Abstract

Trolands are a widely used measure of retinal illuminance in vision science and visual optics, but disagreements exist for the definition and interpretation of this photometric unit. The purpose of this communication is to resolve the confusion by providing a sound conceptual basis for interpreting trolands as a measure of angular flux density incident upon the retina. Using a simplified optical analysis, we show that the troland value of an extended source is the intensity in micro-candelas of an equivalent point source located at the eye’s posterior nodal point that produces the same illuminance in the retinal image as does the extended source. This optical interpretation of trolands reveals that total light flux in the image of an extended object is the product of the troland value of the source and the solid angle subtended by the source at the first nodal point, independent of eye size.

© 2018 Optical Society of America

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References

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  1. J. N. Howard, “Profile in optics: Leonard Thompson Troland,” Opt. Photon. News 19(6), 20–21 (2008).
    [Crossref]
  2. L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
    [Crossref]
  3. H. Kragh, “Photon: new light on an old name,” arxiv:1401.0293 (2014).
  4. Committee on Colorimetry, “The psychophysics of color,” J. Opt. Soc. Am. 34, 245–266 (1944).
    [Crossref]
  5. Committee on Colorimetry, The Science of Color (Optical Society of America, 1953), pp. 1–385.
  6. O. Packer and D. R. Williams, “Light, the retinal image, and photoreceptors,” in The Science of Color, S. K. Shevell, ed., 2nd ed. (Elsevier, 2003), pp. 41–78.
  7. S. A. Burns and R. Webb, “Optical generation of the visual stimulus,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 5.1–5.27.
  8. International Commission on Illumination, “International lighting vocabulary (ILV),” CIE Central Bureau, 2014, http://eilv.cie.co.at .
  9. G. Ziegelberger and I. C. N. Radiati, “ICNIRP guidelines on limits of exposure to incoherent visible and infrared radiation,” Health Phys. 105, 74–96 (2013).
    [Crossref]
  10. R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
    [Crossref]
  11. D. Sliney and M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, 1980).
  12. N. D. Miller, “Visual recovery from brief exposures to high luminance,” J. Opt. Soc. Am. 55, 1661–1669 (1965).
    [Crossref]
  13. G. Westheimer, “The Maxwellian view with an addendum on apodization,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 6.1–6.15.
  14. R. Kohler, “Photometric and radiometric quantities,” in Handbook of Applied Photometry, C. DeCusatis, ed. (American Institute of Physics, 1997), pp. 33–53.
  15. J. M. Enoch and V. Lakshminarayanan, “The problem of correction for the Stiles-Crawford effect of the first kind in radiometry and photometry, a solution,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 9.1–9.18.
  16. D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).
  17. E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics, M. Bass, ed., 2nd ed. (McGraw-Hill, 1995), pp. 24.1–24.7.

2013 (1)

G. Ziegelberger and I. C. N. Radiati, “ICNIRP guidelines on limits of exposure to incoherent visible and infrared radiation,” Health Phys. 105, 74–96 (2013).
[Crossref]

2011 (1)

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

2008 (1)

J. N. Howard, “Profile in optics: Leonard Thompson Troland,” Opt. Photon. News 19(6), 20–21 (2008).
[Crossref]

1965 (1)

1944 (1)

1917 (1)

L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
[Crossref]

Atchison, D. A.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Bostrom, R. G.

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

Burns, S. A.

S. A. Burns and R. Webb, “Optical generation of the visual stimulus,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 5.1–5.27.

Enoch, J. M.

J. M. Enoch and V. Lakshminarayanan, “The problem of correction for the Stiles-Crawford effect of the first kind in radiometry and photometry, a solution,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 9.1–9.18.

Howard, J. N.

J. N. Howard, “Profile in optics: Leonard Thompson Troland,” Opt. Photon. News 19(6), 20–21 (2008).
[Crossref]

Kohler, R.

R. Kohler, “Photometric and radiometric quantities,” in Handbook of Applied Photometry, C. DeCusatis, ed. (American Institute of Physics, 1997), pp. 33–53.

Kragh, H.

H. Kragh, “Photon: new light on an old name,” arxiv:1401.0293 (2014).

Lakshminarayanan, V.

J. M. Enoch and V. Lakshminarayanan, “The problem of correction for the Stiles-Crawford effect of the first kind in radiometry and photometry, a solution,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 9.1–9.18.

Landry, R. J.

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

Miller, N. D.

Miller, S. A.

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

Packer, O.

O. Packer and D. R. Williams, “Light, the retinal image, and photoreceptors,” in The Science of Color, S. K. Shevell, ed., 2nd ed. (Elsevier, 2003), pp. 41–78.

Radiati, I. C. N.

G. Ziegelberger and I. C. N. Radiati, “ICNIRP guidelines on limits of exposure to incoherent visible and infrared radiation,” Health Phys. 105, 74–96 (2013).
[Crossref]

Shi, D. X.

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

Sliney, D.

D. Sliney and M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, 1980).

Sliney, D. H.

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

Smith, G.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Troland, L. T.

L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
[Crossref]

Webb, R.

S. A. Burns and R. Webb, “Optical generation of the visual stimulus,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 5.1–5.27.

Westheimer, G.

G. Westheimer, “The Maxwellian view with an addendum on apodization,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 6.1–6.15.

Williams, D. R.

O. Packer and D. R. Williams, “Light, the retinal image, and photoreceptors,” in The Science of Color, S. K. Shevell, ed., 2nd ed. (Elsevier, 2003), pp. 41–78.

Wolbarsht, M.

D. Sliney and M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, 1980).

Zalewski, E. F.

E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics, M. Bass, ed., 2nd ed. (McGraw-Hill, 1995), pp. 24.1–24.7.

Ziegelberger, G.

G. Ziegelberger and I. C. N. Radiati, “ICNIRP guidelines on limits of exposure to incoherent visible and infrared radiation,” Health Phys. 105, 74–96 (2013).
[Crossref]

Health Phys. (2)

G. Ziegelberger and I. C. N. Radiati, “ICNIRP guidelines on limits of exposure to incoherent visible and infrared radiation,” Health Phys. 105, 74–96 (2013).
[Crossref]

R. J. Landry, R. G. Bostrom, S. A. Miller, D. X. Shi, and D. H. Sliney, “Retinal phototoxicity: a review of standard methodology for evaluating retinal optical radiation hazards,” Health Phys. 100, 417–434 (2011).
[Crossref]

J. Exp. Psychol. (1)

L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Photon. News (1)

J. N. Howard, “Profile in optics: Leonard Thompson Troland,” Opt. Photon. News 19(6), 20–21 (2008).
[Crossref]

Other (11)

G. Westheimer, “The Maxwellian view with an addendum on apodization,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 6.1–6.15.

R. Kohler, “Photometric and radiometric quantities,” in Handbook of Applied Photometry, C. DeCusatis, ed. (American Institute of Physics, 1997), pp. 33–53.

J. M. Enoch and V. Lakshminarayanan, “The problem of correction for the Stiles-Crawford effect of the first kind in radiometry and photometry, a solution,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 9.1–9.18.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics, M. Bass, ed., 2nd ed. (McGraw-Hill, 1995), pp. 24.1–24.7.

Committee on Colorimetry, The Science of Color (Optical Society of America, 1953), pp. 1–385.

O. Packer and D. R. Williams, “Light, the retinal image, and photoreceptors,” in The Science of Color, S. K. Shevell, ed., 2nd ed. (Elsevier, 2003), pp. 41–78.

S. A. Burns and R. Webb, “Optical generation of the visual stimulus,” in Handbook of Optics, M. Bass, ed., 3rd ed. (McGraw-Hill, 2010), pp. 5.1–5.27.

International Commission on Illumination, “International lighting vocabulary (ILV),” CIE Central Bureau, 2014, http://eilv.cie.co.at .

H. Kragh, “Photon: new light on an old name,” arxiv:1401.0293 (2014).

D. Sliney and M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, 1980).

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Figures (2)

Fig. 1.
Fig. 1. Geometry for relating areal flux density (i.e., illuminance, E) and angular flux density (i.e., intensity, I) for a point source of light. Point source has intensity I, and illuminated surface has projected area A. Solid angle Ω=A/d2 is subtended at the source by the illuminated surface.
Fig. 2.
Fig. 2. Optical model of an imaging system. For a closed system such as the eye or a camera, the goal is to determine the illumination of the image of an extended source in terms of parameters observable in object space. Aperture area A and surface areas S, S refer to areas projected into planes normal to the chief ray.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

F=IΩ=IA/d2,
E=F/A=(IA/d2)A=I/d2.
F=LSω.
E=F/S=F/S=LSω/S.
S/S=(z/z)2.
E=Lωz2/z2.
z2=A/ω,
E=LA/z2.
I=LA,
I=Ez2.
I=F/ϕ,
I=F/ϕ.
I=LSω/ϕ,
I=LAω/ω=LA,
F=LAϕ.
F=LAπρ2.

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