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Elliott, C. T.

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

C. T. Elliott, D. Day, D. J. Wilson, “An Integrating Detector for Serial Scan Thermal Imaging,” Infrared Phys. 22, 31 (1982).
[CrossRef]

C. T. Elliott, “New Detector for Thermal Imaging Systems,” Electron. Lett. 17, 312 (1981).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 311–312.

Jenner, M. D.

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Johns, M. D.

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

Lloyd, J. M.

J. M. Lloyd, Thermal Imaging Systems (Plenum, New York, 1975), Chap. 9.

Oliver, K. J.

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 95–96.

Plogstedt, A.

Shepherd, T. J.

D. J. Day, T. J. Shepherd, “Transport in Photo-Conductors—I,” Solid State Electron. 25, 707 (1982).
[CrossRef]

White, A. M.

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

Wilson, D. J.

C. T. Elliott, D. Day, D. J. Wilson, “An Integrating Detector for Serial Scan Thermal Imaging,” Infrared Phys. 22, 31 (1982).
[CrossRef]

Wotherspoon, J. T. M.

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

C. T. Elliott, “New Detector for Thermal Imaging Systems,” Electron. Lett. 17, 312 (1981).
[CrossRef]

Infrared Phys. (3)

C. T. Elliott, D. Day, D. J. Wilson, “An Integrating Detector for Serial Scan Thermal Imaging,” Infrared Phys. 22, 31 (1982).
[CrossRef]

A. Blackburn, M. V. Blackman, D. E. Charlton, W. A. E. Dunn, M. D. Jenner, K. J. Oliver, J. T. M. Wotherspoon, “The Practical Realization and Performance of SPRITE Detectors,” Infrared Phys. 22, 57 (1982).
[CrossRef]

T. Ashley, C. T. Elliott, A. M. White, J. T. M. Wotherspoon, M. D. Johns, “Optimization of Spatial Resolution in SPRITE Detectors,” Infrared Phys. 24, 25 (1984).
[CrossRef]

Solid State Electron. (1)

D. J. Day, T. J. Shepherd, “Transport in Photo-Conductors—I,” Solid State Electron. 25, 707 (1982).
[CrossRef]

Other (4)

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 95–96.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978), pp. 311–312.

S. P. Braim, A. P. Campbell, “TED (SPRITE) Detector MTF,” in Proceedings of the Conference on Advanced IR Detectors and Systems (IEE, London, 1983), Vol. 228, p. 63.

J. M. Lloyd, Thermal Imaging Systems (Plenum, New York, 1975), Chap. 9.

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Figures (4)

Fig. 1
Fig. 1

Basic structure of the SPRITE detector. The image is scanned mechanically in the same direction as the carrier drift, enhancing the signal-to-noise ratio of the resulting image.

Fig. 2
Fig. 2

Geometry for the scanned rectangular detector.

Fig. 3
Fig. 3

Geometry for the scanned nonrectangular detector.

Fig. 4
Fig. 4

Comparison of MTFs for rectangular (lower curve) and tapered (upper curve) photosites.

Equations (39)

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d ( x , y ) = rect ( x X , y Y )
r ( t = 0 ) = X / 2 X / 2 Y / 2 Y / 2 i ( x , y ) d x dy .
r ( t ) = υ t X / 2 υ t + X / 2 Y / 2 Y / 2 i ( x , y ) d x dy .
r ( x s , y s ) = x s X / 2 x s + X / 2 y s Y / 2 y s + Y / 2 i ( x , y ) d x dy ,
r ( x s , y s ) = i ( x , y ) rect [ x x s X , y y s Y ] d x dy ,
r ( x s , y s ) = i ( x , y ) d ( x x s , y y s ) d x dy .
r ( x s , y s ) = i ( x , y ) * * d ( x , y ) .
r ( x s , 0 ) = i ( x , y ) d ( x x s , y ) d x d y ,
r ( x s , 0 ) = [ i ( x , y ) * * d ( x , y ) ] × 1 ( x s ) δ ( y s ) .
R ( ξ ) = { r ( x s , 0 ) } ,
R ( ξ ) = { [ i ( x , y ) * * d ( x , y ) ] × 1 ( x s ) δ ( y s ) } ,
R ( ξ ) = [ I ( ξ , η ) × D ( ξ , η ) ] * * δ ( ξ ) 1 ( η ) .
R ( ξ ) = I ( ξ , η ) × D ( ξ , η ) d η .
R ( ξ ) = I ( ξ , η ) X Y sinc ( X ξ , Y η ) d η .
d x ( x ) D ξ ( ξ ) and d y ( y ) D η ( η ) .
R ( ξ ) = X Y sinc ( X ξ ) I ( ξ , η ) sinc ( Y η ) d η .
i ( x , y ) = i x ( x ) i y ( y ) , i x ( x ) I ξ ( ξ )  and  i y I η ( η ) .
R ( ξ ) = X Y sinc ( X ξ ) I ξ ( ξ ) I η ( η ) sinc ( Y η ) d η ,
R ( ξ ) = X Y I ξ ( ξ ) sinc ( X ξ ) I η ( η ) sinc ( Y η ) d η .
MTF ( ξ ) = R ( ξ ) / I ξ ( ξ ) R ( ξ = 0 )
MTF ( ξ ) = D ξ ( ξ ) / D ξ ( ξ = 0 ) = sinc ( X ξ ) .
R ( ξ ) = I ( ξ , η ) × D ( ξ , η ) d η .
R ( ξ ) = I ξ ( ξ ) I η ( η ) D ( ξ , η ) d η .
R ( ξ ) = I ξ ( ξ ) I η ( η ) D ( ξ , 0 ) d η ,
R ( ξ ) = I ξ ( ξ ) D ( ξ , 0 ) I η ( η ) d η .
MTF ( ξ ) = R ( ξ ) / I ξ ( ξ ) R ( ξ = 0 ) ,
MTF ( ξ ) = D ( ξ , 0 ) / D ( 0 , 0 ) .
D ( ξ , 0 ) { d ( x , 0 ) } .
D ( ξ , η ) = d ( x , y ) exp ( j 2 π ξ x ) exp ( j 2 π η y ) d x d y .
D ( ξ , η ) = exp ( j 2 π ξ x ) y ( x ) y ( x ) exp ( j 2 π η y ) d y d x .
D ( ξ , 0 ) = exp ( j 2 π ξ x ) y ( x ) y ( x ) d y d x ,
D ( ξ , 0 ) = exp ( j 2 π ξ x ) 2 y ( x ) d x = 2 Y ( ξ ) .
MTF ( ξ ) = D ( ξ , 0 ) / D ( 0 , 0 ) = Y ( ξ ) / Y ( 0 ) .
y ( x ) = rect ( x X / 2 X ) exp ( α x ) .
MTF ( ξ ) = Y ( ξ ) / Y ( 0 ) [ rect ( x X / 2 X ) exp ( α x ) ] .
[ rect ( x X / 2 X ) exp ( α x ) ] = [ rect ( x X / 2 X ) ] * [ exp ( α x ) ] .
y rect ( x ) = rect ( x 25 50 )
y taper ( x ) = rect ( x 25 50 ) × exp ( α x ) ,
62.5 exp ( α 50 ) = 15 ; α = 0.0285.

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