288 2 OJ 1 0 � -1 -2 u -3 -4 \ 0 JOURNAL OF COSMETIC SCIENCE Test system 3 6 Cycles T 9 12 Figure 5. Chroma change of red dyed human head in the shampoo and conditioner treatment cycles. DISCUSSION Experimental results showed that the fine asperity on hair fiber surface is related to light introduction and chroma enhancing phenomena. In general, asperities on surface induce diffuse reflection of light. However, if asperities are finer enough than incident light wavelength, diffuse reflection diminishes and light introduction into inside materials develops, and of the most popular example is uneven structure on the surface of moth's eyes. The surface has an asperity of 200nm in height and 300nm in lateral space which allows night view and wide eyesight (Moth-eye structure, 7-9) The structures have been applied to industry such as optical devices, anti-reflection film and so on (10-14). Light introduction phenomena induced by fine structures can be explained by the effective medium approximation (EMA, 15-1 7). EMA is an approximation theory to approximate a refractive index of the surface with a finer structure than an incident light wavelength by a mean value based on volume fractions of air and substrate of the structure (Mono- layer model/EMA, Figure 7). For example, if a fine structure is composed of paraffin (n t = 1.43) and air (n0 = 1.00) and the volume ratio is 1:1, the mean refractive index of the layer is approximated to be 1.22. There is no such a low refractive index material with flat surface in cosmetically available materials, so it can be said that a super fine structure realizes super-low refractive index surface. Lower refractive index surface leads to more light introduction from Snell's law. Furthermore, advanced models by EMA treat a structure with a volume fraction gradient along depth direction like a saw-edged struc- ture to be a longer with a gradual change in the density, i.e. the refractive index density (Multilayer model/EMA, Figure 7). Sizes to characterize the fine structure obtained by

2006 TRI/PRINCETON CONFERENCE 289 Test system Control system (Cycle 12) Figure 6. Ami-fading effect of test system for dyed hair. the test system were estimated at vertically 50nm in peak height or 25nm in roughness, (Figure 8) and laterally 170 nm in correlation length between random by chosen two points (Figure 9). The volume ratio of air and the substrate in the structure was estimated to be about 1: 1. These estimations indicate a possibility of the super low refractive index as 1.2 for the surface on hair fiber. Uneven structure d light ::mw1d ¢ h ¢1 Po + ¢1 = 1 Optically Homogeneous layer □ Mean refractive index □ Pono + ¢1n1 Monolayer/EMA model Gradual density layer Depth: Q_,d Refractive index: n 0 _,n 1 l d Multilayer/EMA model Figure 7. Effective medium approximation. n: refractive index, I: volume fraction (subscript 0: air, 1: substrate).