LIGHT REFLECTION FROM HAIR 309 is an adequate, practical approach for the specular component, in view of the consider- ations by Guiolet et al. (4) and Rennie et al. (14). In analogy to the approaches by Reich and Robbins (6) and Bustard and Smith (1) wd, and w i are introduced as parameters describing the width at half height of the Gaussian distributions for specularly, diffusely, and internally reflected light, respec- tively. The width at half height for a Gaussian peak is given by its standard deviation according to: w -- 2tr[2 ln(2)] •/2 (8) Table I summarizes the locations (mean receptor angle) and widths of the Gaussian peaks for S and D s for black Asian and brown and blonde Caucasian hair, respectively, and at five locations along their length. These were chosen such as to cover the individual lengths of the hair types. Cuticle scale angles were deduced from the location of the angular position of specularly reflected light, that is, from •/• according to equation 1. RESULTS AND DISCUSSION By fitting Gaussian distributions to the GP curves, the locations and widths of the three types of reflected light were determined. From the location of the specular peak, fur- Table I Parameters for Specularly and Diffusely Reflected Light Derived From the GP Curves for Various Hair Types Specular reflection Diffuse reflection Position Cuticle angle Hair type (cm) N % (o) Ws (o) (o) • (o) w• (o) Black Group mean _+ q Brown Group mean _+ q Blonde Group mean + q Grand mean _+ q 1 12 35.7 10.3 2.13 43.3 43.7 5 3 36.1 9.81 1.93 44.7 42.1 10 7 34.2 10.7 2.91 35.2 52.7 15 3 35.1 10.5 2.44 38.9 49.2 20 7 34.0 10.1 3.01 37.1 48.9 35.0 -+ 0.80 10.3 +_ 0.62 2.50 _+ 0.40 39.9 +- 2.09 47.2 _+ 2.66 1 11 35.5 9.18 2.48 43.4 44.8 10 9 38.1 9.70 1.27 47.0 48.7 20 7 37.0 8.21 1.48 44.5 52.4 25 4 34.5 10.2 2.76 44.0 53.6 30 10 35.8 9.76 2.36 45.7 53.6 36.3-+0.81 9.35 +-0.51 2.06+0.39 45.1_+ 1.37 50.0+_2.28 1 9 35.9 9.56 2.04 45.9 45.1 5 9 36.4 9.32 1.79 45.3 45.5 10 8 36.6 9.22 1.70 46.7 49.6 15 9 37.2 8.40 1.40 45.5 46.1 20 10 36.9 8.87 1.53 47.2 46.0 36.6 +_ 0.47 9.07 -+ 0.66 1.70 + 0.24 45.9 _+ 0.96 46.4 _+ 1.49 36.0 +_ 0.40 9.50 -+ 0.35 2.05 +_ 0.20 44.0 _+ 0.92 47.9 -+ 1.20 A number of hairs (N) were measured at various positions relative to the root. For some of the variables, a small number of obviously outlying data was removed (see text). Group and grand mean values are given with their 95% confidence range, q.

310 JOURNAL OF COSMETIC SCIENCE thermore, the tilt angle of the cuticle scales with respect to the fiber axis (cuticle angle) was derived. By far, most GP curves could well be analyzed by the two-component approach, with a narrow peak attributed to specular and a broad peak to diffuse reflection, respectively. Only for the very blonde hair, Di, as a further component of diffuse reflection, had to be considered. All data were checked for outliers, prior to further analysis, by assessing them in so-called normal probability plots as implemented in the applied statistics software (15). In this type of plot, cumulative data frequencies follow a straight line, when the data are normally distributed. A small number of obvious outliers was readily identified ( 10%) in these plots and was removed prior to further analysis of the parameter values. For the cuticle angle, a small number of data ( 10%) with negative values were removed on the basis of physical implausibility. The data given in Table I represent the accepted data and are arithmetic means for measurements taken at a given position on a number of hairs (N) of the same type. For a given hair type, the data are summarized in group means. For a given parameter, data are further summarized over all hair types in the form of grand means. Effects of measurement position and hair type on the parameters were assessed for significance by analysis of variance (ANOVA) and linear regression (LR). In those cases where ANOVA indicated inhomogeneity, multiple comparison of means analysis was conducted, applying the nonconservative LSD test (15). The statistical significance of effects (ANOVA: inhomogeneity of data LSD: differences between data groups LR: slope of regression line) is characterized throughout by the or-value (16), which is the probability of committing a so-called type I-error, namely, by finding an effect that in fact does not exist. In cases where ot 0.05, effects are significant at the usual 95% level and beyond. SPECULAR REFLECTION AND CUTICLE ANGLE With an angle of incidence of 40 ø on the hair for light traveling in the root-to-tip direction, the data in Table I show that the angular position of specularly reflected light is, as expected from the surface structure of human hair (see Figures 3 and 4), system- atically shifted to 36 ø (grand mean). From the results for the receptor angle given by the angular position of the peak for the specular component %., cuticle angles were derived according to equation 1 and are summarized in Table I. There are some apparent changes of cuticle angles along the hair length, namely, a slight increase towards the tip for black hair (LR: ot = 0.07), no change for brown hair (LR: ot = 0.85), and a slight decrease for blonde hair (LR: tx = 0.09). Though none of this is really pronounced, such as being statistically significant at the 95% level, the results are considered to reflect the two counteracting effects of hair grooming, namely, cuticle lifting on the one hand and polishing through abrasion on the other (10,17-19), de- pending on hair diameter, cross-sectional shape, and length. The results for the three hair types are summarized in Figure 8 in the form of a box-and- whisker plot. Analysis of variance shows that the data are inhomogeneous well beyond the 95% level (or = 0.005), where the LSD test identifies the ot levels for the differences,