Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles

Abstract

Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/13/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Abstract. Surface scatter effects from residual optical fabrication errors can severely degrade optical performance. The total integrated scatter (TIS) from a given mirror surface is determined by the ratio of the spatial frequency band-limited "relevant" root-mean-square surface roughness to the wavelength of light. For short-wavelength (extreme-ultraviolet/x-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we first discuss how to calculate the band-limited relevant roughness from surface metrology data, then present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths, and incident angles. Surfaces with both Gaussian and ABC or K -correlation power spectral density functions have been modeled. These parametric TIS predictions provide insight that is useful in determining realistic optical fabrication tolerances necessary to satisfy specific optical performance requirements.

Spectral Dependent Degradation of the Solar Diffuser on Suomi-NPP VIIRS Due to Surface Roughness-Induced Rayleigh Scattering

“…Spectral scattering due to surface roughness has been extensively studied in theory and by experiments [26][27][28][29][30][31][32][33]. Scattering of light depends on the wavelength of the light being scattered and the scale length of surface roughness.…”

“…In this case, the modification of TIS due to oblique light incidence is applied to the root-mean-square surface roughness σ s as a factor of σ s cosθ i [31]. In the case of scattering from surface roughness on SD material, Equation (6) is applicable and the fraction of scattered light that is trapped in the material or transmitted through can be estimated as…”

“…The relationship TISpλq9λ´4 for l ăă λ is due to Rayleigh scattering, which is dominantly elastic scattering. For oblique incident light with an angle of incidence θ i , the scattering can be expressed as [31,33] TISpλq " 64 3…”

An Application of Sensor Array Processing in Characterizing One Dimensional Surface Roughness

“…Concerning the reflection phenomenon, it can divided into three categories, the first is when the surface of reflection is very flat, the reflection is considered specular [7,8,9] the angle of incidence equals the angle of reflection, if the surface presents some protuberances or small irregularities, the reflection beam consists of specular part which contains the majority of energy and the diffuse part where the propagating secondary sources take several directions concentrated around the mean [7,8,9], the last case is when the surface is very rough, the reflection is diffuse such as no direction is privileged [7,8,9]. These three types are valid for both acoustic [10] and electromagnetic   nm) the reflection is specular for plane mirrors and most of the surfaces are considered to be rough.…”

Multisegmented, multilayer-coated mirrors for the Solar Ultraviolet Imager

“…Using Eq. (1), 20,23 we can calculate the surface microroughness, σ t , over the spatial frequency response of the PMM, per use of each objective; for the 2.5× image in Fig. 4(a), we measured a surface microroughness of 5.3 Å Table 2).…”