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

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 non-circular apertures cannot be analyzed with Zemicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zemicke 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.

Frequency-domain analysis of computer-controlled optical surfacing processes

“…(9) and (10) universally satisfy all CCOS technologies, such as CCP, MRF and IBF, and also satisfy all shape TRFs, regardless whether it is rotationally symmetric.…”

“…(9) shows that the MRA of a CCOS process is determined by its TRF, and it just equals the normalized amplitude spectrum of the FT of its TRF. Eq.…”

“…These mid-high spatial frequency errors would degrade the performances of the precision optical systems, such as intense laser systems, shortwave optical systems and high resolution imaging systems [8] . Therefore, these errors should be considered and removed from the CCOS processes [9] . Based on the convolution integral model, which is widely applied in CCOS processes, this study investigates the ability of a CCOS process to correct the errors in view of the availability of material removal.…”

Power spectral density measurement for large aspheric surfaces

“…Traditionally, simple statistical measurements such as Zernike polynomials, peak-to-valley wavefront error and root mean square (RMS) roughness are used to obtain an initial quantitative description of the surfaces [3][4][5][6]. These measurements are based on height information and, for certain types of surfaces, can serve as a good description of their roughness.…”

Modelling and simulation of mid-spatial-frequency error generation in CCOS

“…The researchers in the Lawrence Livermore National Laboratory (LLNL) found that the periodic structure induces the disturbance of amplitude or phase of laser beam through theoretical and experimental methods, which will destroy the performance of high power optical system [10,11]. In order to ensure the beam quality and output energy of NIF laser system, NIF proposed the requirements of optical components in the MSF errors, that PSD-1:A ≤ 1.01ν -1.55 , RMS ≤ 1.8 nm, PSD-2:A ≤ 1.01ν -1.55 , RMS ≤ 1.1 nm [10].…”