An improved random walk scattering model that can be used for soft scattering based on the dispersion of the refractive index difference was developed. This model improves on previous models by introducing a medium thickness parameter and can explain the spectral performance of transparent/diffusive materials with different scatterer concentrations and thicknesses, as well as determine the optimal narrowing conditions for the bandpass spectra by combining Rayleigh-Gans-Debye and Hulst approximation calculations. Guided by the theory, transparent/diffusive media based on CaF2 particles suspended in a PDMS (polydimethylsiloxane) matrix were investigated. Disordered micron-sized CaF2 particles with a narrowed particle distribution were obtained by precipitation and centrifugal separation of ultra-pure milled CaF2 particles to remove the fractions smaller than 1 µm and larger than 20 µm, with removal rates of approximately 75% and 100%, respectively. Consequently, a diffuser material with a high (80 wt.%) concentration CaF2 particles dispersed in a low-viscosity PDMS matrix was successfully fabricated, which exhibited an effective transmittance bandwidth as low as 12 nm FWHM (full width at half maximum). Moreover, different bandpass filter diffuser devices with transmission peaks at 248, 257, and 272 nm were obtained by adjusting the PDMS matrix material. In particular, the 257 nm transmission peak filter diffuser exhibited a true narrow bandwidth of 9 nm in an integrated module containing a UV LED (ultraviolet light-emitting diode).
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