J. Cosmet. Sci., 60, 153–169 (March/April 2009) 153 New luster formula for the characterization of hair tresses using polarization imaging N. LEFAUDEUX, N. LECHOCINSKI, P. CLEMENCEAU, and S. BREUGNOT, Bossa Nova Technologies, 606 Venice Blvd, Suite B, Venice, CA 90291. Synopsis Hair luster is one of the most important parameters of visual appearance perceived by consumers. Current luster formulae (TRI, Reich-Robbins, …) are optimized for goniophotometric measurements. They are based on a mathematical decomposition of refl ected light into specular and diffused light and the meaurement of the shine peak width on the fi tted angular distributions. In this expose, we are describing a polarization imaging system measuring luster of hair tresses with an innovative algorithm. Using polarization imaging allows to physically separating the specular light from the diffused light for each pixel of the imaged tress. Angular distributions of the specular and diffused light are obtained in a few sec- onds. Where conventional methods calculate the shine peak width on the angular distribution, the imaging system imitates the human eye and calculates the shine width directly on the image. The new formula combines different measured parameters to objectively quantify luster. It was designed to exhibit a higher correlation with visual perception along with a higher sensitivity. Results obtained with conventional formulae are compared on different hair tresses, treated and untreated. The new formula is found to be consistent for a whole range of hair colors, from light to dark. INTRODUCTION The analysis of hair visual appearance has become strategic for the hair care industry. It enables product effi cacy evaluation, claims substantiation and improvement of hair prod- uct formulation. For a long time, the evaluation of the visual appearance of hair has been done by experts. In order to deliver more precise and objective data, quantitative tech- niques have been developed (1–3), mainly based on the measurement of the light scat- tered by hair fi ber (individual or hair tress). Goniophotometer is an excellent example of a technique used for the understanding of hair visual appearance. Scientifi c method closer to what the human eye sees is often required and digital image of the hair tress has proved fundamental to analyze its visual appearance. Optical imaging system is very powerful because it can deliver both data and images in real time. Light scattering in hair fi ber is complex and needs a detailed investigation. Polarization analysis is a well known tech- nique to deeply analyze the composition of the light scattered by an object (1–9,15). This paper presents the application of a new polarization imaging technique for the measure- ment of hair visual appearance. A new luster formula enabling the characterization and the measurement on any type of hair is proposed.

JOURNAL OF COSMETIC SCIENCE 154 SCIENTIFIC BACKGROUND POLARIZATION OF LIGHT Light can be described as an electromagetic vibrating wave that can be characterized by three main properties: O Its intensity: it is related to the amplitude of the light vibration. The higher the am- plitude of light vibration is, the more intense the light is. O Its spectrum: it is related to the frequency or wavelength of the light vibration. In the case of visible spectrum, red has a greater wavelength than blue. O Its polarization: it is related to the spatial orientation and coherence of the light vibra- tion. Light can be either polarized (the light vibration has a defi ned orientation) or depolarized. In this case, the light vibrates randomly. Along with intensity and spectrum, polarization of light carries abundant information (10–13) about the sample. Polarization is by far the less investigated of these three fun- damental properties of light, mainly because of the lack of polarization sensor. However, polarization fi nds important applications for visual appearance measurement. One crucial property of polarization is the modifi cation of the polarization of light after interaction with a sample. This modifi cation allows characterizing the interaction. In the case of macroscopic objects, the type of interaction between light and matter can be separated into two main categories: coherent interactions and incoherent interactions (Figure 1). Coherent interactions preserve polarization of light. They include refl ection and refrac- tion at an optical interface. Incoherent interactions destroy polarization of light. They include scattering and diffusion. For instance, if the illumination is polarized, the re- fl ected and refracted light will remain polarized while the scattered light will be depolar- ized. This fundamental property allows to measure independently the diffused light and the refl ected light. The independent measurement of those two components is of prime importance for cosmetic evaluation. INTERACTION OF LIGHT WITH HAIR FIBERS Hair has a very specifi c visual appearance (3,4,8,9,14,15). Hair fi bers can be considered as transparent and partially absorptive fi bers with small steps at its surface due to the hair cuticle. This structure causes the visual appearance of hair fi ber. It is widely accepted that hair visual appearance comes from 3 different interations of light with the hair fi bers re- sulting in three components of light (Figure 2): O The fi rst component is called the shine band. 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, it is “white” (more precisely of the same color as the illuminating light) and it appears as a band on the hair tress. The width of the band is determined by the roughness of the surface and the irregularities on the hair fi bers. The cuticle angle induces a shift of the shine band from the direction a refl ection would have on a fi ber without cuticle. O The second component is called the chroma band. 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 com- ponent only experiences refl ections and refractions, it remains polarized. Since the