Abstract

Detector noise limits the performance of signal-processing-in-the-element detectors. For detectors to be optimized, an expression for the signal and noise must be found. The results of the eigenmode solution to the charge transport problem are used to derive the power spectral density of the noise in analytic form. This result is then coordinated with a similarly obtained modulation transfer function to yield a frequency-dependent signal-to-noise ratio (SNR). The SNR is used to reveal performance trends over several ranges of detector parameters. The most important result is that the contact boundary velocity strongly controls the SNR. The optimum SNR condition occurs when the contacts are not perfectly ohmic but exhibit a partially blocking behavior.

© 1996 Optical Society of America

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References

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  1. C. T. Elliot, “New detector for thermal imaging systems,” Electron. Lett. 17, 312–313 (1981).
    [CrossRef]
  2. D. J. Day, T. J. Shepherd, “Transport in photoconductors—I,” Solid-State Electron. 25, 707–712 (1982).
    [CrossRef]
  3. T. J. Shepherd, D. J. Day, “Transport in photoconductors—II,” Solid-State Electron. 25, 713–718 (1982).
    [CrossRef]
  4. G. D. Boreman, A. E. Plogstedt, “Modulation transfer function and number of equivalent elements for SPRITE detectors,” Appl. Opt. 27, 4331–4335 (1988).
    [CrossRef] [PubMed]
  5. S. P. Braim, A. P. Campbell, “TED (SPRITE) detector MTF,” IEE Conf. Publ. 228, 63–66 (1983).
  6. S. P. Braim, “The measurement and analysis of the noise frequency spectrum for SPRITE infrared detectors,” in Infrared Technology and Applications, L. R. Baker, A. Masson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.590, 164–171 (1985).
  7. F. J. Effenberger, G. D. Boreman, “Modal analysis of transport processes in SPRITE detectors,” Appl. Opt. 34, 4651–4661 (1995).
    [CrossRef] [PubMed]
  8. A. Van der Ziel, Fluctuation Phenomena in Semi-Conductors (Academic, New York, 1959), pp. 33–36.
  9. C. T. Elliot, D. Day, D. J. Wilson, “An integrating detector for serial scan thermal imaging,” Infrared Phys. 22, 31–42 (1982).
    [CrossRef]
  10. P. Fredin, “Optimum choice of anamorphic ratio and boost filter parameters for a SPRITE based IR sensor,” in Infrared Imaging Systems: Design, Analysis, Modeling and Testing II, G. C. Holst, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1488, 432–442 (1991).
  11. P. Fredin, G. D. Boreman, “Resolution-equivalent D* for SPRITE detectors,” Appl. Opt. 34, 7179–7182 (1995).
    [CrossRef] [PubMed]
  12. A. Józwikowska, K. Józwikowski, A. Rogalski, “Performance of mercury cadmium telluride photoconductive devices,” Infrared Phys. 31, 543–554 (1991).
    [CrossRef]

1995

1991

A. Józwikowska, K. Józwikowski, A. Rogalski, “Performance of mercury cadmium telluride photoconductive devices,” Infrared Phys. 31, 543–554 (1991).
[CrossRef]

1988

G. D. Boreman, A. E. Plogstedt, “Modulation transfer function and number of equivalent elements for SPRITE detectors,” Appl. Opt. 27, 4331–4335 (1988).
[CrossRef] [PubMed]

1983

S. P. Braim, A. P. Campbell, “TED (SPRITE) detector MTF,” IEE Conf. Publ. 228, 63–66 (1983).

1982

C. T. Elliot, D. Day, D. J. Wilson, “An integrating detector for serial scan thermal imaging,” Infrared Phys. 22, 31–42 (1982).
[CrossRef]

D. J. Day, T. J. Shepherd, “Transport in photoconductors—I,” Solid-State Electron. 25, 707–712 (1982).
[CrossRef]

T. J. Shepherd, D. J. Day, “Transport in photoconductors—II,” Solid-State Electron. 25, 713–718 (1982).
[CrossRef]

1981

C. T. Elliot, “New detector for thermal imaging systems,” Electron. Lett. 17, 312–313 (1981).
[CrossRef]

Boreman, G. D.

Braim, S. P.

S. P. Braim, A. P. Campbell, “TED (SPRITE) detector MTF,” IEE Conf. Publ. 228, 63–66 (1983).

S. P. Braim, “The measurement and analysis of the noise frequency spectrum for SPRITE infrared detectors,” in Infrared Technology and Applications, L. R. Baker, A. Masson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.590, 164–171 (1985).

Campbell, A. P.

S. P. Braim, A. P. Campbell, “TED (SPRITE) detector MTF,” IEE Conf. Publ. 228, 63–66 (1983).

Day, D.

C. T. Elliot, D. Day, D. J. Wilson, “An integrating detector for serial scan thermal imaging,” Infrared Phys. 22, 31–42 (1982).
[CrossRef]

Day, D. J.

T. J. Shepherd, D. J. Day, “Transport in photoconductors—II,” Solid-State Electron. 25, 713–718 (1982).
[CrossRef]

D. J. Day, T. J. Shepherd, “Transport in photoconductors—I,” Solid-State Electron. 25, 707–712 (1982).
[CrossRef]

Effenberger, F. J.

Elliot, C. T.

C. T. Elliot, D. Day, D. J. Wilson, “An integrating detector for serial scan thermal imaging,” Infrared Phys. 22, 31–42 (1982).
[CrossRef]

C. T. Elliot, “New detector for thermal imaging systems,” Electron. Lett. 17, 312–313 (1981).
[CrossRef]

Fredin, P.

P. Fredin, G. D. Boreman, “Resolution-equivalent D* for SPRITE detectors,” Appl. Opt. 34, 7179–7182 (1995).
[CrossRef] [PubMed]

P. Fredin, “Optimum choice of anamorphic ratio and boost filter parameters for a SPRITE based IR sensor,” in Infrared Imaging Systems: Design, Analysis, Modeling and Testing II, G. C. Holst, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1488, 432–442 (1991).

Józwikowska, A.

A. Józwikowska, K. Józwikowski, A. Rogalski, “Performance of mercury cadmium telluride photoconductive devices,” Infrared Phys. 31, 543–554 (1991).
[CrossRef]

Józwikowski, K.

A. Józwikowska, K. Józwikowski, A. Rogalski, “Performance of mercury cadmium telluride photoconductive devices,” Infrared Phys. 31, 543–554 (1991).
[CrossRef]

Plogstedt, A. E.

G. D. Boreman, A. E. Plogstedt, “Modulation transfer function and number of equivalent elements for SPRITE detectors,” Appl. Opt. 27, 4331–4335 (1988).
[CrossRef] [PubMed]

Rogalski, A.

A. Józwikowska, K. Józwikowski, A. Rogalski, “Performance of mercury cadmium telluride photoconductive devices,” Infrared Phys. 31, 543–554 (1991).
[CrossRef]

Shepherd, T. J.

D. J. Day, T. J. Shepherd, “Transport in photoconductors—I,” Solid-State Electron. 25, 707–712 (1982).
[CrossRef]

T. J. Shepherd, D. J. Day, “Transport in photoconductors—II,” Solid-State Electron. 25, 713–718 (1982).
[CrossRef]

Van der Ziel, A.

A. Van der Ziel, Fluctuation Phenomena in Semi-Conductors (Academic, New York, 1959), pp. 33–36.

Wilson, D. J.

C. T. Elliot, D. Day, D. J. Wilson, “An integrating detector for serial scan thermal imaging,” Infrared Phys. 22, 31–42 (1982).
[CrossRef]

Appl. Opt.

G. D. Boreman, A. E. Plogstedt, “Modulation transfer function and number of equivalent elements for SPRITE detectors,” Appl. Opt. 27, 4331–4335 (1988).
[CrossRef] [PubMed]

Appl. Opt.

Electron. Lett.

C. T. Elliot, “New detector for thermal imaging systems,” Electron. Lett. 17, 312–313 (1981).
[CrossRef]

IEE Conf. Publ.

S. P. Braim, A. P. Campbell, “TED (SPRITE) detector MTF,” IEE Conf. Publ. 228, 63–66 (1983).

Infrared Phys.

C. T. Elliot, D. Day, D. J. Wilson, “An integrating detector for serial scan thermal imaging,” Infrared Phys. 22, 31–42 (1982).
[CrossRef]

A. Józwikowska, K. Józwikowski, A. Rogalski, “Performance of mercury cadmium telluride photoconductive devices,” Infrared Phys. 31, 543–554 (1991).
[CrossRef]

Solid-State Electron.

D. J. Day, T. J. Shepherd, “Transport in photoconductors—I,” Solid-State Electron. 25, 707–712 (1982).
[CrossRef]

T. J. Shepherd, D. J. Day, “Transport in photoconductors—II,” Solid-State Electron. 25, 713–718 (1982).
[CrossRef]

Other

P. Fredin, “Optimum choice of anamorphic ratio and boost filter parameters for a SPRITE based IR sensor,” in Infrared Imaging Systems: Design, Analysis, Modeling and Testing II, G. C. Holst, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1488, 432–442 (1991).

S. P. Braim, “The measurement and analysis of the noise frequency spectrum for SPRITE infrared detectors,” in Infrared Technology and Applications, L. R. Baker, A. Masson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.590, 164–171 (1985).

A. Van der Ziel, Fluctuation Phenomena in Semi-Conductors (Academic, New York, 1959), pp. 33–36.

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Figures (2)

Fig. 1
Fig. 1

Comparison of the noise ASD, the signal strength (MTF), and the resulting SNR for a typical detector by use of the eigenmode method.

Fig. 2
Fig. 2

SNR versus frequency as the detector contact number (Nbz ) varies from 0.01 to 100 times its nominal value.

Equations (17)

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d ρ d t B = G ρ τ .
ρ ( z B , t B ) = 1 exp ( t B τ ) = 1 exp ( z B V τ ) .
σ N ( z B ) = [ 2 exp ( z B V τ ) ] 1 / 2 .
q i ( x , y , z , t ) = δ ( x x 0 ) δ ( y y 0 ) × δ ( z z 0 ) δ ( t ) f ( x 0 , y 0 , z 0 ) .
q i ( x , y , z , t ) = p , q , r c pqr X p ( x ) Y q ( y ) Z r ( z ) × T ( t ) exp ( N d z z ) ,
c pqr = d x d y d z X p ( x ) Y q ( y ) Z r ( z ) exp ( N d z z ) q i ( x , y , z , t ) d x d y d z X p 2 ( x ) Y q 2 ( y ) Z r 2 ( z ) .
c pqr = cos [ k x p x 0 + p ( π / 2 ) ] cos [ k y q y 0 + q ( π / 2 ) ] exp ( N d z z 0 ) cos [ k z r z 0 + r ( π / 2 ) ] [ 1 + | sinc ( 2 k xp ) | ] [ 1 + | sinc ( 2 k y q ) | ] [ 1 + | sinc ( 2 k z r ) | ] f ( x 0 , y 0 , z 0 ) .
Q ( t , x 0 , y 0 , z 0 ) = p , q , r c p q r u ( t ) exp ( k p q r 2 t ) b p q r .
Q ¯ ( ω , x 0 , y 0 , z 0 ) = F { Q } = p , q , r c p q r b p q r 1 k p q r 2 + j ω .
PSD OUT ( ω , x 0 , y 0 , z 0 ) = Q ¯ * ( ω , x 0 , y 0 , z 0 ) Q ¯ ( ω , x 0 , y 0 , z 0 ) × PSD IN ( ω , x 0 , y 0 , z 0 ) .
PSD OUT ( ω , x 0 , y 0 , z 0 ) = p , q , r α , β , γ b p q r b α β γ c p q r c α β γ ( k p q r 2 + j ω ) ( k α β γ 2 j ω ) .
S N ( ω ) = 1 1 d x 0 d y 0 z 0 PSD OUT ( ω , x 0 , y 0 , z ) .
S N ( ω ) = p , q , r , γ b p q r b p q γ a r γ [ 1 + | sinc ( 2 k x p ) | ] [ 1 + | sinc ( 2 k y q ) | ] ( k p q r 2 + j ω ) ( k p q γ 2 j ω ) .
a r γ = Re { exp [ j ( π / 2 ) ( r + γ ) ] sinc [ k z r + k z γ + 2 j N d z ] + exp [ j ( π / 2 ) ( r γ ) ] sinc [ k z r k z γ + 2 j N d z ] } [ 1 + | sinc ( 2 k z r ) | ] [ 1 + | sinc ( 2 k z γ ) | ] .
s N ( ω ) = p , q , r , γ γ r b p q r b p q γ a r γ ( 1 + δ r γ ) ( k p q r 2 k p q γ 2 + ω 2 ) [ 1 + | sinc ( 2 k x p ) | ] [ 1 + | sinc ( 2 k y q ) | ] { ( k p q r 2 k p q γ 2 + ω 2 ) 2 + ( k p q r 2 k p q γ 2 ) 2 ω 2 } ,
S N ( ω ) sinc 2 ( ω l r / ν ) [ 1 + ( D μ 2 E z 2 τ ) 2 ω 2 ] .
S N ( ω ) 1 [ ( 1 + N s x N d z 2 + N s y π 2 / 4 ) 2 + ω 2 ] .

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