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References

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  1. Parry Moon, J. Opt. Soc. Am. 31, 317 (1941); J. Opt. Soc. Am. 31, 482 (1941); J. Opt. Soc. Am. 31, 723 (1941); J. Opt. Soc. Am. 32, 238 (1942); J. Opt. Soc. Am. 32, 293 (1942).
    [Crossref]
  2. Parry Moon and D. E. Spencer, J. Opt. Soc. Am. 35, 399 (1945); “Analytic Expressions in Photometry and Colorimetry,” to appear in J. Math. Phys. Mimeographed copies of the extended tables are available gratis as long as the supply lasts.
    [Crossref]

1945 (1)

1941 (1)

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Figures (5)

Fig. 1
Fig. 1

Six types of reflectance curves.

Fig. 2
Fig. 2

Celotex acoustical tile, natural color. —— experimental curve, – – – analytic approximation, Eq. (1).

Fig. 3
Fig. 3

Masonite wall board. —— experimental curve, – – – analytic approximation, Eq. (2), m=6.

Fig. 4
Fig. 4

White samples. No. 420, flat-tone white paint; No. 426, semi-luster white paint; No. 49, acoustical tile painted white. The numbers correspond to those in Reference 1.

Fig. 5
Fig. 5

Blue paint (Sample No. 461). —— experimental curve, 0 calculated points using 7-term polynomial.

Tables (5)

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Table I Factors for 7-term polynomial representation.

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Table II-A Coefficients for analytic representation by power functions, illuminant A′ (T=2842°K).

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Table II-B Coefficients for analytic representation by power functions, illuminant B′ (T=7000°K).

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Table III Direct integration method. Values of Fk, to be used in Eq. (10).

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Table IV Example of direct computation of X, Y, Z, No. 151 green ceramic tile, Planckian radiation (T=2842°K).

Equations (14)

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ρ ( λ ) = A + B λ ,
ρ ( λ ) = A + B λ m .
ρ ( λ ) = A - B λ - m .
ρ ( λ ) = K 0 + K 1 λ + K 2 λ 2 + + K 6 λ 6 .
ρ ( λ ) / ρ 0 = 0.0388 + 1.466 λ 6 .
K m = k = 0 6 C m k ρ ( λ k ) ,
X = 0 ρ ( λ ) x ¯ ( λ ) J ( λ ) d λ , Y = 0 ρ ( λ ) y ¯ ( λ ) J ( λ ) d λ , Z = 0 ρ ( λ ) z ¯ ( λ ) J ( λ ) d λ ,
L = 0 ρ ( λ ) w ( λ ) J ( λ ) d λ = A C 1 K m Γ ( p + 4 - m ) ( q + n C 2 / T ) p + 4 - m ,
ρ ( λ ) = K m λ m ,             J ( λ ) = C 1 λ 5 exp ( - n C 2 / λ T ) ,
w ( λ ) = A exp ( - p / λ ) / λ q .
L = A C 1 m = 0 k - 1 n = 1 K m Γ ( p + 4 - m ) ( q + n C 2 / T ) p + 4 - m .
K 0 = A = - 0.295 , K 1 = B = 1.350 ;
X = 97871 ( - 0.295 ) + 58214 ( 1.350 ) = 49717 , Y = 89030 ( - 0.295 ) + 50837 ( 1.350 ) = 42367 , Z = 31808 ( - 0.295 ) + 14680 ( 1.350 ) = 10434.
L = k = 0 6 ρ ( λ k ) F k ,