84 JOURNAL OF COSMETIC SCIENCE DERIVING A MEASURE FOR HAIR LUSTER MEASUREMENT AND ANALYSIS OF LIGHT REFLECTANCE FROM HUMAN HAIR The measurement of light reflectance from single human hairs, as described in detail in Part 1 of this paper (1), is based on the determination of the angle-dependent intensity of the light from a green laser (A- = 532 nm) scattered from a single fiber. The wave length was chosen such as to be in that range where the daylight sensitivity of the human eye is at its maximum. The basis for the investigation was three types of hair, namely black Asian and brown and blonde Caucasian hair (see Figure 1). Each sample was taken from the head of a female volunteer and exceeded in all cases 20 cm in length. The hairs were shampooed (LES 15%, pH 5.5), rinsed, dried, and stored under ambient conditions until measure­ ment. The experimental setup (1) is such that the vertically polarized laser beam (approx. 50 µW) meets the hair fiber, arranged horizontally under slight tension and in ambient, though stable, room conditions (approx. 22°C, 50% RH), at an incident angle of 40° (beam spot diameter 100 µm). The detection of the reflected light is conducted within about 100 ms in the horizontal plane containing the fiber and the incident light beam through a range of 6.5° to 173.5° with an Optical Multi-Channel Analyzer. The solid line in Figure 2 shows the so-called goniophotometric (GP) curve, derived by smoothing the angular light intensity data for the most general case, namely light 0,4 § 0,3 .c .!!!. 0 2 � ::= tn C S 0,1 C - * . .. . -!• ... - . .. . . . .. 'I .. - ... I ... ..., , ... ,.. ... ' , , :vi' 40 50 60 O,OL--------=--�•• ----�Jt..-.---- 0 10 20 30 Receptor Angle [°] ... ' ... 70 80 90 Figure 2. GP curve data(--) for a light blonde hair measured at a position near the tip end. Gaussian distributions for specularly (■■■■), diffusely (---), and internally (--) reflected light, as fitted to the GP curve (see Figure 7 in ref. 1).

MEASURE OF HAIR LUSTER 85 blonde, Caucasian hair measured at a pos1t10n near the tip end. In this context it is important to note that the surface of hair is not smooth but features cuticle cells in a tile-like arrangement, where the cell scale edges point towards the fiber tip. To ensure a consistent bias of light reflection due to the cuticle inclination angle (1), all measure­ ments were carried out with the direction of the incident light toward the tip end of the hair. In view of the surface and overall morphological structure of human hair, the reflection of light is subject to a special type of geometry that in turn and with the principles of geometrical optics leads one to expect three principal components of light reflection. These are represented by the three Gaussian distributions fitted to the GP curve in Figure 2. Details of the fitting procedure and the parameters derived thereof are given in Part 1 (1). When the incident beam hits the fiber surface in the root-to-tip (RT) direction at the incident angle E 1 (1), a first fraction of the light, S, is specularly reflected at the receptor angle 'Ys· For the experimental setup, using the incident angle E 1 = 40° and assuming a tilt angle for the cuticle of 2. 5 ° leads to an expectation value for the receptor angle of the specularly reflected light of 'Ys = 35°. At this position, Figure 2 shows the peak describing the intensity distribution of specularly reflected light with a width at half­ height of 9°-10°. A second fraction of light, D5, is diffusely scattered at and near the fiber surface, namely at surface roughnesses (18), at the various interfaces between the cuticle cell layers of human hair (19), at the interface of cuticle and cortex, and at optical imperfections of the cortex, such as voids and inclusions. Figure 2 shows between 40° and 45° the broad Gaussian distribution for diffuse reflec­ tion. It is important to note from Figure 2 that the hair surface cannot be considered as being primarily an ideal, diffuse reflector for which scattering occurs such that the intensity of the diffusely reflected light is uniform. Though on the basis of Reich and Robbins' analysis (11) of GP curves, the existence of a uniform contribution for 0 5 is assumed, its magnitude is obviously small compared to the non-uniform effect and covered by the broad Gaussian distribution for diffuse reflection. A further part of the incident beam is refracted into the fiber according to Snell's or Descartes' law. Inside the hair the light is scattered at voids and inclusions, is partly absorbed by hair pigment and color, and is thus wavelength filtered, depending on the color and its intensity. Diffuse reflection takes place at structural inhomogeneities within the cortex. For lightly colored hair, light may be diffusely reflected at or in the medulla (4,20), a more or less continuous and hollow, tube-like structure in the fiber interior. In very blonde or white hair a significant amount of light may be reflected at the backside of the fiber, that is, from the hair/air surface interface opposite the point of incidence. When this third component of light re-emerges from the fiber, it is experi­ mentally observed, as shown in Figure 2, as a separate peak in the GP curve (5,15,17) at angles around 64 ° with a width of 25° (1). This type of light is considered as a specific fraction of diffusely reflected light, termed D i , since it is related to the internal reflection effect.