2010 TRI/PRINCETON CONFERENCE 87 The fi rst component is called the shine. It is caused by the refl ection of the light on the • surface of the hair fi ber. Since this component consists of an external refl ection, it remains polarized (in case of a polarized illumination) and it is “white” (more precisely of the same color as the illuminating light). The second component is called the chroma. It is caused by the refraction of the incident • light in the hair fi ber and the refl ection on the back surface. Since this component only experiences refl ections and refractions, it remains polarized (in case of a polarized illumination). Since the light travels through the hair fi ber, the chroma is colored The last component is called the diffused light. It is caused by the light is refracted into • the hair fi ber and scattered by pigments inside the hair fi ber. Since this component experiences diffusion, it is depolarized (in case of a polarized illumination). Since the light travels through the hair fi ber, it is colored. To measure the orientation of the hair fi ber, we will focus on the chroma refl ection, which carries the birefringence information as the light is transmitted through the fi ber and back-refl ected. We can then simply describe the interaction of polarized light with hair fi ber using a simple model where the hair fi ber is locally a birefringent material of bire- fringence Δn (Figure 3) with its axis at an angle θ with the vertical axis. If we illuminate the hair fi ber with a polarized light, we detect three components of the backscattered light: Shine: Same polarization as the incident light • Chroma: Polarized light but different polarization due to the birefringence • Diffuse: Un-polarized light • MEASUREMENT OF THE ORIENTATION OF HAIR FIBER In order to measure the orientation of the hair fi ber, we need to detect the infl uence of the chroma and the axis of the birefringence. A simple optical set-up to measure the orienta- tion of the axis of a birefringent material in a transmission mode is to illuminate and detect with parallel polarization (Figure 4). Figure 2. Interactions of light with hair fi ber (left). Illustration on a hair tress placed on a curved surface (right).

JOURNAL OF COSMETIC SCIENCE 88 A simultaneous rotation of both polarizers (Angle ϕ compared to vertical axis) allows the collection of the transmitted light intensity versus the orientation of the polarizer ϕ. The transmitted light intensity I is given by the following formula: ^ ` R R 1 1 1 1 1 cos 1 cos cos 4 4 2 2 _ IT T I ª º Figure 5 shows the transmitted light intensity versus the orientation ϕ of the polarizer for various orientations of angle θ. We observe a sinusoidal signal where the amplitude does not depend on the orientation of the birefringence axis θ but where the phase of the signal is related to θ. We can also observe that there is a 90 degree uncertainty as a vertical birefringent material delivers the same signal as a horizontal one. For hair fi ber, we proceed to a similar set-up, except that we are working in a refl ection mode (Figure 6). The intensity of light backscattered by the hair fi ber is composed of three components: Figure 3. Simple model: Hair fi ber = birefringent material. Figure 4. Birefringence axis measurement set-up (transmission).