Abstract

In support of multiband imaging system performance forecasting, an equation-based triangle orientation discrimination (TOD) model is developed. Specifically, with the characteristic of the test pattern related to spectrum, the mathematical equations for predicting the TOD threshold of the system with distributed fusion architecture in the IR spectrum band are derived based on human vision with the “k/N” fusion rule, with emphasis on the impacts of fusion on the threshold. Furthermore, a figure of merit Q related to the TOD calculation results is introduced to analyze the relation of the discrimination performance of multiband imaging system to the size and the spectral difference of test pattern. The preliminary validation with the experiment results suggests that our proposed model can provide a reasonable prediction of the performance for a multiband imaging system.

© 2011 Optical Society of America

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  1. R. H. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, L.M.Biberman ed. (SPIE, 2000), pp. 1–42.
  2. W. Wittenstein, “Minimum temperature difference perceived- a new approach to assess under-sampled thermal imagers,” Opt. Eng. 38, 773–781 (1999).
    [CrossRef]
  3. P. Bijl and J. M. Valeton, “Triangle orientation discrimination: the alternative to minimum resolvable temperature difference and minimum resolvable contrast,” Opt. Eng. 37, 1976–1983(1998).
    [CrossRef]
  4. R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
    [CrossRef]
  5. T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
    [CrossRef]
  6. W. Wittenstein, “Thermal range model TRM3,” Proc. SPIE 3436, 413–424 (1998).
    [CrossRef]
  7. J. P. Kerekes and J. E. Baum, “Spectral imaging system analytical model for subpixel object detection,” IEEE Trans. Geosci. Remote Sens. 40, 1088–1101 (2002).
    [CrossRef]
  8. J. P. Kerekes and J. E. Baum, “Full-spectrum spectral imaging system analytical model,” IEEE Trans. Geosci. Remote Sens. 43, 571–580 (2005).
    [CrossRef]
  9. M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
    [CrossRef]
  10. J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
    [CrossRef]
  11. P. Bijl and M. A. Hogervorst, “A test method for multi-band imaging sensors,” Proc. SPIE 5076, 208–219 (2003).
    [CrossRef]
  12. X. R. Wang, H. G. Bai, and J. Q. Zhang, “Theoretical model for the performance of a multi-spectral imaging sensor,” Chin. Opt. Lett. 8, 155–158 (2010).
    [CrossRef]
  13. P. Bijl and J. M. Valeton, “TOD, a new method to characterize electro-optical system performance,” Proc. SPIE 3377, 182–193 (1998).
    [CrossRef]
  14. A. M. Fairhurst, A. H. Lettington, and K. S. J. Murphy, “Model to predict the probability of recognition of shapes viewed through a thermal imager,” Proc. SPIE 2744, 611–617(1996).
    [CrossRef]
  15. P. Bijl, M. A. Hogervorst, and J. M. Valeton, “TOD, NVTherm and TRM3 model calculations: a comparison,” Proc. SPIE 4719, 51–62 (2002).
    [CrossRef]
  16. X. R. Wang, J. Q. Zhang, Z. X. Feng, and H. H. Chang, “Equation-based triangle orientation discrimination sensor performance model based on sampling effects,” Appl. Opt. 44, 498–505 (2005).
    [CrossRef]
  17. L. A. Klein, “A Boolean algebra approach to multiple sensor voting fusion,” IEEE Trans. Aerosp. Electon. Syst. 29, 317–327 (1993).
    [CrossRef]
  18. R. Vollmerhausen, R. G. Driggers, and B. L. O’Kane, “Influence of sampling on target recognition and identification,” Opt. Eng. 38, 763–772 (1999).
    [CrossRef]
  19. R. H. Vollmerhausen and R. G. Driggers, “NVTherm: next generation night vision model,” in Proceedings of the 1999 Meeting of the IRIS Passive Sensors (1999), pp. 121–134.
  20. J. D’Agostino and C. Webb, “Three-dimensional analysis framework and measurement methodology for imaging system noise,” Proc. SPIE 1488, 110–121 (1991).
    [CrossRef]
  21. G. C. Holst, Testing and Evaluation of Infrared Imaging Systems, 2nd ed. (SPIE, 1998).
  22. P. Bijl and J. M. Valeton, “Guidelines for accurate TOD measurement,” Proc. SPIE 3701, 14–25 (1999).
    [CrossRef]
  23. Z. Chair and P. K. Varshney, “Optimal data fusion in multiple sensor detection systems,” IEEE Trans. Aerosp. Electon. Syst. 22, 98–101 (1986).
    [CrossRef]

2010 (1)

2007 (1)

M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
[CrossRef]

2005 (3)

J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
[CrossRef]

J. P. Kerekes and J. E. Baum, “Full-spectrum spectral imaging system analytical model,” IEEE Trans. Geosci. Remote Sens. 43, 571–580 (2005).
[CrossRef]

X. R. Wang, J. Q. Zhang, Z. X. Feng, and H. H. Chang, “Equation-based triangle orientation discrimination sensor performance model based on sampling effects,” Appl. Opt. 44, 498–505 (2005).
[CrossRef]

2004 (1)

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

2003 (1)

P. Bijl and M. A. Hogervorst, “A test method for multi-band imaging sensors,” Proc. SPIE 5076, 208–219 (2003).
[CrossRef]

2002 (3)

T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
[CrossRef]

J. P. Kerekes and J. E. Baum, “Spectral imaging system analytical model for subpixel object detection,” IEEE Trans. Geosci. Remote Sens. 40, 1088–1101 (2002).
[CrossRef]

P. Bijl, M. A. Hogervorst, and J. M. Valeton, “TOD, NVTherm and TRM3 model calculations: a comparison,” Proc. SPIE 4719, 51–62 (2002).
[CrossRef]

1999 (3)

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

P. Bijl and J. M. Valeton, “Guidelines for accurate TOD measurement,” Proc. SPIE 3701, 14–25 (1999).
[CrossRef]

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

1998 (3)

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

W. Wittenstein, “Thermal range model TRM3,” Proc. SPIE 3436, 413–424 (1998).
[CrossRef]

P. Bijl and J. M. Valeton, “TOD, a new method to characterize electro-optical system performance,” Proc. SPIE 3377, 182–193 (1998).
[CrossRef]

1996 (1)

A. M. Fairhurst, A. H. Lettington, and K. S. J. Murphy, “Model to predict the probability of recognition of shapes viewed through a thermal imager,” Proc. SPIE 2744, 611–617(1996).
[CrossRef]

1993 (1)

L. A. Klein, “A Boolean algebra approach to multiple sensor voting fusion,” IEEE Trans. Aerosp. Electon. Syst. 29, 317–327 (1993).
[CrossRef]

1991 (1)

J. D’Agostino and C. Webb, “Three-dimensional analysis framework and measurement methodology for imaging system noise,” Proc. SPIE 1488, 110–121 (1991).
[CrossRef]

1986 (1)

Z. Chair and P. K. Varshney, “Optimal data fusion in multiple sensor detection systems,” IEEE Trans. Aerosp. Electon. Syst. 22, 98–101 (1986).
[CrossRef]

Bai, H. G.

Baum, J. E.

J. P. Kerekes and J. E. Baum, “Full-spectrum spectral imaging system analytical model,” IEEE Trans. Geosci. Remote Sens. 43, 571–580 (2005).
[CrossRef]

J. P. Kerekes and J. E. Baum, “Spectral imaging system analytical model for subpixel object detection,” IEEE Trans. Geosci. Remote Sens. 40, 1088–1101 (2002).
[CrossRef]

Bernhardt, M.

M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
[CrossRef]

Bijl, P.

P. Bijl and M. A. Hogervorst, “A test method for multi-band imaging sensors,” Proc. SPIE 5076, 208–219 (2003).
[CrossRef]

P. Bijl, M. A. Hogervorst, and J. M. Valeton, “TOD, NVTherm and TRM3 model calculations: a comparison,” Proc. SPIE 4719, 51–62 (2002).
[CrossRef]

P. Bijl and J. M. Valeton, “Guidelines for accurate TOD measurement,” Proc. SPIE 3701, 14–25 (1999).
[CrossRef]

P. Bijl and J. M. Valeton, “TOD, a new method to characterize electro-optical system performance,” Proc. SPIE 3377, 182–193 (1998).
[CrossRef]

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

Chair, Z.

Z. Chair and P. K. Varshney, “Optimal data fusion in multiple sensor detection systems,” IEEE Trans. Aerosp. Electon. Syst. 22, 98–101 (1986).
[CrossRef]

Chang, H. H.

Clare, P.

M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
[CrossRef]

Cowell, C.

M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
[CrossRef]

D’Agostino, J.

J. D’Agostino and C. Webb, “Three-dimensional analysis framework and measurement methodology for imaging system noise,” Proc. SPIE 1488, 110–121 (1991).
[CrossRef]

Driggers, R. G.

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

T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
[CrossRef]

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

R. H. Vollmerhausen and R. G. Driggers, “NVTherm: next generation night vision model,” in Proceedings of the 1999 Meeting of the IRIS Passive Sensors (1999), pp. 121–134.

Fairhurst, A. M.

A. M. Fairhurst, A. H. Lettington, and K. S. J. Murphy, “Model to predict the probability of recognition of shapes viewed through a thermal imager,” Proc. SPIE 2744, 611–617(1996).
[CrossRef]

Fanning, J.

J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
[CrossRef]

Feng, Z. X.

Freidman, M. H.

T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
[CrossRef]

Halford, C.

J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
[CrossRef]

Hogervorst, M. A.

P. Bijl and M. A. Hogervorst, “A test method for multi-band imaging sensors,” Proc. SPIE 5076, 208–219 (2003).
[CrossRef]

P. Bijl, M. A. Hogervorst, and J. M. Valeton, “TOD, NVTherm and TRM3 model calculations: a comparison,” Proc. SPIE 4719, 51–62 (2002).
[CrossRef]

Holst, G. C.

G. C. Holst, Testing and Evaluation of Infrared Imaging Systems, 2nd ed. (SPIE, 1998).

Jacobs, E.

J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
[CrossRef]

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

Kerekes, J. P.

J. P. Kerekes and J. E. Baum, “Full-spectrum spectral imaging system analytical model,” IEEE Trans. Geosci. Remote Sens. 43, 571–580 (2005).
[CrossRef]

J. P. Kerekes and J. E. Baum, “Spectral imaging system analytical model for subpixel object detection,” IEEE Trans. Geosci. Remote Sens. 40, 1088–1101 (2002).
[CrossRef]

Klein, L. A.

L. A. Klein, “A Boolean algebra approach to multiple sensor voting fusion,” IEEE Trans. Aerosp. Electon. Syst. 29, 317–327 (1993).
[CrossRef]

Lettington, A. H.

A. M. Fairhurst, A. H. Lettington, and K. S. J. Murphy, “Model to predict the probability of recognition of shapes viewed through a thermal imager,” Proc. SPIE 2744, 611–617(1996).
[CrossRef]

Maurer, T.

T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
[CrossRef]

Murphy, K. S. J.

A. M. Fairhurst, A. H. Lettington, and K. S. J. Murphy, “Model to predict the probability of recognition of shapes viewed through a thermal imager,” Proc. SPIE 2744, 611–617(1996).
[CrossRef]

O’Kane, B. L.

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

Richardson, P.

J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
[CrossRef]

Smith, M.

M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
[CrossRef]

Valeton, J. M.

P. Bijl, M. A. Hogervorst, and J. M. Valeton, “TOD, NVTherm and TRM3 model calculations: a comparison,” Proc. SPIE 4719, 51–62 (2002).
[CrossRef]

P. Bijl and J. M. Valeton, “Guidelines for accurate TOD measurement,” Proc. SPIE 3701, 14–25 (1999).
[CrossRef]

P. Bijl and J. M. Valeton, “TOD, a new method to characterize electro-optical system performance,” Proc. SPIE 3377, 182–193 (1998).
[CrossRef]

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

Varshney, P. K.

Z. Chair and P. K. Varshney, “Optimal data fusion in multiple sensor detection systems,” IEEE Trans. Aerosp. Electon. Syst. 22, 98–101 (1986).
[CrossRef]

Vollmerhausen, R.

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

Vollmerhausen, R. H.

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

T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
[CrossRef]

R. H. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, L.M.Biberman ed. (SPIE, 2000), pp. 1–42.

R. H. Vollmerhausen and R. G. Driggers, “NVTherm: next generation night vision model,” in Proceedings of the 1999 Meeting of the IRIS Passive Sensors (1999), pp. 121–134.

Wang, X. R.

Webb, C.

J. D’Agostino and C. Webb, “Three-dimensional analysis framework and measurement methodology for imaging system noise,” Proc. SPIE 1488, 110–121 (1991).
[CrossRef]

Wittenstein, W.

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

W. Wittenstein, “Thermal range model TRM3,” Proc. SPIE 3436, 413–424 (1998).
[CrossRef]

Zhang, J. Q.

Appl. Opt. (1)

Chin. Opt. Lett. (1)

IEEE Trans. Aerosp. Electon. Syst. (2)

Z. Chair and P. K. Varshney, “Optimal data fusion in multiple sensor detection systems,” IEEE Trans. Aerosp. Electon. Syst. 22, 98–101 (1986).
[CrossRef]

L. A. Klein, “A Boolean algebra approach to multiple sensor voting fusion,” IEEE Trans. Aerosp. Electon. Syst. 29, 317–327 (1993).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

J. P. Kerekes and J. E. Baum, “Spectral imaging system analytical model for subpixel object detection,” IEEE Trans. Geosci. Remote Sens. 40, 1088–1101 (2002).
[CrossRef]

J. P. Kerekes and J. E. Baum, “Full-spectrum spectral imaging system analytical model,” IEEE Trans. Geosci. Remote Sens. 43, 571–580 (2005).
[CrossRef]

Opt. Eng. (4)

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

W. Wittenstein, “Minimum temperature difference perceived- a new approach to assess under-sampled thermal imagers,” Opt. Eng. 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. 37, 1976–1983(1998).
[CrossRef]

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

Proc. SPIE (10)

T. Maurer, R. G. Driggers, R. H. Vollmerhausen, and M. H. Freidman, “2002 NVTherm improvements,” Proc. SPIE 4719, 15–23 (2002).
[CrossRef]

W. Wittenstein, “Thermal range model TRM3,” Proc. SPIE 3436, 413–424 (1998).
[CrossRef]

J. D’Agostino and C. Webb, “Three-dimensional analysis framework and measurement methodology for imaging system noise,” Proc. SPIE 1488, 110–121 (1991).
[CrossRef]

M. Bernhardt, P. Clare, C. Cowell, and M. Smith, “A hyperspectral model for target detection,” Proc. SPIE 6565, 65650F (2007).
[CrossRef]

J. Fanning, C. Halford, E. Jacobs, and P. Richardson, “Multispectral imager modeling,” Proc. SPIE 5784, 136–145 (2005).
[CrossRef]

P. Bijl and M. A. Hogervorst, “A test method for multi-band imaging sensors,” Proc. SPIE 5076, 208–219 (2003).
[CrossRef]

P. Bijl and J. M. Valeton, “TOD, a new method to characterize electro-optical system performance,” Proc. SPIE 3377, 182–193 (1998).
[CrossRef]

A. M. Fairhurst, A. H. Lettington, and K. S. J. Murphy, “Model to predict the probability of recognition of shapes viewed through a thermal imager,” Proc. SPIE 2744, 611–617(1996).
[CrossRef]

P. Bijl, M. A. Hogervorst, and J. M. Valeton, “TOD, NVTherm and TRM3 model calculations: a comparison,” Proc. SPIE 4719, 51–62 (2002).
[CrossRef]

P. Bijl and J. M. Valeton, “Guidelines for accurate TOD measurement,” Proc. SPIE 3701, 14–25 (1999).
[CrossRef]

Other (3)

R. H. Vollmerhausen, “Modeling the performance of imaging sensors,” in Electro-Optical Imaging: System Performance and Modeling, L.M.Biberman ed. (SPIE, 2000), pp. 1–42.

G. C. Holst, Testing and Evaluation of Infrared Imaging Systems, 2nd ed. (SPIE, 1998).

R. H. Vollmerhausen and R. G. Driggers, “NVTherm: next generation night vision model,” in Proceedings of the 1999 Meeting of the IRIS Passive Sensors (1999), pp. 121–134.

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