Abstract

Undersampled staring array imagers exhibit sampling artifacts. Dither is a mechanical means of raising the spatial sampling rate without increasing the number of detectors on the focal plane array. Diagonal (two-point or slant-path) dither is easier to implement than rectangular (four-point or bowtie) dither. Also, diagonal dither generates half the data rate of rectangular dither. However, diagonal dither does not sample the image as effectively as rectangular dither. The cost and complexity advantages of diagonal dither must be traded against the expectation of reduced performance. We discuss analytical and empirical predictions of the performance difference between diagonal and rectangular dither. To compare diagonal and rectangular dither empirically, a target identification (ID) experiment was performed. The visual task involved target ID among a set of 12 tactical vehicles. High-resolution (close-up) images of the targets were blurred and downsampled to produce images representative of those seen with a 320 × 240 pixel staring array sensor. The nondithered imagery was poorly sampled, and the imagery with rectangular dither was adequately sampled. The experiment compared the static target ID performance of nondithered, diagonally dithered, and rectangularly dithered sensors. Analytical and empirical results are described.

© 2001 Optical Society of America

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References

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  1. R. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electrooptical Systems (Artech House, Boston, 1999).
  2. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  4. S. K. Park, R. Schowengerdt, M. A. Kaczynski, “Modulation-transfer function analysis for sampled-image systems,” Appl. Opt. 23, 2572–2582 (1984).
    [CrossRef]
  5. K. M. Hock, “Effect of oversampling in pixel arrays,” Opt. Eng. 30, 1281–1287 (1985).
  6. O. Hadar, A. Dogariu, G. D. Boreman, “Angular dependence of sampling modulation transfer function,” Appl. Opt. 36, 7210–7216 (1997).
    [CrossRef]
  7. O. Hadar, G. D. Boreman, “Analysis of Oversampling Requirements in Pixelated-Imager Systems,” Opt. Eng. 38, 782–785 (1999).
    [CrossRef]
  8. F. Houk, N. Halyo, S. Park, “Aliasing and blurring in 2D sampled imagery,” Appl. Opt. 19, 2174–2181 (1980).
    [CrossRef]
  9. R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
    [CrossRef]
  10. R. H. Vollmerhausen, R. G. Driggers, Analysis of Sampled Imaging Systems, Vol. TT39 of SPIE Tutorial Texts in Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 2000).
  11. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 6.
  12. I. Overington, Vision and Acquisition (Crane, Russak, & Co., New York, 1976).
  13. R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
    [CrossRef]
  14. R. G. Driggers, R. H. Vollmerhausen, B. L. O’Kane, “Equivalent blur as a function of spurious response of a sampled imaging system: application to character recognition,” J. Opt. Soc. Am. A 16, 1026–1033 (1999).
    [CrossRef]

1999 (4)

O. Hadar, G. D. Boreman, “Analysis of Oversampling Requirements in Pixelated-Imager Systems,” Opt. Eng. 38, 782–785 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. G. Driggers, R. H. Vollmerhausen, B. L. O’Kane, “Equivalent blur as a function of spurious response of a sampled imaging system: application to character recognition,” J. Opt. Soc. Am. A 16, 1026–1033 (1999).
[CrossRef]

1997 (1)

1985 (1)

K. M. Hock, “Effect of oversampling in pixel arrays,” Opt. Eng. 30, 1281–1287 (1985).

1984 (1)

1980 (1)

Boreman, G. D.

O. Hadar, G. D. Boreman, “Analysis of Oversampling Requirements in Pixelated-Imager Systems,” Opt. Eng. 38, 782–785 (1999).
[CrossRef]

O. Hadar, A. Dogariu, G. D. Boreman, “Angular dependence of sampling modulation transfer function,” Appl. Opt. 36, 7210–7216 (1997).
[CrossRef]

Cox, P.

R. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electrooptical Systems (Artech House, Boston, 1999).

Dogariu, A.

Driggers, R.

R. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electrooptical Systems (Artech House, Boston, 1999).

Driggers, R. G.

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. G. Driggers, R. H. Vollmerhausen, B. L. O’Kane, “Equivalent blur as a function of spurious response of a sampled imaging system: application to character recognition,” J. Opt. Soc. Am. A 16, 1026–1033 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, Analysis of Sampled Imaging Systems, Vol. TT39 of SPIE Tutorial Texts in Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 2000).

Edwards, T.

R. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electrooptical Systems (Artech House, Boston, 1999).

Gaskill, J. D.

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

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 6.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hadar, O.

O. Hadar, G. D. Boreman, “Analysis of Oversampling Requirements in Pixelated-Imager Systems,” Opt. Eng. 38, 782–785 (1999).
[CrossRef]

O. Hadar, A. Dogariu, G. D. Boreman, “Angular dependence of sampling modulation transfer function,” Appl. Opt. 36, 7210–7216 (1997).
[CrossRef]

Halyo, N.

Hock, K. M.

K. M. Hock, “Effect of oversampling in pixel arrays,” Opt. Eng. 30, 1281–1287 (1985).

Houk, F.

Kaczynski, M. A.

O’Kane, B. L.

R. G. Driggers, R. H. Vollmerhausen, B. L. O’Kane, “Equivalent blur as a function of spurious response of a sampled imaging system: application to character recognition,” J. Opt. Soc. Am. A 16, 1026–1033 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

Overington, I.

I. Overington, Vision and Acquisition (Crane, Russak, & Co., New York, 1976).

Park, S.

Park, S. K.

Schowengerdt, R.

Vollmerhausen, R. H.

R. G. Driggers, R. H. Vollmerhausen, B. L. O’Kane, “Equivalent blur as a function of spurious response of a sampled imaging system: application to character recognition,” J. Opt. Soc. Am. A 16, 1026–1033 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, Analysis of Sampled Imaging Systems, Vol. TT39 of SPIE Tutorial Texts in Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 2000).

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Eng. (4)

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

K. M. Hock, “Effect of oversampling in pixel arrays,” Opt. Eng. 30, 1281–1287 (1985).

O. Hadar, G. D. Boreman, “Analysis of Oversampling Requirements in Pixelated-Imager Systems,” Opt. Eng. 38, 782–785 (1999).
[CrossRef]

R. H. Vollmerhausen, R. G. Driggers, B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
[CrossRef]

Other (6)

R. H. Vollmerhausen, R. G. Driggers, Analysis of Sampled Imaging Systems, Vol. TT39 of SPIE Tutorial Texts in Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 2000).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 6.

I. Overington, Vision and Acquisition (Crane, Russak, & Co., New York, 1976).

R. Driggers, P. Cox, T. Edwards, Introduction to Infrared and Electrooptical Systems (Artech House, Boston, 1999).

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (24)

Fig. 1
Fig. 1

Operation of dither mirror. Mirror permits changing sample phase by subpixel translation of the image relative to the FPA.

Fig. 2
Fig. 2

Dither patterns. (a) Rectangular dither. Scene is dithered both horizontally and vertically. The dither can be accomplished in multiple ways, only two of them shown. If the scene is static, then all the dither patterns provide the same result. (b) Diagonal dither. Black dots show sample locations during field 1. Gray dots show sample locations during field 2. Scene sampling has improved, but neither horizontal nor vertical sampling is doubled.

Fig. 3
Fig. 3

Black dots and dark-gray dots, video field 1. White dots and light-gray dots, video field 2. The eye integrates the video fields, and the rectangular dither samples are perceived to be in the correct locations.

Fig. 4
Fig. 4

Diagonal dither reconstruction. (a) The subimage sample sets are indicated by the black and the gray dots. The image is reconstructed by interpolation of adjacent horizontal samples. In this case subimages are not mixed in any one video display field, and motion artifacts are minimized. (b) Diagonal dither samples are shown by black dots and gray dots. Mottled gray dots indicate positions where estimated values are needed. If the scene was static, then a two-dimensional interpolation provides the best estimated values.

Fig. 5
Fig. 5

Sampled imaging system model.

Fig. 6
Fig. 6

Component spectrums in sampled imaging model.

Fig. 7
Fig. 7

Sampled imaging system spectrum.

Fig. 8
Fig. 8

Dithered sampled image spectrum (doubled sample rate).

Fig. 9
Fig. 9

Fourier transforms of sampling patterns. (a) Undithered. (b) Four-point dithered. (c) Slant-path dithered.

Fig. 10
Fig. 10

Frequency-domain depiction of presample MTF’s. (a) Detector MTF. (b) Optics MTF. (c) Presample MTF.

Fig. 11
Fig. 11

(a) MTF of Vollmerhausen interpolation filter. (b) Kernel for Vollmerhausen filter

Fig. 12
Fig. 12

Frequency-domain analysis of sensor 1, undersampled, without dither. (a) Sampled spurious spectrum. (b) Reconstruction MTF. (c) Baseband response. (d) SR.

Fig. 13
Fig. 13

MTF’s without dither.

Fig. 14
Fig. 14

Frequency-domain analysis of sensor 2, adequately sampled, four-point dither. (a) Sampled spurious spectrum. (b) Reconstruction MTF. (c) Baseband response. (d) SR.

Fig. 15
Fig. 15

Four-point dither MTF’s.

Fig. 16
Fig. 16

Frequency-domain analysis of sensor 3, two-point dither, horizontal pixel replication interpolator. (a) Sampled spurious spectrum. (b) Reconstruction MTF. (c) Baseband response. (d) SR.

Fig. 17
Fig. 17

Horizontal pixel replication interpolation MTF.

Fig. 18
Fig. 18

Diagonal Vollmerhausen pixel interpolator kernel.

Fig. 19
Fig. 19

Frequency-domain analysis of sensor 4, two-point dither, diagonal Vollmerhausen pixel interpolator. (a) Sampled spurious spectrum. (b) Reconstruction MTF. (c) Baseband response. (d) SR.

Fig. 20
Fig. 20

Target set.

Fig. 21
Fig. 21

Empirical results of target ID perception experiment.

Fig. 22
Fig. 22

Processed images of M551 Sheridan.

Fig. 23
Fig. 23

Dither ID performance, corrected with MTF squeeze weight of 1.0.

Fig. 24
Fig. 24

Dither ID performance corrected with MTF squeeze weight of 2.0.

Tables (2)

Tables Icon

Table 1 System Parameters

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Table 2 Analysis Summary in Terms of MTF Bandwidth

Equations (11)

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ox, y=ix, y*hx, ysx, y*dx, y,
SR=-spurious_responsedξ-baseband_signaldξ,
SRin=-ν/2ν/2spurious_responsedξ-baseband_signaldξ
SRout=SR-SRin,
sx, yundithered=1acombxa1bcombxb,
sx, y4-pt=2acombxa/22bcombxb/2.
sx, y2-pt=1acombxa1bcombyb+1acombx-a/2a1bcomby-b/2b.
Fξ, ηundithered=FξFη=combaξcombbη.
Fξ, η4-pt=FξFη=comba2ξcombb2η.
Fξ, η2-pt=combaξcombbη+combaξexp×-j2πa/2ξcombbη×exp-j2πb/2η.
Fξ, η2-pt=combaξ2combbη2+comba2ξ-1a×combb2η-1b.

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