Abstract

A method is proposed for realizing the total flux scale of light sources by use of an integrating sphere with an opening to introduce a known amount of flux from a luminous intensity standard or a spectral irradiance standard lamp placed outside the sphere. Computer simulations were made on several models of an integrating sphere, designed to compare the total flux of a test lamp inside the sphere with the flux introduced from an external source. I describe the theory and algorithm of the simulation, present the results of the simulation for varying conditions of sphere geometry such as size and location of the baffles, internal source, and wall reflectance, and predict that one of the models has sufficient accuracy to calibrate lamps for total flux.

© 1994 Optical Society of America

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References

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  1. J. Bastie, B. Andasse, R. Foucart, “Luminous flux measurements with a goniophotometer; study of time effects on data collection,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 45–47.
  2. R. S. Hu, “Importance of axis alignment in goniophotometry,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 21–22.
  3. I. Lewin, R. Laird, B. Carruthers, “Development of new photometer concepts for quality control applications,” J. Illum. Eng. Soc. 19, (2), 90–97 (1990).
  4. R. E. Levin, “Photometric connection,” Light Des. Appl. 12 (9), 28–35 (1982).
  5. T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.
  6. T. M. Goodman, J. R. Moore, N. C. Pearce, D. K. Murray, “The establishment of a new national scale of spectral total flux,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 50–53.
  7. J. Jacquez, H. Kuppenheim, “Theory of the integrating sphere,” J. Opt. Soc. Am. 45, 460–470 (1955).
    [CrossRef]
  8. D. Goebel, “Generalized integrating-sphere theory,” Appl. Opt. 6, 125–128 (1967).
    [CrossRef] [PubMed]
  9. M. Finkei, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
    [CrossRef]
  10. E. Evans, S. Lowenthal, “Moment generator: new role for the integrating sphere,” J. Opt. Soc. Am. 62, 411–415 (1972).
    [CrossRef]
  11. T. Muroi, “Investigation on the luminous flux integration by closed space,” J. Illum. Eng. Inst. Jpn. 43, 52–57 (1959).
    [CrossRef]
  12. L. Morren, “Method for assessing the effect of the screen in an integrating sphere with an application to the photometry of a tubular lamp,” Appl. Opt. 10, 2621–2628 (1971).
    [CrossRef] [PubMed]
  13. F. Rotter, “View into the integrating sphere through the observation window,” Appl. Opt. 10, 2629–2638 (1971).
    [CrossRef] [PubMed]
  14. R. Brown, “A numerical solution of the integral equation describing a photometric integrating sphere,” J. Res. Natl. Bur. Stand. Sect. A 77, 343–351 (1973).
    [CrossRef]
  15. W. Fussel, “Approximate theory of the photometric integrating sphere,” Natl. Bur. Stand. (U.S.) Tech. Note 594-7 (1974).
  16. A. C. M. de Visser, M. van der Woude, “Minimization of the screen effect in the integrating sphere by cariation,” Light. Res. Technol. 12, 42–49 (1980).
    [CrossRef]

1990

I. Lewin, R. Laird, B. Carruthers, “Development of new photometer concepts for quality control applications,” J. Illum. Eng. Soc. 19, (2), 90–97 (1990).

1982

R. E. Levin, “Photometric connection,” Light Des. Appl. 12 (9), 28–35 (1982).

1980

A. C. M. de Visser, M. van der Woude, “Minimization of the screen effect in the integrating sphere by cariation,” Light. Res. Technol. 12, 42–49 (1980).
[CrossRef]

1974

W. Fussel, “Approximate theory of the photometric integrating sphere,” Natl. Bur. Stand. (U.S.) Tech. Note 594-7 (1974).

1973

R. Brown, “A numerical solution of the integral equation describing a photometric integrating sphere,” J. Res. Natl. Bur. Stand. Sect. A 77, 343–351 (1973).
[CrossRef]

1972

1971

1970

M. Finkei, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

1967

1959

T. Muroi, “Investigation on the luminous flux integration by closed space,” J. Illum. Eng. Inst. Jpn. 43, 52–57 (1959).
[CrossRef]

1955

Andasse, B.

J. Bastie, B. Andasse, R. Foucart, “Luminous flux measurements with a goniophotometer; study of time effects on data collection,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 45–47.

Bastie, J.

J. Bastie, B. Andasse, R. Foucart, “Luminous flux measurements with a goniophotometer; study of time effects on data collection,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 45–47.

Brown, R.

R. Brown, “A numerical solution of the integral equation describing a photometric integrating sphere,” J. Res. Natl. Bur. Stand. Sect. A 77, 343–351 (1973).
[CrossRef]

Carruthers, B.

I. Lewin, R. Laird, B. Carruthers, “Development of new photometer concepts for quality control applications,” J. Illum. Eng. Soc. 19, (2), 90–97 (1990).

de Visser, A. C. M.

A. C. M. de Visser, M. van der Woude, “Minimization of the screen effect in the integrating sphere by cariation,” Light. Res. Technol. 12, 42–49 (1980).
[CrossRef]

Evans, E.

Finkei, M.

M. Finkei, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

Foucart, R.

J. Bastie, B. Andasse, R. Foucart, “Luminous flux measurements with a goniophotometer; study of time effects on data collection,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 45–47.

Fukuhara, M.

T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.

Fussel, W.

W. Fussel, “Approximate theory of the photometric integrating sphere,” Natl. Bur. Stand. (U.S.) Tech. Note 594-7 (1974).

Goebel, D.

Goodman, T. M.

T. M. Goodman, J. R. Moore, N. C. Pearce, D. K. Murray, “The establishment of a new national scale of spectral total flux,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 50–53.

Hatanaka, H.

T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.

Hu, R. S.

R. S. Hu, “Importance of axis alignment in goniophotometry,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 21–22.

Jacquez, J.

Kuppenheim, H.

Laird, R.

I. Lewin, R. Laird, B. Carruthers, “Development of new photometer concepts for quality control applications,” J. Illum. Eng. Soc. 19, (2), 90–97 (1990).

Levin, R. E.

R. E. Levin, “Photometric connection,” Light Des. Appl. 12 (9), 28–35 (1982).

Lewin, I.

I. Lewin, R. Laird, B. Carruthers, “Development of new photometer concepts for quality control applications,” J. Illum. Eng. Soc. 19, (2), 90–97 (1990).

Lowenthal, S.

Moore, J. R.

T. M. Goodman, J. R. Moore, N. C. Pearce, D. K. Murray, “The establishment of a new national scale of spectral total flux,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 50–53.

Morren, L.

Muroi, T.

T. Muroi, “Investigation on the luminous flux integration by closed space,” J. Illum. Eng. Inst. Jpn. 43, 52–57 (1959).
[CrossRef]

Murray, D. K.

T. M. Goodman, J. R. Moore, N. C. Pearce, D. K. Murray, “The establishment of a new national scale of spectral total flux,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 50–53.

Noguchi, T.

T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.

Otsuka, T.

T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.

Pearce, N. C.

T. M. Goodman, J. R. Moore, N. C. Pearce, D. K. Murray, “The establishment of a new national scale of spectral total flux,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 50–53.

Rotter, F.

Sakaguchi, T.

T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.

van der Woude, M.

A. C. M. de Visser, M. van der Woude, “Minimization of the screen effect in the integrating sphere by cariation,” Light. Res. Technol. 12, 42–49 (1980).
[CrossRef]

Appl. Opt.

J. Illum. Eng. Inst. Jpn.

T. Muroi, “Investigation on the luminous flux integration by closed space,” J. Illum. Eng. Inst. Jpn. 43, 52–57 (1959).
[CrossRef]

J. Illum. Eng. Soc.

I. Lewin, R. Laird, B. Carruthers, “Development of new photometer concepts for quality control applications,” J. Illum. Eng. Soc. 19, (2), 90–97 (1990).

J. Opt. Soc. Am.

J. Res. Natl. Bur. Stand. Sect. A

R. Brown, “A numerical solution of the integral equation describing a photometric integrating sphere,” J. Res. Natl. Bur. Stand. Sect. A 77, 343–351 (1973).
[CrossRef]

Light Des. Appl.

R. E. Levin, “Photometric connection,” Light Des. Appl. 12 (9), 28–35 (1982).

Light. Res. Technol.

A. C. M. de Visser, M. van der Woude, “Minimization of the screen effect in the integrating sphere by cariation,” Light. Res. Technol. 12, 42–49 (1980).
[CrossRef]

Natl. Bur. Stand. (U.S.) Tech. Note 594-7

W. Fussel, “Approximate theory of the photometric integrating sphere,” Natl. Bur. Stand. (U.S.) Tech. Note 594-7 (1974).

Opt. Commun.

M. Finkei, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

Other

J. Bastie, B. Andasse, R. Foucart, “Luminous flux measurements with a goniophotometer; study of time effects on data collection,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 45–47.

R. S. Hu, “Importance of axis alignment in goniophotometry,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 21–22.

T. Otsuka, H. Hatanaka, T. Sakaguchi, M. Fukuhara, T. Noguchi, “A study on the photometric measurement of floodlights,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 3–4.

T. M. Goodman, J. R. Moore, N. C. Pearce, D. K. Murray, “The establishment of a new national scale of spectral total flux,” in Proceedings of the 22nd Session of the International Commission on Illumination (Commission Internationale de l'Eclairage, Vienna1991), Vol. 1 (1), Div. 2, pp. 50–53.

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Figures (15)

Fig. 1
Fig. 1

Model 1 sphere geometry.

Fig. 2
Fig. 2

Model 2 sphere geometry.

Fig. 3
Fig. 3

Parameters for the computer model: (a) dimensional parameters, (b) other parameters.

Fig. 4
Fig. 4

Total flux Φtot(n) and unabsorbed flux Φun(n) as a function of the number of reflections n. The data are normalized by the maximum value for each curve.

Fig. 5
Fig. 5

Comparison of the simulation results of the illuminance distributions on the sphere wall with Brown's results by using Brown's parameters. North and South refer only to lighting the upper or lower hemisphere, respectively. Parameter R = 1.0, Rd = 0, R0 = 0, R1 = 0.1, R2 = 0, D = 0.31, DL = 0, ρ on all surfaces are 0.90.

Fig. 6
Fig. 6

Interreflection window illuminance factor K(θ, ϕ) of a sphere with parameters used in de Visser and van der Woude's calculation. Parameters R = 1.0, Rd = 0, R0 = 0, R1 = 0.348, R2 = 0, D = 0.663, DL = 0, ρwb1u = ρb1L = 0.90.

Fig. 7
Fig. 7

Window illuminance as a function of the location D of baffle B1 on Model 1 with basic parameters.

Fig. 8
Fig. 8

Interreflection window illuminance factor K(θ, ϕ) of Model 1 with basic parameters as a function of direction θ from the internal source.

Fig. 9
Fig. 9

Window illuminance and total flux by the internal source (Ew1, Φtot1), and by the external source (EW2, Φtot2) as a function of the angle β of baffle B2 on Model 2. Parameters R = 0.254, Rd = 0.02, R0 = 0.06, α = 130°, R1 = 0.02, D = 0.09, DL = 0, R2 = 0.045, D1 = 0.059, D2 = 0.07, θ1 = 110°, θ2 = 150°, ∊a = 0.05, ρ on all surfaces is 0.95.

Fig. 10
Fig. 10

Window illuminance by different direct illuminance distributions as a function of β on Model 2.

Fig. 11
Fig. 11

Window illuminance by the internal source Ew1 and by the external source Ew2 as a function of the location D of baffle B1 on Model 2.

Fig. 12
Fig. 12

Window illuminance by the internal source Ew1 and by the external source Ew2 as a function of the angle β of baffle B2 on Model 2 with different sizes (radius R1) of baffle B1.

Fig. 13
Fig. 13

Window illuminance by the internal source Ew1 and by the external source Ew2 with different wall reflectances ρw.

Fig. 14
Fig. 14

Window illuminance curves with different intensity distributions of the internal source.

Fig. 15
Fig. 15

Window illuminance and total flux on Model 2 with smaller opening and smaller baffle B2. Parameters R0 = 0.045, R2 = 0.038, D1 = 0.084, D2 = 0.10, θ1 = 115°, θ2 = 145°. (Other parameters are as in Fig. 9.)

Tables (1)

Tables Icon

Table 1 Comparison of Calculated Window llluminance for Model 1 a

Equations (31)

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Φ s = E A ( 1 m ) ,
E i ( a ) = 1 π w ρ ( a ) E i 1 ( a ) S ( a , a ) T ( a , a ) d a ,
E ( a ) = i = 0 E i ( a ) .
E i ( θ , ϕ ) = 1 4 π 0 2 π 0 π E i 1 ( θ , ϕ ) ρ w ( θ , ϕ ) × S b 1 w ( θ , ϕ , θ , ϕ ) × S b 2 w ( θ , ϕ , θ , ϕ ) sin θ d θ d ϕ + ρ b 1 u E i 1 ( b 1 u ) a 1 T b 1 u w ( θ , ϕ ) / π + ρ b 1 L E i 1 ( b 1 L ) a 1 T b 1 L w ( θ , ϕ ) S b 2 b 1 ( θ , ϕ ) / π + ρ b 2 r E i 1 ( b 2 r ) a 2 T b 2 r w ( θ , ϕ ) / π + ρ b 2 L E i 1 ( b 2 L ) a 2 T b 2 L w ( θ , ϕ ) S b 1 b 2 ( θ , ϕ ) / π ,
E i ( b 1 u ) = R 2 π 0 2 π 0 π E i 1 ( θ , ϕ ) ρ w ( θ , ϕ ) × T b 1 u w ( θ , ϕ ) sin θ d θ d ϕ ,
E i ( b 1 L ) = R 2 π 0 2 π 0 π E i 1 ( θ , ϕ ) ρ w ( θ , ϕ ) × S b 2 b 1 ( θ , ϕ ) T b 1 L w ( θ , ϕ ) sin θ d θ d ϕ + E i 1 ( b 2 L ) ρ b 2 L a 2 T b 2 b 1 / π ,
E i ( b 2 r ) = R 2 π 0 2 π 0 π E i 1 ( θ , ϕ ) ρ w ( θ , ϕ ) × T b 2 r w ( θ , ϕ ) sin θ d θ d ϕ ,
E i ( b 2 L ) = R 2 π 0 2 π 0 π E i 1 ( θ , ϕ ) ρ w ( θ , ϕ ) S b 1 b 2 ( θ , ϕ ) × T b 2 L w ( θ , ϕ ) sin θ d θ d ϕ + E i 1 ( b 1 L ) ρ b 1 L a 1 T b 1 b 2 / π .
K ( θ , ϕ ) = i = 0 E i ( 0 , 0 ) / Φ b ( lx / lm ) ,
E w = 0 2 π 0 π K ( θ , ϕ ) I ( θ , ϕ ) sin θ d θ d ϕ .
ϕ tot ( n ) = ϕ i n ( 1 + ρ w i = 1 n ρ x i 1 ) ( n 1 ) ,
ϕ u n ( n ) = ϕ i n ρ w ρ x n 1 ( n 2 ) .
( n ) = ϕ tot ( ) ϕ tot ( n ) ϕ tot ( ) ϕ i n = ρ χ n Φ u n ( n ) ϕ i n .
E p = L s s ,
x 1 = R sin θ 1 sin ϕ 1 , y 1 = R sin θ 1 cos ϕ 1 , z 1 = R cos θ 1 ,
x 2 = R sin θ 2 sin ϕ 2 , y 2 = R sin θ 2 cos ϕ 2 , z 2 = R cos θ 2 .
S b 1 w ( θ 1 , ϕ 1 , θ 2 , ϕ 2 ) = 1 for x 0 2 + y 0 2 > R 1 2 = 0 for x 0 2 + y 0 2 R 1 2 ,
x 0 = ( D z 1 ) ( x 2 x 1 ) / ( z 2 z 1 ) + x 1 , y 0 = ( D z 1 ) ( y 2 y 1 ) / ( z 2 z 1 ) + y 1 .
S b 2 w ( θ 1 , ϕ 1 , θ 2 , ϕ 2 ) = 1 for x 0 2 + ( y 0 D 2 ) 2 + ( z 0 + D 1 ) 2 > R 2 2 = 0 for x 0 2 + ( y 0 D 2 ) 2 + ( z 0 + D 1 ) 2 R 2 2 ,
x 0 = x 1 + ( x 2 x 1 ) ( y 0 y 1 ) / ( y 2 y 1 ) , y 0 = ( k n z 1 ) ( y 2 y 1 ) + n y 1 ( z 2 z 1 ) m ( y 2 y 1 ) + n ( z 2 z 1 ) , z 0 = ( k m y 1 ) ( z 2 z 1 ) + m z 1 ( y 2 y 1 ) n ( z 2 z 1 ) + m ( y 2 y 1 ) ,
k = [ D 1 ( D 1 + D 3 ) + D 2 2 ] [ ( D 1 + D 3 ) 2 + D 2 2 ] 1 / 2 , m = D 2 [ ( D 1 + D 3 ) 2 + D 2 2 ] 1 / 2 , n = ( D 1 + D 3 ) [ ( D 1 + D 3 ) 2 + D 2 2 ] 1 / 2 ,
m y + n z = k .
D 3 = D 2 / tan β D 1 .
f ( θ , ϕ ) = | D R cos θ | ( R D cos θ ) ( R 2 + D 2 2 R D cos θ ) 2 , T b 1 u w ( θ , ϕ ) = f ( θ , ϕ ) for D < R cos θ = 0 for D R cos θ ,
T b 1 L w ( θ , ϕ ) = 0 for D < R cos θ = f ( θ , ϕ ) for D R cos θ .
f ( θ , ϕ ) = [ ( y 1 y 0 ) 2 + ( z 1 z 0 ) 2 ] 1 / 2 ( R + D 1 cos θ D 2 cos ϕ sin θ ) [ R 2 + D 1 2 + D 2 2 + 2 R ( D 1 cos θ D 2 sin θ cos ϕ ) ] 2 , T b 2 r w ( θ , ϕ ) = f ( θ , ϕ ) for m y 1 + n z 1 > k = 0 for m y 1 + n z 1 k ,
T b 2 L w ( θ , ϕ ) = 0 for m y 1 + n z 1 > k = f ( θ , ϕ ) for m y 1 + n z 1 k .
T b 1 b 2 = ( D + D 1 ) [ D 2 2 + ( D 1 + D ) ( D 1 + D 3 ) ] [ ( D + D 1 ) 2 + D 2 2 ] 2 [ ( D 3 + D 1 ) 2 + D 2 2 ] 1 / 2 , T b 2 b 1 = T b 1 b 2 .
E 0 ( θ , ϕ ) = I ( θ , ϕ ) ( R D L cos θ ) S b 1 s ( θ , ϕ ) S b 2 s ( θ , ϕ ) ( R 2 + D L 2 2 R D L cos θ ) 3 / 2 ,
E 0 ( b 1 L ) = I ( 0 , 0 ) / ( D D L ) 2 ,
E 0 ( b 2 L ) = I ( α , 0 ) [ D 2 2 + ( D 1 + D 3 ) ( D 1 + D L ) ] [ ( D 1 + D L ) 2 + D 2 2 ] 3 / 2 [ ( D 1 + D 3 ) 2 + D 2 2 ] 1 / 2 .

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