longer any physical meaning as it does in Eq. (8) in the case of the conventional UV-filtering technique. Rather, it only quantifies the relative portions of the contributing spectral components. Hence, this quantity b in Eq. (11) does not have to satisfy the physical constraint expressed in Eq. (10), and it may take any values, even negative or greater than unity. Yet, for the sake of convenience, we do not distinguish b from a or we simply redefine b 5 a .
UV Content Adjustment for a C Illuminant
The UV content adjustment method for a C illuminant is specified in the ISO standard, ISO 2470-1:2009. It relies on a single assigned value, ISO brightness, to define the quantity, a , that is, the portion of light passing through the GG395 UV filter. The task of UV adjustment is then to determine the quantity, a , by matching the measured value of the IR2 to the assigned ISO brightness value. Once this quantity is set, one can use it to simulate a physical measurement of any fluorescent sample, using Eq. (8) or (11). Here, we explain how the UV adjustment is achieved in a practical sense. For convenience of the explanation without losing generality, we use the apparatus having an adjustable filter as an example. Assume that the area por- tion of the GG395 filter is a . From the expression for the spectral radiance factor given in Eq. (8), one can easily obtain the expression for ISO brightness as follows: B 5 a B GG395 1 1 2 a ð Þ B uv - full ; (12) where B uv - full 5 Ð b ð k Þ R uv - full ð k Þ d k and B GG395 5 Ð b ð k Þ R GG395 ð k Þ d k and b ( k ) is the brightness weighting function. With the assigned ISO brightness, B Ass , of the IR2 fluorescent paper pad, one can obtain the following equation:
Fig. 4. The total spectral radiance factors measured with two spectrophotometers: CM3630d (dotted lines) and CT2 (solid lines). UV-full: no UV filter is engaged; UV-reduced: full engagement of the GG395 filter; and UVX: full engage- ment of the cutoff filter (420 nm).
X 5 k ð S ð k Þ R ð k Þ x ð k Þ d k 5 ð 1 2 a Þ X uv - full 1 a X GG395 Y 5 k ð S ð k Þ R ð k Þ y ð k Þ d k 5 ð 1 2 a Þ Y uv - full 1 a Y GG395 Z 5 k ð S ð k Þ R ð k Þ z ð k Þ d k 5 ð 1 2 a Þ Z uv - full 1 a Z GG395 ;
(15)
where T uv - full 5 k Ð S ð k Þ R uv - full ð k Þ t ð k Þ d k and T GG395 5 k Ð S ð k Þ R GG395 ð k Þ t ð k Þ d k with T 5 X , Y , Z and t 5 x ; y ; z . The chromaticity coordinates of the fluorescent sample are given as follows:
X uv - full 2 a X uv - full 2 X GG395 ½
X X 1 Y 1 Z
x 5
5
T uv - full 2 a X T 5 X ; Y ; Z
X T 5 X ; Y ; Z
T uv - full 2 T GG395 ½
:
B uv - full 2 B Ass B uv - full 2 B GG395 :
Y uv - full 2 a Y uv - full 2 Y GG395 ½
Y X 1 Y 1 Z
a 5
(13)
5
y 5
T uv - full 2 a X T 5 X ; Y ; Z
X T 5 X ; Y ; Z
T uv - full 2 T GG395 ½
In the case of motor-driven GG395 filter as is the case of CT2 apparatus, the quantity a corresponds to the motor position at which the reading matches the assigned value.
(16) With the assigned CIE whiteness, W Ass , for the fluores- cent IR2s, one can rewrite Eq. (14) as follows: W Ass 2 800 x n 2 1700 y n 5 Y 2 800 x 2 1700 y : (17) Obviously, Eq. (17) is a quadratic equation of the unknown quantity, a , which is analytically solvable.
UV Content Adjustment of the CIE D-Type Illuminants
The UV-adjustment methods for the D types of illumi- nants, D 65 and D 50 , are specified in the ISO standards. Their UV content adjustments rely on single assigned val- ues, CIE whiteness (D 65 /10 8 ), 5,16 and CIE whiteness (D 50 / 2 8 ), 17 respectively. According to the definitions, the CIE whiteness values are given as follows: W 5 Y 1 800 x n 2 x ð Þ 1 1700 y n 2 y ð Þ ; (14) where x n and y n are the chromaticity coordinates of the standard illuminants. From Eq. (8) or (11), one receives the expressions for the CIE–XYZ color coordinates of a fluorescent sample as follows:
RESULTS AND DISCUSSIONS
Figure 4 shows the total spectral radiance factors of the fluorescent IR2s, measured with two spectrophotometers, CT2 (solid lines) and CM3630d (dotted lines). The illu- minations used in the measurements are of different UV contents, UV-full, UV-reduced with the full engagement of GG395, and UVX (UV-excluded) with the UV cutoff filter (420 nm). When directly illuminated by the bare
Volume 42, Number 1, February 2017
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