Bridging the gap between figure and finish errors

Sub-aperture fabrication techniques such as diamond turning and ion beam figuring are indispensable tools in optical fabrication chain. Representing the residual surface errors poses a challenge due to concurrent formation of deterministic and statistical features particularly in the mid-spatial frequency region. Deterministic polynomials and statistical power spectral density functions are often used to represent form and finish errors, respectively. Moreover, both types of errors are treated differently when analysing their impact on optical performance: i) wave aberrations caused by figure errors and ii) stray light resulting from surface roughness. To fill the gap between the deterministic and statistical descriptions, a general surface description is desired to bring versatility to the entire optical fabrication chain and enable an easy exchange of the relevant surface errors between the three disciplines: design, manufacturing, and characterization. In this work, we present a surface description by means of spectral stitching of amplitude and phase spectra, which allows bridging the gap between figure and roughness as well as representing the mid-spatial frequency errors.