Abstract

The classical radiance–luminance parallelism of units for the measurement of emission and reception of flux applies when visual processing is modeled on principles of physics or engineering. “Energy” has a defined meaning in these disciplines: it is the time integral of flux; the time rate of transfer of flux has the dimension of power. Hence energy is appropriate only when light stimuli are delimited in time, else power is the applicable word. To conform to dimensional specifications in physics, energy models in vision would deal with packets of stimuli of fixed duration, not the time rate of excitation, and have magnitudes expressed in the form of the square root of the integrated squared spatial or spatio-temporal distributions.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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  19. Optical Society of America, The Science of Color (Crowell, 1953).
  20. In some compendia the Greek letter φ is used in place of F to prevent confusion with the standard use of F for force in mechanics, but this does not create any problems here.

1997

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity: energy models, position shifts and disparity shifts,” J. Neurophysiol. 77, 2879-2909 (1997).
[PubMed]

N. Qian and R. A. Anderson, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683-1698 (1997).
[CrossRef] [PubMed]

1985

1983

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best?” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

1968

J. Z. Levinson, “Impulse response of the human visual system,” J. Opt. Soc. Am. 58, 1558 (1968).

1966

G. Westheimer, “The Maxwellian view,” Vision Res. 6(12), 669-682 (1966).
[CrossRef] [PubMed]

1942

S. Hecht, S. Shlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

1939

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64-105 (1939).
[CrossRef]

C. H. Graham, R. H. Brown, and F. A. Mote, “The relative size of stimulus and intensity in the human eye,” J. Exp. Psychol. 24, 55-573 (1939).

Adelson, E. H.

Ahumada, A. J.

Anderson, R. A.

N. Qian and R. A. Anderson, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683-1698 (1997).
[CrossRef] [PubMed]

Barenblatt, G. I.

G. I. Barenblatt, Dimensional Analysis (Gordon & Breach, 1987).

Barlow, H. B.

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best?” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

Bergen, J. R.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Brown, R. H.

C. H. Graham, R. H. Brown, and F. A. Mote, “The relative size of stimulus and intensity in the human eye,” J. Exp. Psychol. 24, 55-573 (1939).

DeAngelis, G. C.

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity: energy models, position shifts and disparity shifts,” J. Neurophysiol. 77, 2879-2909 (1997).
[PubMed]

Freeman, R. D.

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity: energy models, position shifts and disparity shifts,” J. Neurophysiol. 77, 2879-2909 (1997).
[PubMed]

Graham, C. H.

C. H. Graham, R. H. Brown, and F. A. Mote, “The relative size of stimulus and intensity in the human eye,” J. Exp. Psychol. 24, 55-573 (1939).

Hecht, S.

S. Hecht, S. Shlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Levinson, J. Z.

J. Z. Levinson, “Impulse response of the human visual system,” J. Opt. Soc. Am. 58, 1558 (1968).

Mote, F. A.

C. H. Graham, R. H. Brown, and F. A. Mote, “The relative size of stimulus and intensity in the human eye,” J. Exp. Psychol. 24, 55-573 (1939).

Ohzawa, I.

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity: energy models, position shifts and disparity shifts,” J. Neurophysiol. 77, 2879-2909 (1997).
[PubMed]

Pirenne, M. H.

S. Hecht, S. Shlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Qian, N.

N. Qian and R. A. Anderson, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683-1698 (1997).
[CrossRef] [PubMed]

Robson, J. G.

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best?” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

Schelkunoff, S. A.

S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, 1943).

Shlaer, S.

S. Hecht, S. Shlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Sperling, G.

Stiles, W. S.

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64-105 (1939).
[CrossRef]

G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

van Santen, J. P. H.

Watson, A. B.

A. B. Watson and A. J. Ahumada, “Models of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322-342 (1985).
[CrossRef] [PubMed]

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best?” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

Westheimer, G.

G. Westheimer, “The Maxwellian view,” Vision Res. 6(12), 669-682 (1966).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982).

J. Exp. Psychol.

C. H. Graham, R. H. Brown, and F. A. Mote, “The relative size of stimulus and intensity in the human eye,” J. Exp. Psychol. 24, 55-573 (1939).

J. Gen. Physiol.

S. Hecht, S. Shlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

J. Neurophysiol.

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity: energy models, position shifts and disparity shifts,” J. Neurophysiol. 77, 2879-2909 (1997).
[PubMed]

J. Opt. Soc. Am.

J. Z. Levinson, “Impulse response of the human visual system,” J. Opt. Soc. Am. 58, 1558 (1968).

J. Opt. Soc. Am. A

Nature

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best?” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. B

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64-105 (1939).
[CrossRef]

Vision Res.

G. Westheimer, “The Maxwellian view,” Vision Res. 6(12), 669-682 (1966).
[CrossRef] [PubMed]

N. Qian and R. A. Anderson, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683-1698 (1997).
[CrossRef] [PubMed]

Other

S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, 1943).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Optical Society of America, The Science of Color (Crowell, 1953).

In some compendia the Greek letter φ is used in place of F to prevent confusion with the standard use of F for force in mechanics, but this does not create any problems here.

G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982).

G. I. Barenblatt, Dimensional Analysis (Gordon & Breach, 1987).

C.H.Graham, ed., Vision and Visual Perception (Wiley, 1965).

D.Jameson and L.M.Hurvich, eds., Visual Psychophysics, Handbook of Sensory Physiology (Springer, 1972), Vol. VII/4.

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Tables (1)

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Table 1 Dimension of Quantities Used in the Specification of Visual Signals [20]

Equations (6)

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1 μ lumen = F lumen , where F = 10 6 ;
1 μ = L cm , where L = 10 4 ;
Therefore E μ ( μ lumen . μ 2 ) = E L ( lumen . cm 2 ) F . L 2 .
E ( x , y , t ) w ( x , y , t ) d x d y d t ,
E ( x , y , t ) = E b . ( 1 + c ( x , y , t ) ) = E b + E b . c ( x , y , t ) .
c 2 ( x , y , t ) d x d y d t

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