Abstract

The development of staring infrared focal plane arrays has forced potential users to consider the effect of spatial noise on the performance of infrared sensors. We varied the amount of spatial noise present in infrared imagery and measured its effect on the value of the minimum resolvable temperature (MRT). A mathematical model for including the effects of spatial noise on image quality is presented and compared to experimental data. The effect of both the spatial and temporal power spectral density on the MRT is discussed. Excess low-frequency noise in the temporal domain is shown to be a source of spatial noise.

© 1991 Optical Society of America

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References

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  1. J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
  2. J. E. Murguia, J. M. Mooney, W. S. Ewing, “Evaluation of a PtSi infrared camera,” Opt. Eng. 29, 786–794 (1990).
    [Crossref]
  3. F. A. Rosell, R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, Ed. (Plenum, New York, 1973), pp. 167–232.
    [Crossref]
  4. F. A. Rosell, “The Coltman and Anderson experiment,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 205–207.
  5. F. A. Rosell, “Psychophysical experimentation,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 223–235.
  6. W. R. Lawson, J. A. Ratches, “The Night Vision Laboratory static performance model based on the matched filter concept,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 159–179.
  7. O. H. Schade, “Optical and photoelectric analog of the eye,” J. Opt. Soc. Am. 46, 721–739 (1956).
    [Crossref] [PubMed]
  8. J. M. Lloyd, Thermal Imaging Systems (Plenum, New York, 1975), pp. 132–133.
  9. O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Telev. Eng. 73, 81–120 (1964).

1990 (1)

J. E. Murguia, J. M. Mooney, W. S. Ewing, “Evaluation of a PtSi infrared camera,” Opt. Eng. 29, 786–794 (1990).
[Crossref]

1989 (1)

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

1964 (1)

O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Telev. Eng. 73, 81–120 (1964).

1956 (1)

Ewing, W. S.

J. E. Murguia, J. M. Mooney, W. S. Ewing, “Evaluation of a PtSi infrared camera,” Opt. Eng. 29, 786–794 (1990).
[Crossref]

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

Lawson, W. R.

W. R. Lawson, J. A. Ratches, “The Night Vision Laboratory static performance model based on the matched filter concept,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 159–179.

Lloyd, J. M.

J. M. Lloyd, Thermal Imaging Systems (Plenum, New York, 1975), pp. 132–133.

Mooney, J. M.

J. E. Murguia, J. M. Mooney, W. S. Ewing, “Evaluation of a PtSi infrared camera,” Opt. Eng. 29, 786–794 (1990).
[Crossref]

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

Murguia, J. E.

J. E. Murguia, J. M. Mooney, W. S. Ewing, “Evaluation of a PtSi infrared camera,” Opt. Eng. 29, 786–794 (1990).
[Crossref]

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

Ratches, J. A.

W. R. Lawson, J. A. Ratches, “The Night Vision Laboratory static performance model based on the matched filter concept,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 159–179.

Rosell, F. A.

F. A. Rosell, “The Coltman and Anderson experiment,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 205–207.

F. A. Rosell, “Psychophysical experimentation,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 223–235.

F. A. Rosell, R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, Ed. (Plenum, New York, 1973), pp. 167–232.
[Crossref]

Schade, O. H.

O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Telev. Eng. 73, 81–120 (1964).

O. H. Schade, “Optical and photoelectric analog of the eye,” J. Opt. Soc. Am. 46, 721–739 (1956).
[Crossref] [PubMed]

Shepherd, F. D.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

Silverman, J.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

Willson, R. H.

F. A. Rosell, R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, Ed. (Plenum, New York, 1973), pp. 167–232.
[Crossref]

J. Opt. Soc. Am. (1)

J. Soc. Motion Pict. Telev. Eng. (1)

O. H. Schade, “An evaluation of photographic image quality and resolving power,” J. Soc. Motion Pict. Telev. Eng. 73, 81–120 (1964).

Opt. Eng. (2)

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).

J. E. Murguia, J. M. Mooney, W. S. Ewing, “Evaluation of a PtSi infrared camera,” Opt. Eng. 29, 786–794 (1990).
[Crossref]

Other (5)

F. A. Rosell, R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, Ed. (Plenum, New York, 1973), pp. 167–232.
[Crossref]

F. A. Rosell, “The Coltman and Anderson experiment,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 205–207.

F. A. Rosell, “Psychophysical experimentation,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 223–235.

W. R. Lawson, J. A. Ratches, “The Night Vision Laboratory static performance model based on the matched filter concept,” in The Fundamentals of Thermal Imaging Systems, F. Rosell, G. Harvey, eds., (1979), pp. 159–179.

J. M. Lloyd, Thermal Imaging Systems (Plenum, New York, 1975), pp. 132–133.

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Figures (8)

Fig. 1
Fig. 1

Qualitative relationship between various noise sources and the correlation coefficient.

Fig. 2
Fig. 2

Series of four four-bar patterns illustrating the effect of spatial noise on an MRT measurement. The spatial noise is (a) 3% and (b) 0.05% of the mean value as measured over the central one fourth of the image. For the corrected image, a single-point algorithm was used. The ΔT of the bars is the same in both cases.

Fig. 3
Fig. 3

MRT as a function of spatial frequency with and without spatial noise. The spatial noise was obtained by operating the camera with no nonuniformity correction (approximiately 3% non-uniformity). The solid line is from Eq. (13). The data were taken in the 3.4–4.3-μm band with f/2.7 optics (NEΔT = 0.1 K).

Fig. 4
Fig. 4

Measured MRT as a function of single-frame-total noise (pluses) and as a function of accumulated noise (open squares). The data were taken in the 4.5–5.0-μm band with f/2.0 optics at 1/2 Nyquist (NEΔT = 0.26 K).

Fig. 5
Fig. 5

MRT as a function of accumulated noise with spatial frequency as a parameter. The data were taken in the 3.1–4.3-μm band with f/2.7 optics.

Fig. 6
Fig. 6

Probability of detection versus SNR integrated over a bar for various bar aspect ratios. The threshold value is near 3.0 for 50% probability of detection and near 6.0 for 100% probability of detection (taken from Ref. 3).

Fig. 7
Fig. 7

Examples of the effect of colored spatial noise on MRT. Two orientations of bars are shown as imaged by two different spatial noise patterns (that are also of different magnitude). A vertical bar pattern in the spatial noise for the images on the right increases the horizontal MRT. The measured value of MRT is shown adjacent to each example. In each case the bar pattern was accentuated by setting ΔT to 1.0 K. This figure demonstrates that the effect of the spatial noise depends not only on the magnitude of the noise but on its form. The MRT for the noise pattern on the left is strongly dependent on the orientation of the bars, while the pattern on the right is not.

Fig. 8
Fig. 8

Four different spatial noise patterns observed with the same focal plane array. The upper left is uncorrected. The upper right is single-point corrected where the correction frame was made with an illumination level that was much lower than the level of subsequent imagery. The lower left is uncorrected at a very low illumination level. The lower right is 4 h after one-point correction (an example of array 1/f noise).

Equations (19)

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ρ ( t , τ ) = 1 S s = 1 S ( x s t - x t ) ( x s τ - x τ ) σ sft 2 = R ( t , τ ) - x t x τ R ( t , t ) - x t 2 ,
x t = 1 S s = 1 S x s t ,
σ sft 2 = 1 S s = 1 S [ x s t - x t ] 2 = R ( t , t ) - x t 2 ,
R ( t , τ ) = 1 S s = 1 S x s t x s τ .
σ spatial 2 ρ ( t , τ ) σ sft 2 = R ( t , τ ) - x t x τ .
σ temporal 2 [ 1 - ρ ( t , τ ) ] σ sft 2 .
σ acc 2 = k σ temporal 2 + k 2 σ spatial 2 ,
k t eye / t frame ,
signal = Δ T · R · B · k ,
B = ( β / α ) ( ξ N / ξ ) 2 ,
noise = ( B σ acc 2 ) 1 / 2 ,
MRT = σ acc R SNR th k ( α β ) 1 / 2 ξ ξ N .
MRT = N E Δ T SNR th k ( α β ) 1 / 2 σ acc σ temporal ξ ξ N ,
N E Δ T = σ temporal R .
MRT NVL = 0.66 SNR th N E Δ T MTF ( ξ ) ξ [ 4 π Δ x Δ y t frame η ovsc t eye ] 1 / 2 ,
MRT NVL = 0.98 SNR th N E Δ T ξ MTF ( ξ ) ξ N ( α k β ) 1 / 2 ,
σ acc 2 = k σ temporal 2 + k σ spatial 2 .
R ( t , t + t eye ) 0 1 / 2 t eye S ( f ) cos ( 2 π t eye f ) d f ,
R ( t , t + t eye ) = ( x t - x c ) ( x t + t eye - x c ) 1 / 2 π Δ t 1 / 2 t eye S ( f ) cos ( 2 π t eye f ) d f + 1 / 2 π Δ t 1 / 2 t m S ( f ) d f ,

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