# A Novel Fluorescent-Material-Based Simple Method for Sunscreen Evaluation
## 6 Conclusions  
In this study, a measurement system for the hemispherical transmittance of materials that scatter and absorb UV radiation, such as sunscreens, was proposed. Conventionally, an integrating sphere was used to measure hemispherical transmittance. Here, we proposed a fluorescent material instead of the integrating sphere for conducting hemispherical transmittance measurements and demonstrated the application of the method in the evaluation of sunscreens. The feasibility of the proposed system was verified both numerically and experimentally to evaluate the amount of fluorescence generated by the excitation radiation directly incident on the fluorescent material. Because the excitation radiation passing through the scattering and absorbing material enters the fluorescent material in various directions, for the method to be effective, the thickness index of the fluorescent layer must be increased to 6.0 or more. The thickness index of the fluorescent layer can be increased by increasing its concentration and/or actual thickness. The following supporting information can be downloaded from [[https://www.mdpi.com/article/10.3390/app122211521/s1](https://www.mdpi.com/article/10.3390/app122211521/s1)]([https://www.mdpi.com/article/10.3390/app122211521/s1](https://www.mdpi.com/article/10.3390/app122211521/s1)), Figure S1: (a) Absorption spectrum of the UV-G fluorescent material obtained using a spectrophotometer. UV-G was dispersed in water at 0.2 wt% and measured through a 10 mm size quartz cell. V-630 BIO (JASCO Corporation, Tokyo, Japan) was used for the measurement. (b) Emission spectrum of the fluorescent material UV-G at an excitation radiation of 375 nm obtained by absolute PL quantum yield measurement; measured using a C9920-02 (Hamamatsu Photonics, Shizuoka, Japan) with air as the reference signal. Figure S2: Graphical description of Equations (7) and (8). Radiation scattering, absorption, and fluorescence emission of the fluorescent layer. These equations and figures illustrate the conservation of radiative energy for a small volume in a medium. Conceptualization, writing--original draft preparation, K.N. ; validation, T.K. ; writing--review and editing, U.M.R. ; supervision and funding acquisition, J.Y. All authors have read and agreed to the published version of the manuscript. Figure 8: Evaluation of the performance of commercial sunscreens; light blue areas indicate the mean amounts of three times measured by the proposed method, the error bars are the standard deviation, and the purple plots indicate the transmittance at 375 nm of each sunscreen obtained by the classical method. **Funding:** This research was funded by Grants-in-Aid from the Japan Society for the Promotion of Science and Japan Science (grant number:22360090). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature** \begin{tabular}{l l} \(q\) & radiative flux, W\(\cdot\)m\({}^{-2}\) \\ \(I\) & radiative intensity, W\(\cdot\)m\({}^{-2}\)\(\cdot\)sr\({}^{-1}\) \\ \(E\) & radiation energy, W \\ \(\Phi\) & scattering phase function \\ \(\Omega\) & solid angle, sr \\ \(\theta\) & polar angle, degrees \\ \(\varphi\) & azimuthal angle, degrees \\ \(n\) & refractive index \\ \(\tau\) & coordinate along the direction of the distance and thickness indices of the fluorescent layer \\ \(\omega\) & albedo \\ \(\beta\) & extinction coefficient, mm\({}^{-1}\) \\ \(\sigma\) & scattering coefficient, mm\({}^{-1}\) \\ \(\alpha\) & absorbing coefficient, mm\({}^{-1}\) \\ \(x\) & actual distance, mm \\ \(Q\) & fluorescent yield \\ \(R\) & hemispherical reflectance \\ \(T\) & hemispherical transmittance \\ Subscripts \\ \(s\) & scattering/absorbing sample \\ \(e\) & excitation light \\ \(f\) & fluorescent \\ \(t\) & transmitted \\ \(in\) & incident \\ \end{tabular}   
* [PERSON] et al.