Abstract

Photometry has traditionally been conceptualized primarily in terms of measuring light sources. However, all units of photometry can also refer to measurements of light as it is received. A description of how to measure incident light is developed from the basis that light forming an image is just the reverse of light emitted from a source. The incident approach to photometry reveals how to derive luminance from a measure of illuminance and how to correctly calculate the illumination of an image. It is further recommended that photometric specification of incident light be accompanied by a description of its effectiveness relative to the receiver threshold.

© 1983 Optical Society of America

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References

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  1. W. E. K. Middleton, Appl. Opt. 10, 2592 (1971).
    [CrossRef] [PubMed]
  2. S. C. Brown, Benjamin Thompson, Count Rumford (MIT Press, Cambridge, Mass., 1979).
  3. A. Sommer, Photoelectric Tubes (Methuen, London, 1951).
  4. R. J. Phelan, C. A. Hamilton, G. W. Day, Modern Util. Infrared Tech. 62, 159 (1975).
    [CrossRef]
  5. J. J. Gibson, The Senses Considered as Perceptual Systems (Houghton, Boston, 1966).
  6. M. Young, Appl. Opt. 10, 2763 (1971).
    [CrossRef] [PubMed]
  7. D. L. MacAdam, Opt. Soc. of Am. 57, 854 (1967).
  8. J. E. Kaufman, IES Lighting Handbook (Illuminating Engineering Society, New York, 1972).
  9. R. M. Boynton, “The Visual System: Environmental Information,” in Handbook of Perception, E. C. Carterette, M. P. Friedman, Eds. (Academic, New York, 1975), pp. 285–307.
  10. To make a point detector which is less susceptible to local variations in its photosensitive surface, the detector need not be placed directly against the pinhole. As long as the detector receives all the light entering the pinhole, it can be placed at some distance behind the pinhole to involve more of the detector surface without changing the result in principle
  11. It does not matter whether these calculations are performed by us or by the optical and electronic configuration of a more complex photometer than the simple photodetector illustrated in Fig. 3. It is meaningless to ask whether an optical photometer actually calculated luminance in incident or emitted terms.
  12. J. Geist, E. Zelewski, Appl. Opt. 12, 435 (1973).
    [CrossRef] [PubMed]
  13. D. B. Judd, “Correlates Basic of the Visual Stimulus,” in Handbook of Experimental Psychology, S. S. Stevens, Ed. (Wiley, New York, 1951), pp. 811–867.
  14. H. A. E. Keitz, Light Calculations and Measurements (Macmillan, london, 1971).
  15. R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1957).
  16. Certain optical systems such as the Maxwellian view present some particular luminance calibration problems.28
  17. T. H. NilssonBehav. Res. Methods Instrum. 13, 18 (1981).
    [CrossRef]
  18. Nicodemus discusses how to calculate the solid angle of any target, but use of a ciruclar mask may be an easier solution.30
  19. For visual receptors, a correction can be made for the Stiles-Crawford effect.23 Comparable corrections should be possible for other sensors whose structure also results in a certain directional selectivity.
  20. For light incident at angles >20, the effects of Lambert's law become appreciable, but that is a relatively wide angle for imaging systems.
  21. Correction in the final formula can, of course, be made for the transmittance of the optical system.
  22. R. M. Boynton, “Vision,” in Experimental Methods and Instrumentation in Psychology, J. B. Sidowski, Ed. (McGraw-Hill, New York, 1966), pp. 273–330.
  23. Y. LeGrand, Light, Color and Vision (Chapman & Hall, London, 1968).
  24. L. Troland, J. Exp. Psych. 2, 1 (1917).
    [CrossRef]
  25. L. M. Hurvich, D. Jameson, The Perception of Lightness and Darkness (Allyn and Bacon, Boston, 1966);L. A. Riggs, “Light as a Stimulus for Vision,” in Vision and Visual PerceptionC. H. Graham, Ed. (Wiley, New York, 1965), pp. 7–38;M. L. Rubin, G. L. Walls, Fundamentals of Visual Science (Thomas, Springfield, Ill., 1969);H. R. Schiffman, Sensation and Perception (Wiley, New York, 1976).
  26. K. N. Ogle, Optics (Thomas, Springfield, Ill., 1968).
  27. K. J. Kriebel, Appl. Opt. 17, 157 (1978).
    [CrossRef] [PubMed]
  28. S. L. Buck, W. Makous, J. Opt. Soc. Am. 68, 1392 (1978);R. W. Nygaard, T. E. FrumkesVision Res. 22, 433 (1982).
    [CrossRef] [PubMed]
  29. V. Di Lollo, Behav. Res. Methods Instrum. 11, 419 (1979).
    [CrossRef]
  30. F. E. Nicodemus, Self Study Manual on Optical Radiation Measurements: Part 1—Concepts (U.S. G.P.O., Washington, D.C., 1976).
  31. This assumes the source is at infinity and neglects taking into account the projected spherical area of the lens, which for most lenses amounts to a trivial correction.

1981 (1)

T. H. NilssonBehav. Res. Methods Instrum. 13, 18 (1981).
[CrossRef]

1979 (1)

V. Di Lollo, Behav. Res. Methods Instrum. 11, 419 (1979).
[CrossRef]

1978 (2)

K. J. Kriebel, Appl. Opt. 17, 157 (1978).
[CrossRef] [PubMed]

S. L. Buck, W. Makous, J. Opt. Soc. Am. 68, 1392 (1978);R. W. Nygaard, T. E. FrumkesVision Res. 22, 433 (1982).
[CrossRef] [PubMed]

1975 (1)

R. J. Phelan, C. A. Hamilton, G. W. Day, Modern Util. Infrared Tech. 62, 159 (1975).
[CrossRef]

1973 (1)

1971 (2)

1967 (1)

D. L. MacAdam, Opt. Soc. of Am. 57, 854 (1967).

1917 (1)

L. Troland, J. Exp. Psych. 2, 1 (1917).
[CrossRef]

Boynton, R. M.

R. M. Boynton, “The Visual System: Environmental Information,” in Handbook of Perception, E. C. Carterette, M. P. Friedman, Eds. (Academic, New York, 1975), pp. 285–307.

R. M. Boynton, “Vision,” in Experimental Methods and Instrumentation in Psychology, J. B. Sidowski, Ed. (McGraw-Hill, New York, 1966), pp. 273–330.

Brown, S. C.

S. C. Brown, Benjamin Thompson, Count Rumford (MIT Press, Cambridge, Mass., 1979).

Buck, S. L.

S. L. Buck, W. Makous, J. Opt. Soc. Am. 68, 1392 (1978);R. W. Nygaard, T. E. FrumkesVision Res. 22, 433 (1982).
[CrossRef] [PubMed]

Day, G. W.

R. J. Phelan, C. A. Hamilton, G. W. Day, Modern Util. Infrared Tech. 62, 159 (1975).
[CrossRef]

Di Lollo, V.

V. Di Lollo, Behav. Res. Methods Instrum. 11, 419 (1979).
[CrossRef]

Geist, J.

Gibson, J. J.

J. J. Gibson, The Senses Considered as Perceptual Systems (Houghton, Boston, 1966).

Hamilton, C. A.

R. J. Phelan, C. A. Hamilton, G. W. Day, Modern Util. Infrared Tech. 62, 159 (1975).
[CrossRef]

Hurvich, L. M.

L. M. Hurvich, D. Jameson, The Perception of Lightness and Darkness (Allyn and Bacon, Boston, 1966);L. A. Riggs, “Light as a Stimulus for Vision,” in Vision and Visual PerceptionC. H. Graham, Ed. (Wiley, New York, 1965), pp. 7–38;M. L. Rubin, G. L. Walls, Fundamentals of Visual Science (Thomas, Springfield, Ill., 1969);H. R. Schiffman, Sensation and Perception (Wiley, New York, 1976).

Jameson, D.

L. M. Hurvich, D. Jameson, The Perception of Lightness and Darkness (Allyn and Bacon, Boston, 1966);L. A. Riggs, “Light as a Stimulus for Vision,” in Vision and Visual PerceptionC. H. Graham, Ed. (Wiley, New York, 1965), pp. 7–38;M. L. Rubin, G. L. Walls, Fundamentals of Visual Science (Thomas, Springfield, Ill., 1969);H. R. Schiffman, Sensation and Perception (Wiley, New York, 1976).

Judd, D. B.

D. B. Judd, “Correlates Basic of the Visual Stimulus,” in Handbook of Experimental Psychology, S. S. Stevens, Ed. (Wiley, New York, 1951), pp. 811–867.

Kaufman, J. E.

J. E. Kaufman, IES Lighting Handbook (Illuminating Engineering Society, New York, 1972).

Keitz, H. A. E.

H. A. E. Keitz, Light Calculations and Measurements (Macmillan, london, 1971).

Kriebel, K. J.

LeGrand, Y.

Y. LeGrand, Light, Color and Vision (Chapman & Hall, London, 1968).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1957).

MacAdam, D. L.

D. L. MacAdam, Opt. Soc. of Am. 57, 854 (1967).

Makous, W.

S. L. Buck, W. Makous, J. Opt. Soc. Am. 68, 1392 (1978);R. W. Nygaard, T. E. FrumkesVision Res. 22, 433 (1982).
[CrossRef] [PubMed]

Middleton, W. E. K.

Nicodemus, F. E.

F. E. Nicodemus, Self Study Manual on Optical Radiation Measurements: Part 1—Concepts (U.S. G.P.O., Washington, D.C., 1976).

Nilsson, T. H.

T. H. NilssonBehav. Res. Methods Instrum. 13, 18 (1981).
[CrossRef]

Ogle, K. N.

K. N. Ogle, Optics (Thomas, Springfield, Ill., 1968).

Phelan, R. J.

R. J. Phelan, C. A. Hamilton, G. W. Day, Modern Util. Infrared Tech. 62, 159 (1975).
[CrossRef]

Sommer, A.

A. Sommer, Photoelectric Tubes (Methuen, London, 1951).

Troland, L.

L. Troland, J. Exp. Psych. 2, 1 (1917).
[CrossRef]

Young, M.

Zelewski, E.

Appl. Opt. (4)

Behav. Res. Methods Instrum. (2)

V. Di Lollo, Behav. Res. Methods Instrum. 11, 419 (1979).
[CrossRef]

T. H. NilssonBehav. Res. Methods Instrum. 13, 18 (1981).
[CrossRef]

J. Exp. Psych. (1)

L. Troland, J. Exp. Psych. 2, 1 (1917).
[CrossRef]

J. Opt. Soc. Am. (1)

S. L. Buck, W. Makous, J. Opt. Soc. Am. 68, 1392 (1978);R. W. Nygaard, T. E. FrumkesVision Res. 22, 433 (1982).
[CrossRef] [PubMed]

Modern Util. Infrared Tech. (1)

R. J. Phelan, C. A. Hamilton, G. W. Day, Modern Util. Infrared Tech. 62, 159 (1975).
[CrossRef]

Opt. Soc. of Am. (1)

D. L. MacAdam, Opt. Soc. of Am. 57, 854 (1967).

Other (21)

J. E. Kaufman, IES Lighting Handbook (Illuminating Engineering Society, New York, 1972).

R. M. Boynton, “The Visual System: Environmental Information,” in Handbook of Perception, E. C. Carterette, M. P. Friedman, Eds. (Academic, New York, 1975), pp. 285–307.

To make a point detector which is less susceptible to local variations in its photosensitive surface, the detector need not be placed directly against the pinhole. As long as the detector receives all the light entering the pinhole, it can be placed at some distance behind the pinhole to involve more of the detector surface without changing the result in principle

It does not matter whether these calculations are performed by us or by the optical and electronic configuration of a more complex photometer than the simple photodetector illustrated in Fig. 3. It is meaningless to ask whether an optical photometer actually calculated luminance in incident or emitted terms.

D. B. Judd, “Correlates Basic of the Visual Stimulus,” in Handbook of Experimental Psychology, S. S. Stevens, Ed. (Wiley, New York, 1951), pp. 811–867.

H. A. E. Keitz, Light Calculations and Measurements (Macmillan, london, 1971).

R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1957).

Certain optical systems such as the Maxwellian view present some particular luminance calibration problems.28

J. J. Gibson, The Senses Considered as Perceptual Systems (Houghton, Boston, 1966).

S. C. Brown, Benjamin Thompson, Count Rumford (MIT Press, Cambridge, Mass., 1979).

A. Sommer, Photoelectric Tubes (Methuen, London, 1951).

Nicodemus discusses how to calculate the solid angle of any target, but use of a ciruclar mask may be an easier solution.30

For visual receptors, a correction can be made for the Stiles-Crawford effect.23 Comparable corrections should be possible for other sensors whose structure also results in a certain directional selectivity.

For light incident at angles >20, the effects of Lambert's law become appreciable, but that is a relatively wide angle for imaging systems.

Correction in the final formula can, of course, be made for the transmittance of the optical system.

R. M. Boynton, “Vision,” in Experimental Methods and Instrumentation in Psychology, J. B. Sidowski, Ed. (McGraw-Hill, New York, 1966), pp. 273–330.

Y. LeGrand, Light, Color and Vision (Chapman & Hall, London, 1968).

L. M. Hurvich, D. Jameson, The Perception of Lightness and Darkness (Allyn and Bacon, Boston, 1966);L. A. Riggs, “Light as a Stimulus for Vision,” in Vision and Visual PerceptionC. H. Graham, Ed. (Wiley, New York, 1965), pp. 7–38;M. L. Rubin, G. L. Walls, Fundamentals of Visual Science (Thomas, Springfield, Ill., 1969);H. R. Schiffman, Sensation and Perception (Wiley, New York, 1976).

K. N. Ogle, Optics (Thomas, Springfield, Ill., 1968).

F. E. Nicodemus, Self Study Manual on Optical Radiation Measurements: Part 1—Concepts (U.S. G.P.O., Washington, D.C., 1976).

This assumes the source is at infinity and neglects taking into account the projected spherical area of the lens, which for most lenses amounts to a trivial correction.

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Figures (5)

Fig. 1
Fig. 1

Inverse to a radiator of light, the eye can be regarded as a receiver of the light which happens to be incident at a point from various directions in the environment.

Fig. 2
Fig. 2

Upper: Luminous intensity is usually measured in terms of the luminous flux L emitted over a solid angle α from a point source. L (in lumens)/α (in steradians) = candela. Middle: When the light emitted from a point source is incident on a point receiver, the measured luminous power L represents the flux in a single ray. This ray flux bears the same relationship to luminous intensity as instantaneous velocity to velocity. Lower: Luminous intensity can also be measured in terms of the luminous flux L incident over a solid angle ψ on a point receiver; L (lumen)/ψ (steridian) = candela.

Fig. 3
Fig. 3

Upper: Luminance can be measured in terms of the luminous flux L emitted over a solid angle α by a source of area S2. L (lumen)/α (steradian)/S2 (meters) = candela/meter2. Lower: Luminance can also be measured in terms of the luminous flux L incident over a solid angle ψ on a receiver of area P2. L (lumen)/ψ (steradian)/P2 (meters) = candela/meter2.

Fig. 4
Fig. 4

Definition of incident luminance indicates that luminance can be calculated from illuminance simply dividing it by the solid angle ψ subtended by the source. A circular target subtends a solid angle which, measured in steradians, equals its projected area on a sphere divided by the sphere's radius squared. That projected area has a radius r which can be calculated in terms of the sphere's radius d and the plane visual angle γ of the target r = d sin(γ/2). The projected area then equals π(d sinγ/2)2, and γ equals π ( d sin γ / 2 ) 2 / d 2 steradians. Consequently, when illuminance has been measured from a circular stimulus of visual angle γ, luminance = illuminance/π(sinγ/2)2.

Fig. 5
Fig. 5

An understanding of the relationships between incident and emitted luminances indicated how to calculate the illuminance of an image from a measure of the luminance incident on the focusing lens. It can be shown (see text) that image luminance = L/Ω/B2 = L/ψ/A2 = the luminance incident on the lens. Furthermore, image illuminance = L/B2 = (L/Ω/B2) × Ω. Measured in steradians, the solid angle Ω subtended by the lens with respect to the image equals A2/f2 when A2 is the aperture area of the lens and f its focal length. Substituting incident lens luminance for L/Ω/B2 and A2/f2 for Ω we get image illuminance = incident luminance × (A2/f2).

Tables (2)

Tables Icon

Table I Photometric Units Conceptualized for Incident Light Measurements

Tables Icon

Table II Photometric Units Reported In Certain Visual Research Journals 1978 & 81

Equations (7)

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candela / meter 2 = ( lumen / meter 2 ) / π ( sin γ / 2 ) 2 .
( L / B 2 / Ω ) × Ω = L / B 2 .
( L / ψ / A 2 ) × Ω = L / B 2 .
image illumination = incident luminance × ( aperture area / focal length 2 ) .
retinal illuminance in lumen / meter 2 = incident luminance × pupil area in millimeter 2 × ( 1.6 × 10 3 ) .
watt steradian meter 2
Candela meter 2

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