HAIR GLOSS 307 The resulting indicatrix in Figure 7 shows that for receptor angles ½2 50ø, only a small (and for other angles a large) deviation from the ideal horizontal line occurs (indicatrix b in Figure 2). These deviations were checked several times a day and were used as correction functions. Therefore, all indicatrices of hair strands represent luminance distributions, scaled in respect to an ideal diffuse-reflecting surface. CHARACTERIZATION OF THE PHOTOMETRIC DATA To achieve a compromise between the demand for collecting as much data as possible and an acceptable time for the measurements, the influence of the horizontal and the vertical receptor angles was checked and plotted as a pseudo-three-dimensional lumi- nance distribution function in Figure 8. It is composed of ten indicatrices relating to the horizontal receptor angle as an inde- pendent variable and a fixed vertical receptor angle between -15 ø and + 60 ø as a parameter. Additionally, contour lines are drawn, representing iso-luminances, point- ing to combinations of horizontal and vertical receptor angles with constant luminance. They are more or less parallel to the axis of the vertical receptor angle and prove that the ten indicatrices do not contain much different information. Investigations were therefore restricted to one cut in the two-dimensional scan at a vertical receptor angle of 0 ø. The representation of important photometric properties by this one indicatrix depends very much on its reproducibility, which is mainly influenced by the sample itself. Using one of the hair samples described in RESULTS AND DISCUSSION below and illumi- nating it under ½• = 30 ø results in the initial luminance indicatrix A in Figure 9. Without removing the sample from the goniophotometer, a second measurement was made 1 hour later. The corresponding indicatrix B is identical within the line width of the drawing, which means a very good reproducibility. luminanee (arbifrary unifs) 60 0,0 horjz. recepfor angle .._____.._•._.•0 BO Figure 8. Two-dimensional distribution of light reflected by hair.

308 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS ,øø t 160 20 luminanee {arbifrary unifs} -5.0 25.0 55.0 85.0 recepfor angle/degrees Figure 9. Reproducibility test for measured hair indicatrices. Sometimes the sample has to be removed from the turntable, e.g., for an additional treatment. If it is possible to remove the hair strands, fixed in the sample holder mentioned in SAMPLES AND THE PREPARATION OF SAMPLES below, a rather good reproducibility can be achieved after reinserring the sample holder in its former place. This is shown in indicatrix C. The importance of always referring to the same sample area is demonstrated by indicatrix D. It belongs to the adjacent area at a distance of about 10 mm. The indicatrix shape has changed remarkably, and the reproducibility is bad. A similar problem may occur if the hair has to be removed from its sample holder for a treatment. Due to the flexibility of the hair fibers, they are then arranged in a new order representing a slightly different surface. Fixing the hair again in the sample holder results in indicatrix E, which now has to be compared with indicatrix D. The difference is remarkable, and fixing the sample requires some precaution. Because each hair indicatrix has several data points standing for different viewing directions, a gloss-related data compression is advisable, taking into account the gloss parameters mentioned in VISUAL GLOSS EXAMINATION above. Most indicatrix shapes are similar to Gaussian or normal distribution (Figure 4) and can be described by two parameters: the peak height or maximum and the indicatrix width. The latter stands for the angular spread of the reflected light representing the reduction of the brightness when changing the viewing direction. It is often associated with the sharp- ness of the reflected light source image. One possibility for characterizing this range is to measure the angular distance between indicatrix parts halfway between the minimum and the maximum of the indicatrix. Then the angular range is called the half-value angle. SAMPLES AND THE PREPARATION OF SAMPLES The companies Gustav Kerling (Backnang) and Heinrich G. Herzig (Schwetzingen)