General surface definition for describing figure and finish errors

Sub-aperture fabrication techniques such as diamond turning, ion beam figuring, bonnet polishing are indispensable tools in the modern fabrication chain of optical surfaces. Each of these tools address different figure and roughness components in different spatial frequency ranges. The individual processing steps, however, cannot be regarded as independent due to the simultaneous formation of figure and finish errors. Known that, the deterministic Zernike polynomials and the statistical power spectral density function are often used to represent figure and finish errors, respectively. To fill the gap between the deterministic and statistical descriptions, a generic surface description is of great importance. Further, both types of errors are treated differently when analyzing their impact on optical performance: 1) wave aberrations caused by figure errors and 2) stray light resulting from surface finish. In this work, both worlds are bridged by a phase spectrum definition as an extension to the classical power spectral density function to enable combined analysis of figure and finish errors including mid-spatial frequency errors with both deterministic and statistical properties.