Kindly provide Sa and Sz (optical surface roughness) definition with references - tlooto, The Most Powerful AcademicGPT

Sa and Sz (optical surface roughness) are key parameters used to quantify the topography of a surface, particularly in optical engineering and materials science. Sa is defined as the arithmetic mean height of a surface, calculated as the mean of the absolute values of the surface departures from the mean plane within a given area. It provides a single value that represents the overall roughness of a surface without regard to spatial distribution of peaks and valleys. Mathematically, Sa can be expressed as: $$ Sa = \frac{1}{A} \int{A} |z(x,y)| dx dy $$ where $ z(x, y) $ represents the height at the point (x, y) on the measured area A of the surface [1][2][3][4]. Sz, on the other hand, is defined as the maximum height of the surface, calculated as the sum of the height of the highest peak and the depth of the deepest valley within the defined area. In other words, Sz gives the total vertical distance between the extreme points on the surface. Sz is particularly important for understand