Kindly provide Sa and Sz (optical surface roughness) definition with references

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:

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 understanding the range of surface irregularities, which can influence optical performance and contact properties. The formula for Sz is:

where $z_{p}$ is the height of the highest peak and $z_{v}$ is the depth of the deepest valley within the measured area [1][4].

Explanation of references used:References were selected from the "Research Articles" that specifically define and/or use the surface roughness parameters Sa and Sz in the context of optical or material surface engineering. Reference [1] discusses the measurement and calculation of Sa and Sz, explicitly providing context and definitions relevant to optical coatings. Reference [2] and [3] report on the use of Sa for surface roughness characterization in biomedical and coating applications, ensuring coverage of both definition and practical measurement. Reference [4] specifically details both Sa and Sz, their measurement on dental and optical materials, and provides explicit formula-based context using optical profilometry. These references are therefore directly relevant to the definitions requested in the Question.