Method of controlling optical surface roughness based on stray light requirements
Authors: Song Yan-Song  , Yang Jian-Feng  , Li Fu  , Ma Xiao-Long  , Wang Hong  ,   Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China;,   University of Chinese Academy of Sciences, Beijing 100049, China}
Published: December 2020

Scattering introduced by optical surface fabrication errors could degrade optical performance severely. Therefore, the optical designers are required to provide a roughness index for describing the specific surface or even all surfaces to ensure the final imaging performance. The surface root-mean-square (RMS) roughness is a common index to quantify surface topography. And there are also some available methods to acquire the surface RMS roughness based on bidirectional scattering distribution function theory or the angle spread function theory. However, the influence of the optical surface scattering on the optical system cannot be accurately revealed by the surface RMS roughness determined by these methods. On the one hand, the RMS roughness corresponds to an excessively wide spatial frequency range from 0 to 1/, where is the wavelength of the light. Consequently, it is difficult to measure the RMS roughness during manufacture. On the other hand, what really worsens the stray light performance of the system is only the surface profile located within a certain subinterval of the aforementioned frequency range, to put it in another way, the surface RMS roughness identified by the methods above is incompetent to quantify the amount of the energy that is surfacescattered to the detector. To address the issues above, in this paper we propose a novel approach to identifying the surface roughness. This method seeks to deduce the relation between optical surface RMS roughness and the stray light requirement of the system by dint of partial integrated scattering (PIS). In contrast to total integrated scattering, PIS counts the scattering light energy that could reach the detector. Hence, the RMS roughness identified in this way corresponds to the effective spatial frequency range that contributes to the stray light in the system. Firstly, the effective frequency range concerned with the system stray light level is identified through the analysis of the propagation path of the scattered light. Then, the surface RMS roughness would be measured within the established range according to the stray light requirement of the system and used to control the surface roughness as the roughness index during the optical manufacture process. The method not only considers the scattering as the surface characteristic, but also takes into account the influence of scattering on the system. Taking the solar magnetic field telescope (MFT) for example, the validity of the method is verified by comparing with the traditional methods. As manifested in the outcome, the effective frequency range of primary mirror is from 0 to 18 mm-1, and the surface RMS roughness identified in such a new way can stage the stray light performance of MFT in a more precise manner, which is more reliable to serve as a surface roughness index.