Abstract

This paper explores practical design considerations for selecting Q for an electro-optical earth imaging system, where Q is defined as (λ FN) / pixel pitch. Analytical methods are used to show that, under imaging conditions with high SNR, increasing Q with fixed aperture cannot lead to degradation of image quality regardless of the angular smear rate of the system. The potential for degradation of image quality under low SNR is bounded by an increase of the detector noise scaling as Q. An imaging test bed is used to collect representative imagery for various Q configurations. The test bed includes real world errors such as image smear and haze. The value of Q is varied by changing the focal length of the imaging system. Imagery is presented over a broad range of parameters.

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References

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  1. R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng.38(7), 1229–1240 (1999).
    [CrossRef]
  2. R. D. Fiete and T. A. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng.40(4), 574–585 (2001).
    [CrossRef]
  3. J. R. Fienup, “MTF and Integration Time versus Fill Factor for Sparse-Aperture Imaging Systems,” in Imaging Technology and Telescopes, edited by J. W. Bilbro, J. B. Breckinridge, R. A. Carreras, S. R. Czyzak, M. J. Eckart, R. D. Fiete, P. S. Idell, Proc. SPIE 4091 (2000).
  4. R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).
  5. A. T. Cochrane, G. C. Robins, G. J. Baker, R. M. Bell, V. G. Zarifis, and B. J. Herman, “Practical aspects of image system validation using transillumination,” in Modeling, Systems Engineering, and Project Management for Astronomy II, edited by M. J. Cullum, G. Z. Angeli, Proc. SPIE 6271 (2006).
  6. J. W. Goodman, Introduction to Fourier Optics, Second Edition (The McGraw-Hill Companies, Inc., 1996), Chap. 6.
  7. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Second Edition (Cambridge University Press, 1997), Chap. 13.
  8. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A4(12), 2379–2394 (1987).
    [CrossRef] [PubMed]

2011

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

2001

R. D. Fiete and T. A. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng.40(4), 574–585 (2001).
[CrossRef]

1999

R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng.38(7), 1229–1240 (1999).
[CrossRef]

1987

Bell, R.

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

Cochrane, A.

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

Field, D. J.

Fiete, R. D.

R. D. Fiete and T. A. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng.40(4), 574–585 (2001).
[CrossRef]

R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng.38(7), 1229–1240 (1999).
[CrossRef]

Kendrick, R. L.

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

Schulz, K.

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

Smith, E.

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

Tantalo, T. A.

R. D. Fiete and T. A. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng.40(4), 574–585 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng.38(7), 1229–1240 (1999).
[CrossRef]

R. D. Fiete and T. A. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng.40(4), 574–585 (2001).
[CrossRef]

Proc. SPIE

R. L. Kendrick, A. Cochrane, K. Schulz, R. Bell, and E. Smith, “Image Quality effects due to image plane sampling: Experimental Results,” in Sensors, Systems, and Next-Generation Satellites XV, Proc. SPIE, 8176 (2011).

Other

A. T. Cochrane, G. C. Robins, G. J. Baker, R. M. Bell, V. G. Zarifis, and B. J. Herman, “Practical aspects of image system validation using transillumination,” in Modeling, Systems Engineering, and Project Management for Astronomy II, edited by M. J. Cullum, G. Z. Angeli, Proc. SPIE 6271 (2006).

J. W. Goodman, Introduction to Fourier Optics, Second Edition (The McGraw-Hill Companies, Inc., 1996), Chap. 6.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Second Edition (Cambridge University Press, 1997), Chap. 13.

J. R. Fienup, “MTF and Integration Time versus Fill Factor for Sparse-Aperture Imaging Systems,” in Imaging Technology and Telescopes, edited by J. W. Bilbro, J. B. Breckinridge, R. A. Carreras, S. R. Czyzak, M. J. Eckart, R. D. Fiete, P. S. Idell, Proc. SPIE 4091 (2000).

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Figures (13)

Fig. 1
Fig. 1

The zoom lens for varying the system focal length is shown in the 1x and 2x configuration. The positions of the two doublets are varied to adjust the system focal length.

Fig. 2
Fig. 2

MTF measurements for variable zoom.

Fig. 3
Fig. 3

. Example object amplitude spectrum estimation

Fig. 4
Fig. 4

. Image filtering example.

Fig. 5
Fig. 5

Q = 1 image examples at each SNR level: (a) High SNR (b) Low SNR

Fig. 6
Fig. 6

High SNR, 0.0p Smear, Variable Exposure.(CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 7
Fig. 7

High SNR, 0.0p Smear, Fixed Exposure (CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 8
Fig. 8

Low SNR, 0.0p Smear, Variable Exposure (CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 9
Fig. 9

Low SNR, 0.0p Smear, Fixed Exposure (CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 10
Fig. 10

High SNR, 0.8p Smear, Variable Exposure (CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 11
Fig. 11

High SNR, 0.8p Smear, Fixed Exposure (CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 12
Fig. 12

Low SNR, 0.8p Smear, Variable Exposure (CW from upper left: Q = 0.98, 1.51, 1.95)

Fig. 13
Fig. 13

Low SNR, 0.8p Smear, Fixed Exposure (CW from upper left: Q = 0.98, 1.51, 1.95, 1.95 low-pass filtered)

Tables (2)

Tables Icon

Table 1 Results of smear characterization and validation.

Tables Icon

Table 2 Summary of SNR levels.

Equations (14)

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i( x )=o( x )h( x )+n( x )
i ˜ ( υ )= o ˜ ( υ )×OTF( υ )+ n ˜ ( υ )
SNR( υ )= | o ˜ ( υ ) |MTF( υ ) n ˜ ( υ ) 2 1 2
SNR( υ )= P/N P/ N 2 + P haze / N 2 + σ 2 | o ˜ ( υ ) | | o ˜ ( 0 ) | MTF( υ )
υ Nyquist = Q 2 υ cut
SN R frequency ( υ;Q ) SN R frequency ( υ; Q 0 ) = sinc( p 0 Q υ ) sinc( p 0 Q 0 υ )
SN R frequency ( υ;Q ) SN R frequency ( υ; Q 0 ) = 1+ N 0 2 σ 2 P+ P haze 1+ ( Q Q 0 ) 2 N 0 2 σ 2 P+ P haze sinc( p 0 Q υ ) sinc( p 0 Q 0 υ )
SN R frequency ( υ;Q ) SN R frequency ( υ; Q 0 ) = 1+ σ 2 l 1+ ( Q Q 0 ) 2 σ 2 l sinc( p 0 Q υ ) sinc( p 0 Q 0 υ )
σ= Q Q 0 σ 0
MT F det ( υ )=exp( αυ )sinc( υ )
o ˜ e ( υ )= i ˜ ( υ ) OTF( υ ) ×Φ( υ )
Φ( υ )= 1 1+ c SNR ( υ ) 2
o ˜ ( υ )= 1 υ α
log 10 { i ˜ ( υ ) }=α log 10 ( υ )+ log 10 { MTF( υ ) }

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