Abstract

Radiometric and photometric quantities rely on a geometric description of the beam subtended by a source and a receptor. In this paper, a generalization of this description is proposed as the product of the apparent size of the source times the receptor angular extent, whatever the natures of these elements: point, line, surface, or volume. The obtained flux density per geometric extent expressions are then applied to the determination of the irradiances induced in the near field and far field by a rectilinear source represented as a point source, a line source, and a surface source.

© 2013 Optical Society of America

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References

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  1. P. Bouguer, Essai d’optique, sur la gradation de la lumière (Jombert, 1729) (in French).
  2. P. Bouguer, Traité d’optique sur la gradation de la lumière(M. l’abbé de La Caille, 1760) (in French, posthumous).
  3. J. H. Lambert, Photometria, sive de Mensura et gradibus luminis, colorum et umbræ (Sumptibus Vidae Eberhardi Klett, 1760) (in Latin and French).
  4. G. Gehlhoff and H. Schering, “Über ein neues Photometer sehr hoher Empfindlichkeit und einige Anwendungen,” Z. Tech. Phys. I247–256 (1920) (in German).
  5. A. Blondel, “Rapport sur les unités photométriques,” Tech. Rep. (Congrés International des Électriciens, 1896).
  6. Commission Internationale de L’Éclairage (CIE), “International lighting vocabulary,” publication 17, revision 5 (CIE, 2011).
  7. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed.(Wiley-Interscience, 2000).
  8. Technical Committee 1-37, “CIE supplementary system of photometry,” Tech. Rep. (CIE, 2011).
  9. Technical Committee 1-58, “Recommended system for mesopic photometry based on visual performance,” Tech. Rep. (CIE, 2010).
  10. Technical Committee 8-01, “A colour appearance model for colour management systems: CIECAM02,” Tech. Rep. (CIE, 2004).
  11. D. DiLaura, K. Houser, R. Mistrick, and G. Steffy, eds., IESNA Lighting Handbook, 10th ed. (Illumination Engineering Society, 2011).
  12. M. S. Langer and S. W. Zucker, “What is a light source?” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings (IEEE, 1997), pp. 172–178.
  13. M. S. Langer and S. W. Zucker, “Casting light on illumination: a computational model and dimensional analysis of sources,” Comput. Vis. Image Underst. 65, 322–335 (1997).
    [CrossRef]
  14. Illuminating Engineering Society, “ANSI/IESNA LM-63-02: ANSI approved standard file format for electronic transfer of photometric data and related information,” revision 4 (Illuminating Engineering Society of North America, 2002).
  15. P. Y. Ngai, “On near-field photometry,” J. Illum. Eng. Soc. 16129–136 (1987).
  16. I. Ashdown, “Near-field photometry: a new approach,” J. Illum. Eng. Soc. 22, 163–180 (1993).
  17. P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).
  18. S. M. Jacob and J. S. Dranoff, “Light intensity profiles in a perfectly mixed photoreactor,” AIChE J. 16359–363(1970).
    [CrossRef]
  19. J. R. Bolton, “Calculation of ultraviolet fluence rate distributions in an annular reactor: significance of refraction and reflection,” Water Res. 34, 3315–3324 (2000).
    [CrossRef]

2008

P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).

2000

J. R. Bolton, “Calculation of ultraviolet fluence rate distributions in an annular reactor: significance of refraction and reflection,” Water Res. 34, 3315–3324 (2000).
[CrossRef]

1997

M. S. Langer and S. W. Zucker, “Casting light on illumination: a computational model and dimensional analysis of sources,” Comput. Vis. Image Underst. 65, 322–335 (1997).
[CrossRef]

1993

I. Ashdown, “Near-field photometry: a new approach,” J. Illum. Eng. Soc. 22, 163–180 (1993).

1987

P. Y. Ngai, “On near-field photometry,” J. Illum. Eng. Soc. 16129–136 (1987).

1970

S. M. Jacob and J. S. Dranoff, “Light intensity profiles in a perfectly mixed photoreactor,” AIChE J. 16359–363(1970).
[CrossRef]

1920

G. Gehlhoff and H. Schering, “Über ein neues Photometer sehr hoher Empfindlichkeit und einige Anwendungen,” Z. Tech. Phys. I247–256 (1920) (in German).

Ashdown, I.

I. Ashdown, “Near-field photometry: a new approach,” J. Illum. Eng. Soc. 22, 163–180 (1993).

Blondel, A.

A. Blondel, “Rapport sur les unités photométriques,” Tech. Rep. (Congrés International des Électriciens, 1896).

Bolton, J. R.

J. R. Bolton, “Calculation of ultraviolet fluence rate distributions in an annular reactor: significance of refraction and reflection,” Water Res. 34, 3315–3324 (2000).
[CrossRef]

Bouguer, P.

P. Bouguer, Essai d’optique, sur la gradation de la lumière (Jombert, 1729) (in French).

P. Bouguer, Traité d’optique sur la gradation de la lumière(M. l’abbé de La Caille, 1760) (in French, posthumous).

Boulenguez, P.

P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).

Carré, S.

P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).

Dranoff, J. S.

S. M. Jacob and J. S. Dranoff, “Light intensity profiles in a perfectly mixed photoreactor,” AIChE J. 16359–363(1970).
[CrossRef]

Gehlhoff, G.

G. Gehlhoff and H. Schering, “Über ein neues Photometer sehr hoher Empfindlichkeit und einige Anwendungen,” Z. Tech. Phys. I247–256 (1920) (in German).

Jacob, S. M.

S. M. Jacob and J. S. Dranoff, “Light intensity profiles in a perfectly mixed photoreactor,” AIChE J. 16359–363(1970).
[CrossRef]

Lambert, J. H.

J. H. Lambert, Photometria, sive de Mensura et gradibus luminis, colorum et umbræ (Sumptibus Vidae Eberhardi Klett, 1760) (in Latin and French).

Langer, M. S.

M. S. Langer and S. W. Zucker, “Casting light on illumination: a computational model and dimensional analysis of sources,” Comput. Vis. Image Underst. 65, 322–335 (1997).
[CrossRef]

M. S. Langer and S. W. Zucker, “What is a light source?” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings (IEEE, 1997), pp. 172–178.

Ngai, P. Y.

P. Y. Ngai, “On near-field photometry,” J. Illum. Eng. Soc. 16129–136 (1987).

Perraudeau, M.

P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).

Piranda, B.

P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).

Schering, H.

G. Gehlhoff and H. Schering, “Über ein neues Photometer sehr hoher Empfindlichkeit und einige Anwendungen,” Z. Tech. Phys. I247–256 (1920) (in German).

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed.(Wiley-Interscience, 2000).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed.(Wiley-Interscience, 2000).

Zucker, S. W.

M. S. Langer and S. W. Zucker, “Casting light on illumination: a computational model and dimensional analysis of sources,” Comput. Vis. Image Underst. 65, 322–335 (1997).
[CrossRef]

M. S. Langer and S. W. Zucker, “What is a light source?” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings (IEEE, 1997), pp. 172–178.

AIChE J.

S. M. Jacob and J. S. Dranoff, “Light intensity profiles in a perfectly mixed photoreactor,” AIChE J. 16359–363(1970).
[CrossRef]

Comput. Vis. Image Underst.

M. S. Langer and S. W. Zucker, “Casting light on illumination: a computational model and dimensional analysis of sources,” Comput. Vis. Image Underst. 65, 322–335 (1997).
[CrossRef]

J. Illum. Eng. Soc.

P. Y. Ngai, “On near-field photometry,” J. Illum. Eng. Soc. 16129–136 (1987).

I. Ashdown, “Near-field photometry: a new approach,” J. Illum. Eng. Soc. 22, 163–180 (1993).

J. Light Eng.

P. Boulenguez, S. Carré, B. Piranda, and M. Perraudeau, “A new method of near-field photometry,” J. Light Eng. 16, 89–95(2008).

Water Res.

J. R. Bolton, “Calculation of ultraviolet fluence rate distributions in an annular reactor: significance of refraction and reflection,” Water Res. 34, 3315–3324 (2000).
[CrossRef]

Z. Tech. Phys.

G. Gehlhoff and H. Schering, “Über ein neues Photometer sehr hoher Empfindlichkeit und einige Anwendungen,” Z. Tech. Phys. I247–256 (1920) (in German).

Other

A. Blondel, “Rapport sur les unités photométriques,” Tech. Rep. (Congrés International des Électriciens, 1896).

Commission Internationale de L’Éclairage (CIE), “International lighting vocabulary,” publication 17, revision 5 (CIE, 2011).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed.(Wiley-Interscience, 2000).

Technical Committee 1-37, “CIE supplementary system of photometry,” Tech. Rep. (CIE, 2011).

Technical Committee 1-58, “Recommended system for mesopic photometry based on visual performance,” Tech. Rep. (CIE, 2010).

Technical Committee 8-01, “A colour appearance model for colour management systems: CIECAM02,” Tech. Rep. (CIE, 2004).

D. DiLaura, K. Houser, R. Mistrick, and G. Steffy, eds., IESNA Lighting Handbook, 10th ed. (Illumination Engineering Society, 2011).

M. S. Langer and S. W. Zucker, “What is a light source?” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings (IEEE, 1997), pp. 172–178.

Illuminating Engineering Society, “ANSI/IESNA LM-63-02: ANSI approved standard file format for electronic transfer of photometric data and related information,” revision 4 (Illuminating Engineering Society of North America, 2002).

P. Bouguer, Essai d’optique, sur la gradation de la lumière (Jombert, 1729) (in French).

P. Bouguer, Traité d’optique sur la gradation de la lumière(M. l’abbé de La Caille, 1760) (in French, posthumous).

J. H. Lambert, Photometria, sive de Mensura et gradibus luminis, colorum et umbræ (Sumptibus Vidae Eberhardi Klett, 1760) (in Latin and French).

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Figures (4)

Fig. 1.
Fig. 1.

Rendering (gray scale and isolux) of a wall luminaire (measured data) using (a) far-field, (b) distributed point source, and (c) near-field representations. In more detail, (a) point source of luminous intensity Φ 02 , (b)  N S point sources of luminous intensities Φ 02 , k { 1 , , N S } distributed on a surface, and (c) surface source of luminance Φ 22 .

Fig. 2.
Fig. 2.

Geometry of the rectilinear light source S .

Fig. 3.
Fig. 3.

Radiant intensity Φ 02 indicatrix of the rectilinear source S from Eq. (12).

Fig. 4.
Fig. 4.

Irradiance ratio at the position P induced by the near-field and far-field approaches [respectively from Eqs. (16) and (14)].

Tables (6)

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Table 1. Notation Employed throughout the Paper

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Table 2. Emitted and Received Flux Densities in Terms of the Spatial Extents of a Source S or a Receptor R

Tables Icon

Table 3. Elementary Apparent Sizes of a Source S as Seen from a Receptor R

Tables Icon

Table 4. Elementary Angular Extents of the Light Beam from a Source S to a Receptor R

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Table 5. Elementary Geometric Extents d i X d j Y and Related Flux Densities Φ i j

Tables Icon

Table 6. Spatial Flux Density at a Receptor R Induced by the Far-Field, Distributed Point Source, and Near-Field Approaches

Equations (18)

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

Φ i j = i + j Φ i X j Y [ W · { 1 , m 1 , m 2 } · { 1 , rad 1 , sr 1 } ] .
Φ i j = i Φ 0 j i X = i Φ i 0 i Y [ W · { 1 , m 1 , m 2 } · { 1 , rad 1 , sr 1 } ] .
Φ = X Y Φ i j d i X d j Y [ W ] .
Φ 0 j = L S Φ 1 j d L S ap [ W · { 1 , rad 1 , sr 1 } ] ,
Φ 0 j = A S Φ 1 j d 2 A S ap [ W · { 1 , rad 1 , sr 1 } ] .
d 2 Φ R d 2 A R = Φ 02 cos θ R S R [ W · m 2 ] ,
d i Φ 0 j = Φ i j d i X [ W · { 1 , rad 1 , sr 1 } ] .
Φ 0 j , k = Φ i j , k Δ i X k [ W · { 1 , rad 1 , sr 1 } ] .
Φ S = space L S Φ 12 d L S ap d 2 Ω S = Φ 12 L S B = 0 2 π β = 0 π sin 2 β d β d B = π 2 Φ 12 L S [ W ] .
d Φ S d L S = π 2 Φ 12 [ W · m 1 ] .
Φ 02 = L S Φ 12 d L S ap = Φ 12 L S cos θ S [ W · sr 1 ] ,
Φ 02 = Φ S π 2 cos θ S = Φ S π 2 sin β [ W · sr 1 ] .
d 2 Φ R d 2 A R ( R ) = Φ S π 2 cos θ S cos θ R S R 2 = Φ S π 2 h 2 1 + x 2 h 2 ( 1 + x 2 + y 2 h 2 ) 2 [ W · m 2 ] .
d 2 Φ R d 2 A R ( P ) = Φ S π 2 h 2 [ W · m 2 ] .
d 2 Φ R d 2 A R ( P ) = 2 y = 0 L S 2 Φ 12 cos θ S cos θ R S R 2 d y = 2 y = 0 L S 2 Φ 12 h 2 ( y 2 + h 2 ) 2 d y [ W · m 2 ] .
d 2 Φ R d 2 A R ( P ) = Φ S π 2 ( 2 L S 2 + 4 h 2 + 1 L S h arctan L S 2 h ) [ W · m 2 ] .
Φ S = Φ 22 π 2 L S D S [ W ] .
Φ 12 = lim D S 0 Φ 22 D S [ W · m 1 · sr 1 ] .

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