JOURNAL OF COSMETIC SCIENCE 86 where ne and no are the refractive indices for polarization parallel (extraordinary) and perpendicular (ordinary) to the axis of anisotropy respectively. The retardance R of the birefringent material is given by R = 2π/λ Δn d, where d is the thickness of the material and λ the wavelength of the light. R = π (or 180 degree) corresponds to a half-wave plate (Δn d = λ/2) and R = π/2 (or 90 degree) to a quarter-wave plate (Δn d = λ/4). Hair fi ber exhibits a birefringence in the visible and near-infrared spectrum. Numerous papers have been published about the measurement of the birefringence of hair using dif- ferent methods (4). The birefringence of hair fi ber is mainly due to the geometry of the cortical region of the human hair, which also gives hair its elasticity properties. Typical birefringence values are Δn = 1-0.5%. The birefringence axis is parallel and perpendicu- lar to the fi ber axis (Figure 1). The analysis of the birefringence of hair can also lead to the identifi cation of hair defects (5). INTERACTION OF POLARIZED LIGHT WITH HAIR FIBERS Hair has a very specifi c visual appearance. Hair fi bers can be considered as transparent and partially absorptive fi bers with small steps at their surface (hair cuticle). This structure causes the visual appearance of hair fi ber. It is widely accepted that hair visual appearance comes from three different interactions of light with the hair fi bers resulting in three components of light (Figure 2): Figure 1. Birefringence axis of hair fi ber.

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).