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).

290 75 j 50 rn 25 rn ..§ 0 � -25 0 � -50 -75 0 JOURNAL OF COSMETIC SCIENCE o;. ms =24nm /J0 = 0.49 0.5 1 1.5 2 Horizontal Distance [µm] Figure 8. Vertical size and volume fraction estimations of the fine structure (o-rms: root mean square roughness, p0 and p 1 : volume fraction of air and substrate in o-rms). To explain the light introduction phenomenon for the test system, simulation study on light reflection (Matrix method, 14) was conducted. In the case of homogeneous top surface of a typical organic material (n 1 = 1.45) on hair cuticle (n2 = 1. 5 5 ), remarkable light introduction doesn't occur even though the thickness is less than light wavelength (d 100 nm, Monolayer in Figure 10). However, the change of refractive index to the order of 1.2 is expected to occur more light introduction (d 100 nm, Monolayer/EMA, Figure 10). Satisfiable consistency was obtained between the experimental result (Figure 4) and the simulation result (d = 50 nm, EMA in Figure 10). The light introduction 1 0.75 =170nm 0.25 200 400 600 800 r [nm] Figure 9. Lateral size estimation of the fine structure (� correlation length, C(r): correlation function, r: horizontal distance between random two points).