Simple estimates for the effects of mid-spatial-frequency surface errors on image quality

Abstract

Mid-spatial-frequency surface errors can be introduced by various manufacturing processes. These errors bridge the gap between traditional figure and finish errors. Although the effects of mid-spatial-frequency errors on the imagery of an optical system can be modeled with a ray-based approach, simply tracing rays provides little insight. We present an alternative method that treats surface errors as perturbations to the nominal surface profile. This approach, combined with standard statistical methods, allows one to make simple back-of-the-envelope predictions of the effects of mid-spatial-frequency errors for various measures of optical performance. Two examples illustrating the effectiveness of this approach are presented.

Poincaré sphere representation for spatially varying birefringence

“…x y u x u y Figure 4: Exit-telecentric imaging system with a BM and aperture at the front focal plane of a lens with focal length f . the pupil plane, an approximation from aberration theory can be used in which the errors are accumulated at the pupil by transporting them there along the system's nominal rays [34].) In what follows, we study the effect of a BM at the pupil plane on the point-spread function (PSF).…”

Nano-Accuracy Surface Figure Metrology of Precision Optics

“…Optical surface errors are general divided into three categories: a) low-spatial frequency (LSF): as surface figure error; b) mid-spatial frequency (MSF): as ripple, and c) high frequency: as surface finish roughness (Youngworth & Stone, 2000;Youngworth et al, 2008). The low-spatial frequency surface error is defined over the spatial period range from 5-10 mm to the entire surface dimension, while the mid-spatial-frequency (MSF) surface error is roughly defined in the range between 0.1 to 5-10 mm spatial periods.…”

Efficient specification and characterization of surface roughness for extreme ultraviolet optics

“…In the following we briefly present the quantities used in this paper. More detailed information can be found in [1,6,7].…”

“…Optimizing the roughness properties in the low spatial frequency range usually impairs the roughness properties at high spatial frequencies and vice versa. Typical examples are the mid-spatial frequency ripples caused by sub-aperture polishing such as magnetorheological finishing [1] or increased high-spatial frequency roughness through ion beam figuring [2]. Meeting the roughness specifications over the entire range of relevant spatial frequencies is a challenging process that is often extremely time consuming and unique for the mirror at hand.…”