Abstract

A simple method is described for transforming field visual target acquisition data (the standard data) to apply to different meteorological conditions, imaging system parameters, and visual acquisition levels (e.g., detection and recognition). For each probability of target acquisition in the standard data, a new value of range is computed which is appropriate to the new conditions. As an example, the method is applied to the case of optical sights for different values of magnification and for different meteorological visibilities and ambient luminances.

© 1983 Optical Society of America

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References

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  1. H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).
    [CrossRef] [PubMed]
  2. F. L. van Nes, M. A. Bouman, J. Opt. Soc. Am. 57, 401 (1967).
    [CrossRef]
  3. A. van Meeteren, J. J. Vos, Vision Res. 12, 825 (1972).
    [CrossRef] [PubMed]
  4. F. W. Campbell, R. H. S. Carpenter, J. Z. Levinson, J. Physiol. London 204, 283 (1969).
    [PubMed]
  5. I. Overington, Opt. Eng. 21, 2 (1982).
    [CrossRef]
  6. J. Johnson, “Analysis of Image Forming Systems,” in Proceedings, Image Intensifier Symposium, Fort Belvoir, Va., 6–7 Oct. 1958, pp. 249–273; AD220160.
  7. L. M. Biberman, Perception of Displayed Information (Plenum, New York, 1973).
    [CrossRef]
  8. W. E. K. Middleton, Vision Through the Atmosphere (Oxford U.P., London, 1958).
  9. F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
    [PubMed]
  10. J. G. Robson, N. Graham, Vision Res. 21, 409 (1981).
    [CrossRef] [PubMed]
  11. G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
  12. J. Nachmias, J. Opt. Soc. Am. 57, 421 (1967).
    [CrossRef]
  13. J. A. Ratches et al., “Night Vision Laboratory Static Performance Model for Thermal Viewing Systems,” U.S. Army Electronics Command, Night Vision Laboratory, Fort Belvoir, Va. AD-A011-212 (Apr.1975).
  14. H. B. Barlow, J. Physiol. London 136, 469 (1957).
    [PubMed]
  15. D. G. Pelli, “Effects of Visual Noise,” Ph.D. Thesis, U. Cambridge, England (1981).
  16. H. B. Barlow, W. R. Levick, J. Physiol. London 200, 1 (1969).
    [PubMed]

1982 (1)

I. Overington, Opt. Eng. 21, 2 (1982).
[CrossRef]

1981 (1)

J. G. Robson, N. Graham, Vision Res. 21, 409 (1981).
[CrossRef] [PubMed]

1972 (1)

A. van Meeteren, J. J. Vos, Vision Res. 12, 825 (1972).
[CrossRef] [PubMed]

1969 (2)

F. W. Campbell, R. H. S. Carpenter, J. Z. Levinson, J. Physiol. London 204, 283 (1969).
[PubMed]

H. B. Barlow, W. R. Levick, J. Physiol. London 200, 1 (1969).
[PubMed]

1968 (1)

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

1967 (2)

1957 (1)

H. B. Barlow, J. Physiol. London 136, 469 (1957).
[PubMed]

1946 (1)

Barlow, H. B.

H. B. Barlow, W. R. Levick, J. Physiol. London 200, 1 (1969).
[PubMed]

H. B. Barlow, J. Physiol. London 136, 469 (1957).
[PubMed]

Biberman, L. M.

L. M. Biberman, Perception of Displayed Information (Plenum, New York, 1973).
[CrossRef]

Blackwell, H. R.

Bouman, M. A.

Campbell, F. W.

F. W. Campbell, R. H. S. Carpenter, J. Z. Levinson, J. Physiol. London 204, 283 (1969).
[PubMed]

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

Carpenter, R. H. S.

F. W. Campbell, R. H. S. Carpenter, J. Z. Levinson, J. Physiol. London 204, 283 (1969).
[PubMed]

Graham, N.

J. G. Robson, N. Graham, Vision Res. 21, 409 (1981).
[CrossRef] [PubMed]

Johnson, J.

J. Johnson, “Analysis of Image Forming Systems,” in Proceedings, Image Intensifier Symposium, Fort Belvoir, Va., 6–7 Oct. 1958, pp. 249–273; AD220160.

Levick, W. R.

H. B. Barlow, W. R. Levick, J. Physiol. London 200, 1 (1969).
[PubMed]

Levinson, J. Z.

F. W. Campbell, R. H. S. Carpenter, J. Z. Levinson, J. Physiol. London 204, 283 (1969).
[PubMed]

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (Oxford U.P., London, 1958).

Nachmias, J.

Overington, I.

I. Overington, Opt. Eng. 21, 2 (1982).
[CrossRef]

Pelli, D. G.

D. G. Pelli, “Effects of Visual Noise,” Ph.D. Thesis, U. Cambridge, England (1981).

Ratches, J. A.

J. A. Ratches et al., “Night Vision Laboratory Static Performance Model for Thermal Viewing Systems,” U.S. Army Electronics Command, Night Vision Laboratory, Fort Belvoir, Va. AD-A011-212 (Apr.1975).

Robson, J. G.

J. G. Robson, N. Graham, Vision Res. 21, 409 (1981).
[CrossRef] [PubMed]

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

van Meeteren, A.

A. van Meeteren, J. J. Vos, Vision Res. 12, 825 (1972).
[CrossRef] [PubMed]

van Nes, F. L.

Vos, J. J.

A. van Meeteren, J. J. Vos, Vision Res. 12, 825 (1972).
[CrossRef] [PubMed]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

J. Opt. Soc. Am. (3)

J. Physiol. London (4)

H. B. Barlow, J. Physiol. London 136, 469 (1957).
[PubMed]

H. B. Barlow, W. R. Levick, J. Physiol. London 200, 1 (1969).
[PubMed]

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

F. W. Campbell, R. H. S. Carpenter, J. Z. Levinson, J. Physiol. London 204, 283 (1969).
[PubMed]

Opt. Eng. (1)

I. Overington, Opt. Eng. 21, 2 (1982).
[CrossRef]

Vision Res. (2)

J. G. Robson, N. Graham, Vision Res. 21, 409 (1981).
[CrossRef] [PubMed]

A. van Meeteren, J. J. Vos, Vision Res. 12, 825 (1972).
[CrossRef] [PubMed]

Other (6)

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

J. Johnson, “Analysis of Image Forming Systems,” in Proceedings, Image Intensifier Symposium, Fort Belvoir, Va., 6–7 Oct. 1958, pp. 249–273; AD220160.

L. M. Biberman, Perception of Displayed Information (Plenum, New York, 1973).
[CrossRef]

W. E. K. Middleton, Vision Through the Atmosphere (Oxford U.P., London, 1958).

D. G. Pelli, “Effects of Visual Noise,” Ph.D. Thesis, U. Cambridge, England (1981).

J. A. Ratches et al., “Night Vision Laboratory Static Performance Model for Thermal Viewing Systems,” U.S. Army Electronics Command, Night Vision Laboratory, Fort Belvoir, Va. AD-A011-212 (Apr.1975).

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Figures (3)

Fig. 1
Fig. 1

Contrast sensitivity function data are shown by circles and crosses and are taken from two investigations.3,9 Only values for frequencies above the peak of the CSF are shown. Continuous and broken lines describe straight line functions fitted by the least squares method. The retinal illuminance is shown adjacent to the corresponding line.

Fig. 2
Fig. 2

Estimates of the two curve fitting parameters, A1 and A2 in Eq. (5), are shown in (A) and (B), respectively. Values are plotted on logarithm scales against the retinal illuminance and are shown for the three investigations2,3,9 indicated in the figure. The curves are the functions described by Eqs. (7a) and (7b) and were fitted to minimize the sum of the squared deviations.

Fig. 3
Fig. 3

Examples of the transformation technique are shown for three typical optical sights: 4 × 24, 7 × 50, and 10 × 35 mm. For each sight, the transmission was 0.7. The starting field (standard) data are plotted as circles and describe the probability of recognition (N = 4) against range. Parameters for the standard data are given both in the text and in the figure. Those values which are changed to derive the transformed data (crosses) are shown adjacent to the corresponding curves: (A) effect of changing the magnification for two values of visibility; (B) effect of decreasing the luminance from a bright daylight horizon sky level down to late dusk; (C) change in performance at two visibilities for detection, recognition, and identification; (D) the psychometric function derived from the standard data and plotted as a probability against logarithm normalized contrast so that P = 0.5 for an abscissa value of 0.0. The inherent target contrast C0 is calculated as 0.118.

Equations (17)

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f = 1000 R π N 180 M W 17.5 N R M W cycles / deg .
C 0 = ( L 0 - D 0 ) / B 0 .
L R = L 0 exp ( - α R ) + H [ 1 - exp ( - α R ) ] ,
D R = D 0 exp ( - α R ) + H [ 1 - exp ( - α R ) ] ,
B R = B 0 exp ( - α R ) + H [ 1 - exp ( - α R ) ] ,
C R = C 0 exp ( - α R ) / [ S + ( 1 - S ) exp ( - α R ) ] ,
C = A 2 exp ( f A 1 ) ,
d e = 5 - 3 tanh [ 0.4 log 10 ( B / 3.183 ) ] ,
A 1 = 0.088 I - 0.26 + 0.085 ; I < 200 , A 1 = 0.107 ; I 200 ,
A 2 = 0.011 I - 0.40 + 0.0024 ; I < 1000 , A 2 = 0.0031 ; I 1000 ,
C P = Q ( P ) A 2 exp ( f A 1 ) .
C 0 exp ( - 3.91 R / V ) S + ( 1 - S ) exp ( - 3.91 R / V ) = Q ( P ) A 2 exp ( 17.5 N R A 1 M W ) ,
B = B R = ( H / S ) [ S + ( 1 - S ) exp ( - 3.91 R / V ) ] .
C 0 / Q ( P ) = A 2 K exp [ ( Z + 3.91 / V ) R ] ,
K = S + ( 1 - S ) exp ( - 3.91 R / V ) ,
Z = 17.5 N A 1 / ( M W ) .
R R * ( Z * + 3.91 / V * ) ( Z + 3.91 / V ) ,

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