Methods for the analysis of full-spectrum spatial-frequency errors considering a freeform-surface process chain

A method for analyzing as-built freeform mirrors after manufacturing over the whole frequency band is provided. For this, a definition of the separation between different spatial frequency bands is considered, and certain process-motivated types of synthetic data with different parameters for the investigation are defined, which are later fitted by Zernike and Q polynomials. Further, the calculation of the PSD curve is described. The Zernike and Q spectra are similar and show certain identifiable structures for certain types of data depending on the parameters. They complement the spectral information provided by the PSD curve. Both approaches are compared. The publication provides the tools and methods for a follow-up paper in which mirrors of manufactured optical systems are investigated over the whole process chain. In the third paper, the as-built results will be imported into the nominal optical design to assess the impact of deviations on the optical performance over a wide spatial frequency band.