SKIN SURFACE ANALYSIS 319 • L.a 400 HALE SUBJECTS ABDOHEN 350 300 250 200 • --3' .... I I' • 30 [iiO 90 120 150 oleg Figure 7. La (Xa) as a function of scan directions (the O-degree angular direction represents the body axis). HORIZONTAL DISTRIBUTIONS OF ASPERITIES (FIGURES 8a, 8b) Skin anisotropy can be characterized by applying the autocorrelation function to dif- ferent scan directions on a plane surface. N-h R([3) - N 0 '2 z(i) ß z(i + h) i= The number of steps between two experimental points of the profile studies is h, and z(i), z(i + h) are equal to the heights of two points of a profile spaced by h ß steps. This function can give the relation between two points in a profile separated by a distance 13 = (h ß steps). If the correlation is required between two points having the same position (i.e., between a point and itself of a profile), we use the R ([3) formula (with h = 0), N-h R([3 = 0) = N0.2 i= 1 Z(i ) Z(i) -- •-•' 0.2 : 1 Therefore N 1 Z z(i). z(i ) __ = 0.2 (variance). mi=l

320 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS I\ s?o 177o Figure 8a. Autocorrelation function R ([3) obtained using a scan direction of 10 degrees from the body axis on an abdominal positive replica of a 55-year-old male. Figure 8b. Autocorrelation function R (•) obtained using a scan direction of 70 degrees from the body axis on an abdominal positive replica of a 55-year-old male. A profile can be taken, representing one direction x if z•, z2, z 3, z4 ß ß ß Z n are the points' heights separated by equidistant intervals (h), any two such points separated by n steps (i.e., by a quantity [3 = n ß h) will have an autocorrelation if the sum of the height products zi ß Zi+n h is big. For example, for [3 = [3• = 3 h,