# A Novel Fluorescent-Material-Based Simple Method for Sunscreen Evaluation
## 2 Concept of Proposed Measurement Method  
Generally, hemispherical transmittance is used as an indicator of radiation [24]. \[T=q_{t}/q_{in} \tag{1}\]  
where \(q_{in}\) and \(q_{t}\) are the incident and transmitted flux, respectively. In a conventional measurement system, as shown in Figure 1, to obtain the incident radiation flux, the incident radiation is first made to enter directly into the integrating sphere, and then a portion of the emitted radiation is measured. Next, to obtain the transmitted flux through the sunscreen sample, the incident radiation through the sample is made to enter the integrating sphere, and a portion of the emitted radiation is measured in the same manner that the incident flux was obtained. Because the measured values obtained by the photodetector are proportional to the amount of radiative energy detected, \(E_{(A\to S)}\), they are expressed by Equation (2)using the radiative intensity \(I(\theta,\,\varphi)\) emitted from the integrating sphere. Here, \(A\) and \(S\) represent the apertures of the integrating sphere and photodetector, respectively. \[E_{(A\to S)}=I(\theta,\varphi)\cos\theta\frac{\Delta S}{L^{2}}\Delta A \tag{2}\]  
where \(\Delta\Omega\) is the area of the integrating sphere aperture, \(\Delta S\) is the area of the photodetector, \(L\) is the distance between the integrating sphere aperture and photodetector, and \(\theta\) and \(\varphi\) are the polar angle and azimuthal angle from the integrating sphere aperture to the photodetector, respectively. In most integrating-sphere measurement systems, although a photodetector is installed directly at the aperture of the integrating sphere (Figure 1), the integrating-sphere aperture and photodetector are shown separately to correspond to the system proposed in this study. Generally, \(\theta,\,\varphi,\,\Delta S,\,L,\) and \(\Delta A\) are constants in the experimental apparatus because the positional relationship between the aperture of the integrating sphere and detector is fixed. Therefore, the measured value obtained by the detector is proportional to the radiative intensity \(I\). Because the radiation is not directional, the relationship between the emitted flux from the integrating sphere \(q\) and intensity \(I\) is given by Equation (3). \[ \begin{array}{ll}q&=\int_{2\pi}\int_{\pi/2}I\cos\theta\cdot\sin\theta d \theta d\varphi\\ &=\pi\ I\end{array}  \tag{3}\]  
If the radiation escaping from the aperture is negligible, the amounts of radiation entering the integrating sphere and being emitted are equal. Therefore, in a measurement system using an integrating sphere, the hemispherical transmittance \(T\) can be obtained using Equation (4):  
\[T=E_{t}/E_{in} \tag{4}\]  
where \(E_{in}\) is the measured value of the radiation passing through the integrating sphere without a sample and \(E_{t}\) is the measured value of the radiation through the sample and integrating sphere. Because the measured values are proportional to the amount of detected radiation energy, they are represented by the symbol \(E\). Thus, to measure the hemispherical transmission, the radiation has to diffuse in order to be detected by the photodetector and thus would require a diffuser. This study proposes a layer that includes a fluorescent material placed behind the sample, as shown in Figure 2. The radiation transmitted through the sample penetrated the fluorescent layer, which in turn emitted fluorescence. The emitted fluorescent radiation is proportional to the excitation radiation incident on the material and is always isotropic. Therefore, having a fiber to detect the emitted fluorescence would make it possible to measure the hemispherical transmittance from Equations (1) to (4). Figure 1: Schematic diagram of transmitted radiation measurement from a diffuser surface using integrating sphere.