Abstract

This paper presents a new theory to predict the impact of sampling on target acquisition. The aliased signal that results from sampling is treated as noise. The aliased signal is different from detector noise in two ways. First, aliasing disappears as the target contrast decreases. Second, the image corruption due to aliasing gets worse with increased range. This is because sampling is constant in angle space, and targets become poorly sampled as range increases. The theory is presented, along with the results of three experiments. The match between model and experiment is excellent.

© 2008 Optical Society of America

Full Article  |  PDF Article

Errata

Richard H. Vollmerhausen, Ronald G. Driggers, and David L. Wilson, "Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise: erratum," J. Opt. Soc. Am. A 26, 2418-2418 (2009)
https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-26-11-2418

References

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  1. R. G. Driggers, R. H. Vollmerhausen, and B. O'Kane, “Character recognition as a function of spurious response,” J. Opt. Soc. Am. A 16, 1026-1033 (1999).
    [CrossRef]
  2. R. Vollmerhausen, R. G. Driggers, and B. L. O'Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. (Bellingham) 38, 763-772 (1999).
    [CrossRef]
  3. S. Park and R. Hazra, “Aliasing as noise: a quantitative and qualitative assessment,” Proc. SPIE 1969, 54-65 (1993).
    [CrossRef]
  4. R. H. Vollmerhausen and R. G. Driggers, Analysis of Sampled Imaging Systems (SPIE Press, 2000).
    [CrossRef]
  5. S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
    [CrossRef]
  6. W. Wittenstein, “Minimum temperature difference perceived-a new approach to assess undersampled thermal imagers,” Opt. Eng. (Bellingham) 38, 773-781 (1999).
    [CrossRef]
  7. P. Bijl and J. M. Valeton, “Triangle orientation discrimination: the alternative to minimum resolvable temperature difference and minimum resolvable contrast,” Opt. Eng. (Bellingham) 37, 1976-1983 (1998).
    [CrossRef]
  8. R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004).
    [CrossRef]
  9. R. Vollmerhausen and A. L. Robinson, “Modeling target acquisition tasks associated with security and surveillance,” Appl. Opt. 46, 4209-4221 (2007).
    [CrossRef] [PubMed]
  10. R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).
  11. P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231-238 (2004).
    [CrossRef]
  12. R. Vollmerhausen, “Incorporating display limitations into night vision performance models,” in IRIS Passive Sensors, Proceedings of the Infrared Information Symposium (Environmental Research Institute of Michigan, 1995), Vol. 2, pp. 11-31.
  13. R. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, LucienM.Biberman, ed. (SPIE Press, 2000), pp. 12-1-12-41.
  14. I. Overington, Vision and Acquisition (Crane, Russak & Co., 1976).
  15. R. H. Vollmerhausen, S. Moyer, K. Krapels, R. G. Driggers, J. G. Hixson, and A. L. Robinson, “Predicting the probability of facial identification using a specific object model,” Appl. Opt. 47, 751-759 (2008).
    [CrossRef] [PubMed]

2008

2007

2005

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).

2004

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231-238 (2004).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004).
[CrossRef]

2001

S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
[CrossRef]

2000

R. H. Vollmerhausen and R. G. Driggers, Analysis of Sampled Imaging Systems (SPIE Press, 2000).
[CrossRef]

R. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, LucienM.Biberman, ed. (SPIE Press, 2000), pp. 12-1-12-41.

1999

R. G. Driggers, R. H. Vollmerhausen, and B. O'Kane, “Character recognition as a function of spurious response,” J. Opt. Soc. Am. A 16, 1026-1033 (1999).
[CrossRef]

W. Wittenstein, “Minimum temperature difference perceived-a new approach to assess undersampled thermal imagers,” Opt. Eng. (Bellingham) 38, 773-781 (1999).
[CrossRef]

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

1998

P. Bijl and J. M. Valeton, “Triangle orientation discrimination: the alternative to minimum resolvable temperature difference and minimum resolvable contrast,” Opt. Eng. (Bellingham) 37, 1976-1983 (1998).
[CrossRef]

1995

R. Vollmerhausen, “Incorporating display limitations into night vision performance models,” in IRIS Passive Sensors, Proceedings of the Infrared Information Symposium (Environmental Research Institute of Michigan, 1995), Vol. 2, pp. 11-31.

1993

S. Park and R. Hazra, “Aliasing as noise: a quantitative and qualitative assessment,” Proc. SPIE 1969, 54-65 (1993).
[CrossRef]

1976

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

Barten, P. G. J.

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231-238 (2004).
[CrossRef]

Bijl, P.

P. Bijl and J. M. Valeton, “Triangle orientation discrimination: the alternative to minimum resolvable temperature difference and minimum resolvable contrast,” Opt. Eng. (Bellingham) 37, 1976-1983 (1998).
[CrossRef]

Driggers, R. G.

R. H. Vollmerhausen, S. Moyer, K. Krapels, R. G. Driggers, J. G. Hixson, and A. L. Robinson, “Predicting the probability of facial identification using a specific object model,” Appl. Opt. 47, 751-759 (2008).
[CrossRef] [PubMed]

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004).
[CrossRef]

S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
[CrossRef]

R. H. Vollmerhausen and R. G. Driggers, Analysis of Sampled Imaging Systems (SPIE Press, 2000).
[CrossRef]

R. G. Driggers, R. H. Vollmerhausen, and B. O'Kane, “Character recognition as a function of spurious response,” J. Opt. Soc. Am. A 16, 1026-1033 (1999).
[CrossRef]

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

Friedman, M.

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).

Hazra, R.

S. Park and R. Hazra, “Aliasing as noise: a quantitative and qualitative assessment,” Proc. SPIE 1969, 54-65 (1993).
[CrossRef]

Hixson, J.

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).

Hixson, J. G.

Jacobs, E.

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004).
[CrossRef]

Krapels, K.

Krapels, K. A.

S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
[CrossRef]

Moyer, S.

Moyer, S. K.

S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
[CrossRef]

O'Kane, B.

O'Kane, B. L.

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

Overington, I.

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

Park, S.

S. Park and R. Hazra, “Aliasing as noise: a quantitative and qualitative assessment,” Proc. SPIE 1969, 54-65 (1993).
[CrossRef]

Robinson, A. L.

Valeton, J. M.

P. Bijl and J. M. Valeton, “Triangle orientation discrimination: the alternative to minimum resolvable temperature difference and minimum resolvable contrast,” Opt. Eng. (Bellingham) 37, 1976-1983 (1998).
[CrossRef]

Vollmerhausen, R.

R. Vollmerhausen and A. L. Robinson, “Modeling target acquisition tasks associated with security and surveillance,” Appl. Opt. 46, 4209-4221 (2007).
[CrossRef] [PubMed]

R. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, LucienM.Biberman, ed. (SPIE Press, 2000), pp. 12-1-12-41.

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

R. Vollmerhausen, “Incorporating display limitations into night vision performance models,” in IRIS Passive Sensors, Proceedings of the Infrared Information Symposium (Environmental Research Institute of Michigan, 1995), Vol. 2, pp. 11-31.

Vollmerhausen, R. H.

R. H. Vollmerhausen, S. Moyer, K. Krapels, R. G. Driggers, J. G. Hixson, and A. L. Robinson, “Predicting the probability of facial identification using a specific object model,” Appl. Opt. 47, 751-759 (2008).
[CrossRef] [PubMed]

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004).
[CrossRef]

S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
[CrossRef]

R. H. Vollmerhausen and R. G. Driggers, Analysis of Sampled Imaging Systems (SPIE Press, 2000).
[CrossRef]

R. G. Driggers, R. H. Vollmerhausen, and B. O'Kane, “Character recognition as a function of spurious response,” J. Opt. Soc. Am. A 16, 1026-1033 (1999).
[CrossRef]

Wittenstein, W.

W. Wittenstein, “Minimum temperature difference perceived-a new approach to assess undersampled thermal imagers,” Opt. Eng. (Bellingham) 38, 773-781 (1999).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng. (Bellingham)

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

W. Wittenstein, “Minimum temperature difference perceived-a new approach to assess undersampled thermal imagers,” Opt. Eng. (Bellingham) 38, 773-781 (1999).
[CrossRef]

P. Bijl and J. M. Valeton, “Triangle orientation discrimination: the alternative to minimum resolvable temperature difference and minimum resolvable contrast,” Opt. Eng. (Bellingham) 37, 1976-1983 (1998).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. (Bellingham) 43, 2806-2818 (2004).
[CrossRef]

Proc. SPIE

S. Park and R. Hazra, “Aliasing as noise: a quantitative and qualitative assessment,” Proc. SPIE 1969, 54-65 (1993).
[CrossRef]

S. K. Moyer, R. G. Driggers, R. H. Vollmerhausen, and K. A. Krapels, “Target identification performance as a function of spurious response; aliasing with respect to the half sample rate,” Proc. SPIE 4372, 51-61 (2001).
[CrossRef]

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231-238 (2004).
[CrossRef]

Other

R. Vollmerhausen, “Incorporating display limitations into night vision performance models,” in IRIS Passive Sensors, Proceedings of the Infrared Information Symposium (Environmental Research Institute of Michigan, 1995), Vol. 2, pp. 11-31.

R. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, LucienM.Biberman, ed. (SPIE Press, 2000), pp. 12-1-12-41.

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

R. H. Vollmerhausen and R. G. Driggers, Analysis of Sampled Imaging Systems (SPIE Press, 2000).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The targeting task performance (TTP) metric: a new model for predicting target acquisition performance,” Tech. Rep. (DTIC AMSEL-NV-TR-230, U.S. Army Research, Development and Engineering Command, Communications and Electronics Research, Development and Engineering Center, Night Vision and Electronic Sensors Directorate, 10221 Burbeck Rd., Ft. Belvoir, VA 22060-5806, 2005).

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Figures (18)

Fig. 1
Fig. 1

Pictures of a clock taken with an undersampled imager. The numerals become harder to read as range increases.

Fig. 2
Fig. 2

Linear size of bar chart at top (a) grows in proportion to range. The linear size of bar chart at bottom (b) is constant.

Fig. 3
Fig. 3

Alias spectrum and transfer response for experiment 25, lines 1 and 4.

Fig. 4
Fig. 4

Alias spectrum and transfer response for experiment 36, lines 1 and 3.

Fig. 5
Fig. 5

Alias spectra and transfer response for Experiment 21(d), cell F. In-band aliasing is line 1, mid-band is line 2, and out-of-band is line 3.

Fig. 6
Fig. 6

PID versus range for experiment 36, line 1.

Fig. 7
Fig. 7

PID versus range for experiment 36, line 2.

Fig. 8
Fig. 8

PID versus range for experiment 36, line 3.

Fig. 9
Fig. 9

PID versus range for experiment 36, line 4.

Fig. 10
Fig. 10

PID versus range for experiment 25, line 1.

Fig. 11
Fig. 11

PID versus range for experiment 25, line 2.

Fig. 12
Fig. 12

PID versus range for experiment 25, line 3.

Fig. 13
Fig. 13

PID versus range for experiment 25, line 4.

Fig. 14
Fig. 14

PID versus range for experiment 25, line 5.

Fig. 15
Fig. 15

PID versus range for experiment 25, line 6.

Fig. 16
Fig. 16

Model predicted PID (ordinate) versus measured PID (abscissa) for experiment 21. The straight line represents a perfect fit between model and data. Display-to-eye distance is assumed to be fixed at 46 cm .

Fig. 17
Fig. 17

Model predicted PID (ordinate) versus measured PID (abscissa) for experiment 21. Display-to-eye distance is allowed to vary between 30 and 75 cm .

Fig. 18
Fig. 18

Picture of clock showing how display raster can hide the underlying image.

Tables (3)

Tables Icon

Table 1 Display Interpolations a , System Magnifications, and Detector Fill-Factors for Sampling Experiments

Tables Icon

Table 2 Preblur, Downsample, Postblur for Each Cell of Experiment 21

Tables Icon

Table 3 Model Fit Criteria

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

O ( ξ , η ) = [ I ( ξ , η ) H pre ( ξ , η ) comb ( a ξ , b η ) ] D ( ξ , η ) .
O ( ξ , η ) = [ I ( ξ , η ) H pre ( ξ , η ) m = 0 n = 0 δ ( ξ n a , η m b ) ] D ( ξ , η ) ,
A ( ξ , η ) = [ I ( ξ , η ) H pre ( ξ , η ) m & n 0 δ ( ξ n a , η m b ) ] D ( ξ , η ) .
A ( ξ , η ) = [ T con H pre ( ξ , η ) m & n 0 δ ( ξ n a , η m b ) ] D ( ξ , η )
= [ T con m & n 0 H pre ( ξ n ν , η m γ ) ] D ( ξ , η ) .
Φ = [ δ ( C TGT CTF sys ( ξ ) ) C TGT CTF sys ( ξ ) d ξ R ng δ ( C TGT CTF sys ( η ) ) C TGT CTF sys ( η ) d η R ng ] 1 2 .
Φ = δ ( C TGT CTF sys ( ξ ) ) C TGT CTF sys ( ξ ) d ξ R ng ,
C TGT = T con 2 SCN .
CTF ( ξ ) = [ a ξ e b ξ 1 + 0.06 e b ξ ] 1 ,
a = 540 ( 1 + 0.2 L ) 0.2 1 + 12 w a 2 ( 1 + 5.8 ξ ) 2 and b = 5.24 ( 1 + 29.2 L ) 0.15 .
CTF sys ( ξ ) = CTF ( ξ smag ) H sys ( ξ ) ( 1 + α 2 Γ det 2 Q ( ξ , η ) SCN 2 ) 1 2 ,
Q ( ξ , η ) = B ( ξ smag ) D ( ξ ) H eye ( ξ smag ) 2 d ξ D ( η ) H eye ( η smag ) 2 d η .
δ ( C TGT CTF sys ( ξ ) ) { = 1 for C TGT CTF sys ( ξ ) 1 = 0 for C TGT CTF sys ( ξ ) < 1 } .
PID ( Φ Φ 84 ) = erf ( Φ Φ 84 ) = 2 π 0 Φ Φ 84 e t 2 d t .
A ( ξ , η ) = [ t eye T con m & n 0 H pre ( ξ n ν ) δ ( η 0 ) ] D ( ξ ) D ( η ) .
CTF sys ( ξ ) = CTF ( ξ smag ) H sys ( ξ ) ( 1 + α 2 Γ det 2 Q ( ξ , η ) SCN 2 + α 2 t eye T con 2 R ng 2 Q a ( ξ , η ) SCN 2 ) 1 2 ,
Q a ( ξ , η ) = δ ( η 0 ) D ( η ) d η n = n 0 H pre ( ξ n ν ) B ( ξ smag ) D ( ξ ) H eye ( ξ smag ) 2 d ξ .
ξ m = ξ R ng .
G ( ξ , η , R ng ) = I m ( ξ R ng , η R ng ) R ng 2 .
aliasing noise ( units ) α 2 ( Hertz ) t eye ( second ) T con 2 ( w m 2 sr 1 mrad ) 2 R ng 2 ( m 2 mrad 2 ) ( mrad ) 2 SCN 2 ( w m 2 sr 1 m ) 2 .
detector noise ( units ) α 2 ( Hertz mrad 2 ) Γ det 2 ( second 1 2 w m 2 sr 1 mrad ) 2 ( mrad ) 2 SCN 2 ( w m 2 sr 1 mrad ) 2 ,
aliasing noise ( units ) α 2 ( Hertz mrad 2 ) t eye ( second ) T con 2 ( w m 2 sr 1 mrad ) 2 R ng 2 ( m 2 mrad 2 ) ( mrad ) 2 SCN 2 ( w m 2 sr 1 m ) 2 .
c i = sinc ( i b ) exp [ π ( i 4 b ) 2 ] ,

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