An overview of power spectral density (PSD) calculations

Specifications for optical surfaces have traditionally been given in terms of low frequency and high frequency components, often with a separate classification for surface slope. Low spatial frequency components are commonly referred to as figure errors and can be described by the standard 37-term Zernike polynomial set. High spatial frequency errors are commonly referred to as finish and are quantified using rms roughness. Specification with the qualitative scratch and dig classification is done usually for cosmetic or aesthetic purposes. Mid-spatial frequency errors such as waviness, ripple, and quilting can be important and are not explicitly covered by such traditional figure and finish specifications. In order to bridge the gap to cover mid-spatial frequencies, in terms of quantifying surface characteristics, Power Spectral Density (PSD) can be utilized. For such usage, it is important for the greater optics community to understand the metric, how to calculate it, and how to use it. The purpose of this paper is to provide an overview of PSD, its application in optics, and an outline of calculations needed to effectively apply it to specify optical surfaces.