Abstract

A nomogram is presented for predicting the sighting range for white, steady-burning signal lights. The theoretical and experimental bases are explained and instructions are provided for its use for a variety of practical problems concerning the visibility of signal lights. The nomogram is appropriate for slant path as well as horizontal sightings, and the gain of range achieved by utilizing binoculars can be predicted by use of it.

© 1975 Optical Society of America

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References

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  1. S. Q. Duntley, J. Opt. Soc. Am. 38, 237 (1948).
  2. The correction will be explained in the next section.
  3. S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage, Summary Tech. Rept. of Div. 16, NDRC (Columbia U. P., New York, 1946), Vol. 2, p. 129.
  4. W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952), p. 139.
  5. M. H. Horman, J. Opt. Soc. Am. 57, 1516 (1967).
  6. Ricco, Annali di Ottal. 6, 373 (1877).
  7. A. D. Schnitzler, J. Opt. Soc. Am. 63, 1365 (1973). Schnitzler expresses this relationship in terms of contrast rather than luminance difference, but the two expressions are consistent.
  8. H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).
  9. The adaptation luminance is the apparent background luminance to which the eye is fully adapted.
  10. Reference 8, Fig. 17.
  11. Reference 3, p. 128.
  12. Reference 3, Appendix.
  13. The detection and false-alarm probability functions are not fully defined for the Tiffany data because spurious-behavior responses were not measured. However, it was found that, in order to obtain confident sightings, the level of probability of response needed to be greater than 90%. The factor of 2 increases the probability of response to above 90%, according to the average probability curve for the Tiffany experiments (Ref. 8, Fig. 7 and p. 630).
  14. A. C. Hardy, J. Opt. Soc. Am. 57, 46 (1967).
  15. Hardy's Table I is comparable to a table of threshold illuminance difference. His Table II is comparable to a table of threshold illuminance.
  16. Equation (3) is rigorously true only for monochromatic radiances. However, because monochromatic visual-threshold data are not available, it is used as a reasonable engineering approximation for luminances measured with a photopically filtered sensor.
  17. R. D. Douglass and D. P. Adams, Elements of Nomography (McGraw—Hill, New York and London, 1947), Ch. XV.
  18. R. Tousey and E. O Hulburt, J. Opt. Soc. Am. 37, 87 (1947); D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 475 (1951); M. J. Koomen, C. Lock, D. M. Packer, R. Scolnik, R. Tousey, and E. O. Hulburt, J. Opt. Soc. Am. 42, 354 (1952); E. O. Hulburt, Jr., Geophys. Res. 54, 226 (1949).
  19. F. S. Johnson, J. Meteorol. 11, 431 (1954).
  20. N. N. Sytinskaya, Sov. Astron. 1, 870 (1957).
  21. H. N. Russel, Astrophys. J. 43, 117 (1916).
  22. From an unpublished report of the results of an NBS study of the relationship between meteorological observations of visual range and measurements using the Douglas transmissometer.
  23. E. O. Hulburt, J. Opt. Soc. Am. 31, 469 (1941), Table II.
  24. In the G. E. Large Lamp Catalog, a 100 W bulb is rated in 1700 lm. I = 1700 Im/4π = 135 cd. The diameter is 20/8 in. =0.0635 m.
  25. S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957).
  26. A. R. Boileau, Appl. Opt. 3, 570 (1964).
  27. A. R. Boileau and J. I. Gordon, Appl. Opt. 5, 808 (1966).
  28. S. Q. Duntley, J. Opt. Soc. Am. 38, 187 (1948).
  29. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 325 (1944).
  30. H. S. Coleman, J. Opt. Soc. Am. 37, 434 (1947).
  31. H. S. Coleman, J. Opt. Soc. Am. 37, 899 (1947).
  32. S. G. DeGroot and J. W. Gebhard, J. Opt. Soc. Am. 42, 492 (1952).
  33. Reference 29, p. 320, Fig. 1.
  34. Reference 32, p. 492, Fig. 1.
  35. Reference 30, p. 443 and an unpublished NAVORD report.

Adams, D. P.

R. D. Douglass and D. P. Adams, Elements of Nomography (McGraw—Hill, New York and London, 1947), Ch. XV.

Blackwell, H. R.

H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).

Boileau, A. R.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957).

A. R. Boileau and J. I. Gordon, Appl. Opt. 5, 808 (1966).

A. R. Boileau, Appl. Opt. 3, 570 (1964).

Coleman, H. S.

H. S. Coleman, J. Opt. Soc. Am. 37, 434 (1947).

H. S. Coleman, J. Opt. Soc. Am. 37, 899 (1947).

DeGroot, S. G.

S. G. DeGroot and J. W. Gebhard, J. Opt. Soc. Am. 42, 492 (1952).

Douglass, R. D.

R. D. Douglass and D. P. Adams, Elements of Nomography (McGraw—Hill, New York and London, 1947), Ch. XV.

Duntley, S. Q.

S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage, Summary Tech. Rept. of Div. 16, NDRC (Columbia U. P., New York, 1946), Vol. 2, p. 129.

S. Q. Duntley, J. Opt. Soc. Am. 38, 187 (1948).

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957).

S. Q. Duntley, J. Opt. Soc. Am. 38, 237 (1948).

Gebhard, J. W.

S. G. DeGroot and J. W. Gebhard, J. Opt. Soc. Am. 42, 492 (1952).

Gordon, J. I.

A. R. Boileau and J. I. Gordon, Appl. Opt. 5, 808 (1966).

Hardy, A. C.

A. C. Hardy, J. Opt. Soc. Am. 57, 46 (1967).

Horman, M. H.

M. H. Horman, J. Opt. Soc. Am. 57, 1516 (1967).

Hulburt, E. O

R. Tousey and E. O Hulburt, J. Opt. Soc. Am. 37, 87 (1947); D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 475 (1951); M. J. Koomen, C. Lock, D. M. Packer, R. Scolnik, R. Tousey, and E. O. Hulburt, J. Opt. Soc. Am. 42, 354 (1952); E. O. Hulburt, Jr., Geophys. Res. 54, 226 (1949).

Hulburt, E. O.

E. O. Hulburt, J. Opt. Soc. Am. 31, 469 (1941), Table II.

Johnson, F. S.

F. S. Johnson, J. Meteorol. 11, 431 (1954).

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952), p. 139.

Moon, P.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 325 (1944).

Preisendorfer, R. W.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957).

Russel, H. N.

H. N. Russel, Astrophys. J. 43, 117 (1916).

Schnitzler, A. D.

A. D. Schnitzler, J. Opt. Soc. Am. 63, 1365 (1973). Schnitzler expresses this relationship in terms of contrast rather than luminance difference, but the two expressions are consistent.

Spencer, D. E.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 325 (1944).

Sytinskaya, N. N.

N. N. Sytinskaya, Sov. Astron. 1, 870 (1957).

Tousey, R.

R. Tousey and E. O Hulburt, J. Opt. Soc. Am. 37, 87 (1947); D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 475 (1951); M. J. Koomen, C. Lock, D. M. Packer, R. Scolnik, R. Tousey, and E. O. Hulburt, J. Opt. Soc. Am. 42, 354 (1952); E. O. Hulburt, Jr., Geophys. Res. 54, 226 (1949).

Other

S. Q. Duntley, J. Opt. Soc. Am. 38, 237 (1948).

The correction will be explained in the next section.

S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage, Summary Tech. Rept. of Div. 16, NDRC (Columbia U. P., New York, 1946), Vol. 2, p. 129.

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Toronto, 1952), p. 139.

M. H. Horman, J. Opt. Soc. Am. 57, 1516 (1967).

Ricco, Annali di Ottal. 6, 373 (1877).

A. D. Schnitzler, J. Opt. Soc. Am. 63, 1365 (1973). Schnitzler expresses this relationship in terms of contrast rather than luminance difference, but the two expressions are consistent.

H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).

The adaptation luminance is the apparent background luminance to which the eye is fully adapted.

Reference 8, Fig. 17.

Reference 3, p. 128.

Reference 3, Appendix.

The detection and false-alarm probability functions are not fully defined for the Tiffany data because spurious-behavior responses were not measured. However, it was found that, in order to obtain confident sightings, the level of probability of response needed to be greater than 90%. The factor of 2 increases the probability of response to above 90%, according to the average probability curve for the Tiffany experiments (Ref. 8, Fig. 7 and p. 630).

A. C. Hardy, J. Opt. Soc. Am. 57, 46 (1967).

Hardy's Table I is comparable to a table of threshold illuminance difference. His Table II is comparable to a table of threshold illuminance.

Equation (3) is rigorously true only for monochromatic radiances. However, because monochromatic visual-threshold data are not available, it is used as a reasonable engineering approximation for luminances measured with a photopically filtered sensor.

R. D. Douglass and D. P. Adams, Elements of Nomography (McGraw—Hill, New York and London, 1947), Ch. XV.

R. Tousey and E. O Hulburt, J. Opt. Soc. Am. 37, 87 (1947); D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 475 (1951); M. J. Koomen, C. Lock, D. M. Packer, R. Scolnik, R. Tousey, and E. O. Hulburt, J. Opt. Soc. Am. 42, 354 (1952); E. O. Hulburt, Jr., Geophys. Res. 54, 226 (1949).

F. S. Johnson, J. Meteorol. 11, 431 (1954).

N. N. Sytinskaya, Sov. Astron. 1, 870 (1957).

H. N. Russel, Astrophys. J. 43, 117 (1916).

From an unpublished report of the results of an NBS study of the relationship between meteorological observations of visual range and measurements using the Douglas transmissometer.

E. O. Hulburt, J. Opt. Soc. Am. 31, 469 (1941), Table II.

In the G. E. Large Lamp Catalog, a 100 W bulb is rated in 1700 lm. I = 1700 Im/4π = 135 cd. The diameter is 20/8 in. =0.0635 m.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957).

A. R. Boileau, Appl. Opt. 3, 570 (1964).

A. R. Boileau and J. I. Gordon, Appl. Opt. 5, 808 (1966).

S. Q. Duntley, J. Opt. Soc. Am. 38, 187 (1948).

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 325 (1944).

H. S. Coleman, J. Opt. Soc. Am. 37, 434 (1947).

H. S. Coleman, J. Opt. Soc. Am. 37, 899 (1947).

S. G. DeGroot and J. W. Gebhard, J. Opt. Soc. Am. 42, 492 (1952).

Reference 29, p. 320, Fig. 1.

Reference 32, p. 492, Fig. 1.

Reference 30, p. 443 and an unpublished NAVORD report.

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