To calculate Y x y and L* a* b* values, the tristimulus values (X Y Z) values must first be calculated from the measured spectrum.
<Basic equation>
where
S(λ) : Energy distribution of standard illuminate
ऱ(λ), ў(λ), ž(λ) : weighting factor
𝞃(λ) : Transmittance
2 degree 10 degree Standard illuminate
In the table above, S(λ) belongs to the standard illuminate item and the values ऱ, ў, and ž are two or ten viewing of angle, and this table is only a fraction of them are excerpted.
For the values of the entire wavelength range, you can find the appendix of KS A 0061 or JIS Z 8781-3 standard method.
<Calculation>
Example] For calculation in condition of D65/10 the X Y Z is
about the calculation for item 385nm are
1) S(λ) ऱ(λ) = 0.0007 x 52.31 = 0.036617
2) S(λ) ў(λ) = 0.0001 x 52.31 = 0.005231
3) S(λ) ž(λ) = 0.0029 x 52.31 = 0.151699
The transmittance value of the measured spectrum is 83.78% at 385 nm.
1) S(λ) ऱ(λ) 𝞃(λ) = 0.036617 x 0.8378 = 0.030679
2) S(λ) ў(λ) 𝞃(λ) = 0.005231 x 0.8378 = 0.004383
3) S(λ) ž(λ) 𝞃(λ) = 0.151699 x 0.8378 = 0.127097
The sum of y^(λ) value, denominator value, in the table above is 2324.14, So, k = 100 / 2324.14 = 0.043027
Therefore, the X Y Z and the color coordinates x and y can be calculated by the following equation.
X = 1947.202 x 0.043027 = 83.7816
Y = 2072.514 x 0.043027 = 89.1734
Z = 2211.909 x 0.043027 = 95.1715
Y = 89.17
x = X / (X + Y + Z) = 83.7816 / 268.1266 = 0.3125
y = Y / (X + Y + Z) = 89.1734 / 268.1266 = 0.3326
Comparison of Y, x, y results between calculated value with EXCEL and by using calculation Program
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