JOURNAL OF COSMETIC SCIENCE 382 given direction in the image. In the case of hair, if fi bers are predominantly oriented in one direction, the spatial intensities in the perpendicular direction will be high. As an example of fi ber straightening, Figure 2 contains images of African hair in its native state (A) and at increasing levels of relaxer treatment (B and C). Visual observation clearly reveals the change in fi ber curvature when comparing untreated hair with partially (B) and fully (C) relaxed hair. The corresponding two-dimensional Fourier transform images are shown adjacent to the original images of hair and provide us with a measure of fi ber alignment. In the case of untreated African hair, there is no directionality apparent in the transformed image. The Fourier transform distribution is omnidirectional. However, when we examine the partially relaxed hair sample, a more narrow distribution appears demonstrating that fi bers are beginning to exhibit a repeating pattern. In the fully re- laxed hair, the distribution becomes even more narrow and intense, indicating fi ber align- ment along a principle axis. Since the Fourier transform images are symmetrical, only half of the image needs to be quantifi ed. A 180° arc is drawn circumferentially from one axis of the Fourier transform image to another, allowing us to measure light intensity (luminosity) along the arc. From the plot of luminosity versus arc angle, we observe a peak corresponding to fi ber alignment distribution. In the case of untreated African hair, the peak is very wide (177°) however, the partially and fully relaxed hair samples had peak widths of 35° and 18°, respectively. In this case, we demonstrate the utility of two- dimensional Fourier transform analysis for characterizing relaxer treatments of African hair. It may also be applied to quantifying other chemical or physical treatments of hair, thereby resulting in geometrical changes of the fi ber assembly, or even to characterize hair styling confi gurations such as brading. HAIR CURLINESS It is often desirable to measure the degree of hair curliness to evaluate the effi cacy of cos- metic treatments, or just to investigate the curliness of a given hair type. Using a method proposed by Loussouarn and coworkers, the length of the hair is measured at rest, then fully stretched, to calculate the curl index (CI) (13): rest stretched Length CI= Length (2) In the original method, fi ber measurements are conducted without the aid of image analysis or imaging equipment. In this study, we obtain images of hair with a fl atbed scanner, which is calibrated with a measuring scale. Images of three hair types, African, artifi cially curled, and frizzy, are provided in Figure 3. Representative fi bers are shown in the relaxed and stretched state. Applying Equation 1 to the distance measurements yields curl indices of 2.25 ± 0.15, 1.58 ± 0.16, and 1.19 ± 0.24 for African, artifi cially curled, and frizzy hair, respectively. These data represent an average of measurements for fi ve fi bers of each hair type. HAIR VOLUME The volume of a hair fi ber assembly can be measured with great facility using a three- dimensional laser stereometer (14). Such a device can be constructed utilizing an x-y

HAIR SHAPE AND DAMAGE FROM RE-SHAPING HAIR 383 two-dimensional translational stage and a laser device, which provides distance informa- tion in the z direction. The distance data are obtained by triangulation of the refl ecting red laser beam from the surface of the measured object, in this case hair. Since hair fi ber Figure 2. Images and their corresponding two-dimensional Fourier transform for (A) untreated African hair and the same hair type that underwent a (B) partial and (C) full chemical relaxation procedure.