J. Cosmet. Sci., 62, 85–100 (March/April 2011) 85 Fiber orientation measurement using polarization imaging N. LECHOCINSKI and S. BREUGNOT, Bossa Nova Technologies, 606 Venice Blvd, Suite B, Venice, CA 90291. Synopsis In this paper, we present a new technique to determine the orientation of hair fi ber, a key parameter in the evaluation of visual appearance of hair. Using polarization imaging and image analysis tools, we are able to measure the orientation of hair fi ber for each pixel in the image. A theoretical analysis of the optical set-up is presented. Experimental data on a single fi ber, hair tress, and complete head are given. Application to sham- poo and conditioner is also demonstrated. INTRODUCTION Visual appearance of hair is defi ned by multiple parameters: color, shine (external refl ec- tion), and chroma (internal refl ection). Another important parameter is the orientation of the hair fi ber. Different methods have been presented to measure fi ber orientation. These methods are using conventional imaging followed by image processing, which analyzes the texture in order to deduct the orientation of the fi ber (1–3). Automatic measurement of the orientation of the hair fi ber can be a diffi cult task as the image processing tech- niques are strongly affected by parameters such as the quality of the illumination and the color of the fi ber. In this paper, we propose a new technique to measure the orientation of hair fi ber. Based on polarization analysis, this technique allows the measurement of a physical parameter directly connected to the orientation of the fi ber for each pixel of the image. This tech- nique operates for every kind of hair, dark to blond, straight to curly. SCIENTIFIC BACKGROUND BIREFRINGENCE OF HAIR FIBER Birefringence is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, depending on the polarization of the light. This effect can occur only if the structure of the material is anisotropic (directionally dependent). If the material has a single axis of anisotropy, bire- fringence can be formalized by assigning two different refractive indices to the material for different polarizations. The birefringence magnitude is then defi ned by Δn = ne − no,

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.