ð l < 400 nm
I uv - full ð l Þ f ð l ; k Þ d l I uv - full k ð Þ I uv - full ð l Þ f ð l ; k Þ d l I in k ð Þ ; I GG395 ð l Þ f ð l ; k Þ d l I GG395 k ð Þ I GG395 ð l Þ f ð l ; k Þ d l I in k ð Þ :
R L ; uv - full k ð Þ 5
(5)
ð l < 400 nm
5
and
ð l < 400 nm
R L ; GG395 k ð Þ 5
(6)
ð l < 400 nm
5
UV radiations, and the second term for the light flux that passes through the GG395 filter. The quantity, a , takes different values when adjusted to illuminations of differ- ent UV contents. In a modern spectrophotometer, the UV filter is motor-driven, and the quantity, a , is defined by the motor position. To elucidate the principle behind the UV-adjustment technique, we demonstrate how the expression for the total spectral radiance factors of a luminance specimen is derived, before going into details on how to determine the parameter, a , from the assigned values. When the luminance specimen is illuminated by a light source that contains UV, the radiance of the specimen consists of two portions. One of the portions comes from the ordinary light reflection and another from fluorescent emission. When only the visible spectrum is considered, that is, k > 400 nm, the total spectral radiance of the specimen can be expressed as follows 23 : I ð k Þ 5 I in ð k Þ R S ð k Þ 1 I in ð k Þ R L ð k Þ ; (2) where Fig. 3. Illustration of the conventional UV-filtering tech- nique with one moveable UV filter (in yellow). The UV con- tent of the illumination is adjusted by changing the portion (area) of the UV filter.
Here, we have assumed that the GG395 filter only removes UV light of wavelengths shorter than 400 nm and is ideally transparent above 400 nm. Hence, I in ð k Þ 5 I uv - full ð k Þ 5 I GG395 ð k Þ : (7) Then, the total spectral radiance factor is given as follows:
I ð k Þ I in ð k Þ
R ð k Þ 5
5 ð 1 2 a Þ R uv - full ð k Þ 1 a R GG395 ð k Þ ;
(8)
where
R uv - full ð k Þ 5 R S ð k Þ 1 R L ; uv - full ð k Þ ; R GG395 ð k Þ 5 R S ð k Þ 1 R L ; GG395 ð k Þ :
(9)
Equation (8) indicates that the total spectral radiance factor, R ( k ), is a superposition of the total spectral radi- ance factors measured under the UV-full and the UV- reduced illumination condition filtered by the GG395 fil- ter. This equation is the corner stone of the UV-filtering techniques. For a spectrophotometer using an adjustable filter, one should bear in mind that all the factors, a and (1 2 a ) in Eq. (8), are neither negative nor greater than unity, as they represent the area percentages. Hence, the quantity, a , in Eqs. (1) and (8) subjects to the following constraint: 0 a 1 : (10) This is an important difference when compared with an instrument using numerical UV-filtering technique, as described below. The total spectral radiance factors of the luminescent sample, when measured with the CM3630d, are actually the superposition of two separate measurements: R ð k Þ 5 b R uv - full ð k Þ 1 ð 1 2 b Þ R GG395 ð k Þ ; (11) where the R uv-full and R GG395 are the total spectral radi- ance factors of the luminescent sample when illuminated by the lamp without any UV filter coverage and the lamp fully covered by the GG395 filter, respectively. Equation (11) shares exactly the same mathematical form as Eq. (8). Nevertheless, the quantity b in Eq. (11) has no
ð l < 400nm
I in ð l Þ f ð l ; k Þ d l I in k ð Þ
R L k ð Þ 5
(3)
is the luminance radiance factor with the quantity, f ( l , k ), corresponding to the quantum efficiency of the fluorescent whitening agents (FWAs) that convert UV light into visible. The quantity, R S ( k ), is the spectral reflective radiance factor. By inserting Eq. (1) into Eqs. (2) and (3), one obtains the following equation: I ð k Þ 5 ð 1 2 a Þ I uv - full ð k Þ R S ð k Þ 1 R L ; uv - full ð k Þ
1 a I GG395 ð k Þ R S ð k Þ 1 R L ; GG395 ð k Þ 5 I in ð k Þ½ð 1 2 a Þ R S ð k Þ 1 R L ; uv - full ð k Þ 1 a R S ð k Þ 1 R L ; GG395 ð k Þ ;
(4)
where
22
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