308 JOURNAL OF COSMETIC SCIENCE 0,015 •' 0,010 . - • 0,005 • •.. - __••••,• 0,000 , 0 10 20 30 40 50 60 70 80 90 Receptor Angle [ø] Figure 6. GP curve data (--) for a medium brown hair measured at a position of about 30 cm from the root. Distributions for specularly ( .... ) and diffusely (---) reflected light, as fitted to the GP curve. 0 10 20 30 40 50 60 70 80 90 Receptor Angle [ø] Figure 7. GP curve data (--) for a light blonde hair measured at a position near the tip end. Distributions for specularly ( .... ), diffusely (---), and internally (---) reflected light, as fitted to the GP curve. 0,45 0,40 0,35 0,30 0,25 0,20 0,15 0,10 0,05 0,00 reflected light, respectively, are determined by simultaneously fitting to the GP curve up to three Gaussian distributions, each of which is given by: I = A/[(2'rr)1/20'] exp{-1/2 [(y - p)/cr] 2} (7) where I is the intensity count of a given type of reflected light at a given angle % cr is the standard deviation of the Gaussian distribution, describing its width, and p its mean, signifying the position of the peak maximum. A is a scaling parameter related to the area of the peak. The Gaussian peaks are fitted to the GP curves, applying nonlinear optimization strat- egies implemented in QuattroPro (Corel) and PeakFit (Jandel). The distributions are shown in Figures 5-7. The correlation coefficient, being the appropriate measure for the fraction of explained variance for the individual fits, always well exceeded 0.9. The distributions are descriptions of the horizontal indicatrices (9) for the different fractions of light, reflected from a single hair. The choice of the Gaussian distribution

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.