Abstract

A theoretical study has been made of the optical properties of two-component phosphor blends for fluorescent lamps. The component spectral energy distributions were taken to be gaussian when the number of emitted photons is plotted vs energy. Mercury lines were added. The widths, positions, and proportions of the components were systematically varied in such a way as to keep the blend chromaticity coordinates constant. Luminosity and color-rendering indices were computed. Optimum blends for daylight, cool white, white, and warm white lamps were determined in terms of a quality index, which measures the combination of brightness and color rendition.

© 1971 Optical Society of America

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References

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  1. H. F. Ivey, J. Opt. Soc. Amer. 53, 1185 (1963).
    [CrossRef]
  2. O. J. Sovers, L. J. Bodi, J. Opt. Soc. Amer. 55, 1643 (1965).
    [CrossRef]
  3. Private communication.
  4. J. L. Ouweltjes, Die Farbe 9, 207 (1960).
  5. Amer. Nat. Standards Inst. C78.376a (1966). The warm white coordinates given are newly proposed and have not yet been officially accepted.
  6. D. Curie, Luminescence in Crystals (Methuen, London, 1963), p. 44; B. DiBartolo, Optical Interactions in Solids (Wiley, New York, 1968), p. 421.
  7. E. Ejder, J. Opt. Soc. Amer. 59, 223 (1969).
    [CrossRef]
  8. K. H. Butler, J. E. Eby, Sylvania Engineering Report E-753 (1966, unpublished).
  9. Committee on Colorimetry of the Optical Society of America, The Science of Color (Optical Society of America, Wash., D.C., 1963).
  10. The indices 1 and 2 refer to the two components.
  11. D. Nickerson, C. W. Jerome, Illum. Eng. 60, 262 (1965).
  12. Kindly given to us by C. W. Jerome.

1969

E. Ejder, J. Opt. Soc. Amer. 59, 223 (1969).
[CrossRef]

1966

Amer. Nat. Standards Inst. C78.376a (1966). The warm white coordinates given are newly proposed and have not yet been officially accepted.

1965

O. J. Sovers, L. J. Bodi, J. Opt. Soc. Amer. 55, 1643 (1965).
[CrossRef]

D. Nickerson, C. W. Jerome, Illum. Eng. 60, 262 (1965).

1963

H. F. Ivey, J. Opt. Soc. Amer. 53, 1185 (1963).
[CrossRef]

1960

J. L. Ouweltjes, Die Farbe 9, 207 (1960).

Bodi, L. J.

O. J. Sovers, L. J. Bodi, J. Opt. Soc. Amer. 55, 1643 (1965).
[CrossRef]

Butler, K. H.

K. H. Butler, J. E. Eby, Sylvania Engineering Report E-753 (1966, unpublished).

Curie, D.

D. Curie, Luminescence in Crystals (Methuen, London, 1963), p. 44; B. DiBartolo, Optical Interactions in Solids (Wiley, New York, 1968), p. 421.

Eby, J. E.

K. H. Butler, J. E. Eby, Sylvania Engineering Report E-753 (1966, unpublished).

Ejder, E.

E. Ejder, J. Opt. Soc. Amer. 59, 223 (1969).
[CrossRef]

Ivey, H. F.

H. F. Ivey, J. Opt. Soc. Amer. 53, 1185 (1963).
[CrossRef]

Jerome, C. W.

D. Nickerson, C. W. Jerome, Illum. Eng. 60, 262 (1965).

Nickerson, D.

D. Nickerson, C. W. Jerome, Illum. Eng. 60, 262 (1965).

Ouweltjes, J. L.

J. L. Ouweltjes, Die Farbe 9, 207 (1960).

Sovers, O. J.

O. J. Sovers, L. J. Bodi, J. Opt. Soc. Amer. 55, 1643 (1965).
[CrossRef]

Amer. Nat. Standards Inst. C78.376a

Amer. Nat. Standards Inst. C78.376a (1966). The warm white coordinates given are newly proposed and have not yet been officially accepted.

Die Farbe

J. L. Ouweltjes, Die Farbe 9, 207 (1960).

Illum. Eng.

D. Nickerson, C. W. Jerome, Illum. Eng. 60, 262 (1965).

J. Opt. Soc. Amer.

H. F. Ivey, J. Opt. Soc. Amer. 53, 1185 (1963).
[CrossRef]

O. J. Sovers, L. J. Bodi, J. Opt. Soc. Amer. 55, 1643 (1965).
[CrossRef]

E. Ejder, J. Opt. Soc. Amer. 59, 223 (1969).
[CrossRef]

Other

K. H. Butler, J. E. Eby, Sylvania Engineering Report E-753 (1966, unpublished).

Committee on Colorimetry of the Optical Society of America, The Science of Color (Optical Society of America, Wash., D.C., 1963).

The indices 1 and 2 refer to the two components.

Private communication.

D. Curie, Luminescence in Crystals (Methuen, London, 1963), p. 44; B. DiBartolo, Optical Interactions in Solids (Wiley, New York, 1968), p. 421.

Kindly given to us by C. W. Jerome.

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Figures (5)

Fig. 1
Fig. 1

Chromaticity diagram for photon-gaussian spectral emission distribution. The solid lines are curves of constant σ, while the dashed lines represent constant peak wavelength (λm). E is the equal energy point.

Fig. 2
Fig. 2

Chromaticity diagram for photon-gaussian distributions including mercury lines. The solid lines are curves of constant σ, while the dashed lines represent constant λm. The chromaticity points of the standard lamps are shown with the following notation: DL, daylight; CW, cool white; W, white; and WW, warm white. HG is the chromaticity point of the mercury lines alone.

Fig. 3
Fig. 3

Maximum brightness of binary blends for fluorescent lamps as a function of the general color-rendering index.

Fig. 4
Fig. 4

Variation of brightness, general color-rendering, and quality indices with λm1 for cool white blends with σ1 = 2.0 and σ2 = 0.5.

Fig. 5
Fig. 5

Dependence of the quality index on σ1 and σ2 for cool white blends with λm1 = 500 nm.

Tables (5)

Tables Icon

Table I Chromaticity Coordinates for Standard Lamps

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Table II Relationship Between σ and the Width of the Photon-Gaussian Distribution on a Wavelength Scale

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Table III Binary Blends with Maximum Brightnessa

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Table IV Brightness and General Color-Rending Index for Average Production Lamps

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Table V Theoretical Lamp Blends with Maximum Quality Index

Equations (16)

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N ν d n / d ν = n σ - 1 ( 2 π ) 1 2 exp [ - ( ν 0 - ν ) 2 / 2 σ 2 ] .
I ν d P / d ν = h c ν N ν .
I λ d P / d λ = ( d P / d ν ) ( d ν / d λ ) = - λ - 2 I ν .
I λ = h c n σ - 1 ( 2 π ) - 1 2 λ - 3 exp [ - ( 1 / λ 0 - 1 / λ ) 2 / 2 σ 2 ] .
h c n = h c n e q = P e λ e q ,
I λ = P e λ e q σ - 1 ( 2 π ) - 1 2 λ - 3 exp [ - ( 1 / λ 0 - 1 / λ ) 2 / 2 σ 2 ] .
1 / λ m = ν 0 / 2 + [ ( ν 0 / 2 ) 2 + 3 σ 2 ] 1 2 .
x = ( m 1 x 1 + m 2 x 2 ) / ( m 1 + m 2 ) , y = ( m 1 y 1 + m 2 y 2 ) / ( m 1 + m 2 ) .
m i = f i Y i / y i ,             i = 1 , 2 ,
f 2 / f 1 = ( Y 1 / Y 2 ) ( y 2 / y 1 ) ( x - x 1 ) / ( x 2 - x ) R .
f 1 + f 2 = 1 ,
f 1 = 1 / ( 1 + R ) , f 2 = R / ( 1 + R ) .
u = 4 x / ( - 2 x + 12 y + 3 ) , v = 6 y / ( - 2 x + 12 y + 3 ) , W = 25 Y 1 3 - 17.
R a = 100 - ( 4.6 / 8 ) i = 1 8 Δ E i , Δ E i = 800 { [ ( u k i - u k ) - ( u 0 i - u 0 ) ] 2 + [ ( v k i - v k ) - ( v 0 i - v 0 ) ] 2 } 1 2 .
R i = 100 - 4.6 Δ E i , Δ E i = { ( W k i - W 0 i ) 2 + 169 [ W k i ( u k i - u k ) - W 0 i ( u 0 i - u 0 ) ] 2 + 169 [ W k i ( v k i - v i ) - W 0 i ( v 0 i - v 0 ) ] 2 } 1 2 .
B . I . = 100 L / L m ,

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