Abstract

A method for calculating the modulation transfer function (MTF) of charge-coupled devices (CCD) is presented. The analysis accommodates both the time- and space-variant properties of CCDs as well as input images moving with constant velocity within a scan interval. The model developed accounts for both the static and the dynamic MTF of CCD imaging systems.

© 1990 Optical Society of America

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References

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  1. W. S. Boule, G. E. Smith, “Charge Coupled Semiconductor Devices,” Bell Syst. Tech. J. 49, 587–593 (1970).
  2. J. W. Coltman, “The Specification of Imaging Properties by Response to a Sine Wave Input,” J. Opt. Soc. Am. 44, 468–471 (1954).
    [CrossRef]
  3. S. B. Campana, “Techniques for Evaluating Charge Coupled Imagers,” Opt. Eng. 16, 267–274 (1977).
    [CrossRef]
  4. A. Nordbryhn, “The Dynamic Sampling Effect with CCD Imagers,” presented at SPIE Technical Symposium-East, Washington, DC (Mar. 1978).
  5. A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).
  6. L. Levi, “Spatiotemporal Transfer Function: Recent Developments,” Appl. Opt. 22, 4038–4041 (1983).
    [CrossRef] [PubMed]
  7. S. K. Park, R. Schowengerdt, M. Kaczynski, “Modulation-Transfer-Function Analysis for Sampled Image Systems,” Appl. Opt. 23, 2572–2582 (1984).
    [CrossRef] [PubMed]
  8. W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
    [CrossRef]

1989 (1)

A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).

1984 (1)

1983 (1)

1982 (1)

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
[CrossRef]

1977 (1)

S. B. Campana, “Techniques for Evaluating Charge Coupled Imagers,” Opt. Eng. 16, 267–274 (1977).
[CrossRef]

1970 (1)

W. S. Boule, G. E. Smith, “Charge Coupled Semiconductor Devices,” Bell Syst. Tech. J. 49, 587–593 (1970).

1954 (1)

Awwal, A. A. S.

A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).

Baars, J.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
[CrossRef]

Boule, W. S.

W. S. Boule, G. E. Smith, “Charge Coupled Semiconductor Devices,” Bell Syst. Tech. J. 49, 587–593 (1970).

Campana, S. B.

S. B. Campana, “Techniques for Evaluating Charge Coupled Imagers,” Opt. Eng. 16, 267–274 (1977).
[CrossRef]

Cherri, A. K.

A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).

Coltman, J. W.

Fontanella, J. C.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
[CrossRef]

Kaczynski, M.

Karim, M. A.

A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).

Levi, L.

Moon, D. L.

A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).

Newberry, A. R.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
[CrossRef]

Nordbryhn, A.

A. Nordbryhn, “The Dynamic Sampling Effect with CCD Imagers,” presented at SPIE Technical Symposium-East, Washington, DC (Mar. 1978).

Park, S. K.

Schowengerdt, R.

Smith, G. E.

W. S. Boule, G. E. Smith, “Charge Coupled Semiconductor Devices,” Bell Syst. Tech. J. 49, 587–593 (1970).

Wittenstein, W.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

W. S. Boule, G. E. Smith, “Charge Coupled Semiconductor Devices,” Bell Syst. Tech. J. 49, 587–593 (1970).

J. Opt. Soc. Am. (1)

Opt. Acta (1)

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Acta 29, 42–50 (1982).
[CrossRef]

Opt. Eng. (1)

S. B. Campana, “Techniques for Evaluating Charge Coupled Imagers,” Opt. Eng. 16, 267–274 (1977).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. A. S. Awwal, A. K. Cherri, M. A. Karim, D. L. Moon, “Dynamic Response of an Electro-Optical Imaging System,” Proc. Soc. Photo-Opt. Instrum. Eng. 1116, 185–197 (1989).

Other (1)

A. Nordbryhn, “The Dynamic Sampling Effect with CCD Imagers,” presented at SPIE Technical Symposium-East, Washington, DC (Mar. 1978).

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Figures (13)

Fig. 1
Fig. 1

Definition of spatial parameters.

Fig. 2
Fig. 2

Definition of offset parameters.

Fig. 3
Fig. 3

Definition of pixel index and critical offset.

Fig. 4
Fig. 4

Definition of parameters for the case of image velocity.

Fig. 5
Fig. 5

Frame transfer (FT) and interline transfer (IT) CCD geometries and transfer paths.

Fig. 6
Fig. 6

MTF variation due to phase parameter with no image velocity.

Fig. 7
Fig. 7

MTF variation due to phase parameter with image velocity.

Fig. 8
Fig. 8

Static MTF.

Fig. 9
Fig. 9

Static MTF.

Fig. 10
Fig. 10

Dynamic MTF.

Fig. 11
Fig. 11

Dynamic MTF.

Fig. 12
Fig. 12

Error introduced by separating the velocity effects from the dynamic MTF when not justified.

Fig. 13
Fig. 13

Mean MTF for several image velocities.

Tables (1)

Tables Icon

Table 1 Comparison of the Actual Dynamic MTF with the Dynamic MTF Calculated by Using the Velocity Separation Approximation

Equations (19)

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I = 0.5 [ 1 + cos ( s ) ] ,
MTF = B max - B min B max + B min ,
α = π T α / T N ,
β = π T β / T N ,
- β 2 ψ H β 2 ,
- β 2 ψ L β 2 .
n = int ( T N / T β ) + 1 ,
ψ H * = π - ( n - 1 / 2 ) β .
ψ L = ψ H + k β ,
k = { n : ψ H ψ H * , n - 1 : ψ H > ψ H * .
B max = θ = ψ H - α / 2 ψ H + α / 2 0.5 [ 1 + cos ( θ ) ] d θ = 0.5 [ α + 2 sin ( α / 2 ) cos ( ψ H ) ] ,
B min = θ = ψ L - α / 2 ψ L + α / 2 0.5 [ 1 + cos ( θ ) ] d θ = 0.5 [ α + 2 sin ( α / 2 ) cos ( ψ L ) ] .
MTF = sin ( α / 2 ) [ cos ( ψ H ) - cos ( ψ H + k β ) ] α + sin ( α / 2 ) [ cos ( ψ H ) + cos ( ψ H + k β ) ] ,
MTF = 2 sin ( α / 2 ) cos ( ψ H ) α .
ν = π v / T N .
B max = t = - γ / 2 γ / 2 θ = ψ H + ν t - α / 2 ψ H + ν t + α / 2 0.5 [ 1 + cos ( θ ) ] d θ d t = 0.5 [ α γ + ( 2 / ν ) sin ( α / 2 ) sin ( ν γ / 2 ) cos ( ψ H ) ] ,
B min = t = - γ / 2 γ / 2 θ = ψ L + ν t - α / 2 ψ L + ν t + α / 2 0.5 [ 1 + cos ( θ ) ] d θ d t = 0.5 [ α γ + ( 2 / ν ) sin ( α / 2 ) sin ( ν γ / 2 ) cos ( ψ L ) ] .
MTF = sin ( α / 2 ) sin ( ν γ / 2 ) [ cos ( ψ H ) - cos ( ψ H - k β ) ] α ν γ / 2 + sin ( α / 2 ) sin ( ν γ / 2 ) [ cos ( ψ H ) + cos ( ψ H + k β ) ] .
MTF = sin ( ν γ / 2 ) ν γ / 2 MTF stat ,

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