<title>Specification of optical components using the power spectral density function</title>

TLDR

Optical components with large, noncircular apertures (up to 800 mm) cannot be fully characterized by Zernike polynomials, which are limited to circular apertures and low‑frequency aberrations. The study aims to use Fourier‑based power spectral density analysis to provide a more complete representation of optical wavefronts. Fourier analysis yields a power spectral density that represents the amplitude of frequency components, relates to scattered intensity versus angle, and enables calculation and optimization of wavefront shape or focal spot for complex multi‑component laser systems. The authors demonstrate PSDs for several precision optical components and show that these PSDs can be used to calculate and optimize the wavefront shape or focal spot of complex multi‑component laser systems.

Abstract

This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density (PSD) function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up to 800 mm. The wavefronts of components with noncircular apertures cannot be analyzed with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zernicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as 'residuals'. A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi- component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.