Hybrid height and slope figuring method for grazing-incidence reflective optics

Abstract

Grazing-incidence reflective optics are commonly used in synchrotron radiation and free-electron laser facilities to transport and focus the emitted X-ray beams. To preserve the imaging capability at the diffraction limit, the fabrication of these optics requires precise control of both the residual height and slope errors. However, all the surface figuring methods are height based, lacking the explicit control of surface slopes. Although our preliminary work demonstrated a one-dimensional (1D) slope-based figuring model, its 2D extension is not straightforward. In this study, a novel 2D slope-based figuring method is proposed, which employs an alternating objective optimization on the slopes in the x- and y-directions directly. An analytical simulation revealed that the slope-based method achieved smaller residual slope errors than the height-based method, while the height-based method achieved smaller residual height errors than the slope-based method. Therefore, a hybrid height and slope figuring method was proposed to further enable explicit control of both the height and slopes according to the final mirror specifications. An experiment to finish an elliptical-cylindrical mirror using the hybrid method with ion beam figuring was then performed. Both the residual height and slope errors converged below the specified threshold values, which verified the feasibility and effectiveness of the proposed ideas.

A comprehensive review of dwell time optimization methods in computer-controlled optical surfacing

“…Moreover, the LSQR solution balances the total dwell time along different TIFs, thereby advancing the overall processing efficiency [58]. Furthermore, the matrix-form discretization can facilitate multi-objective optimization problems, where desired residual error criteria are set for height and slope [5,55,60]. Instead of building separate R 𝑖 matrices for different TIFs, R 𝑥 and R 𝑦 are utilized, representing the convolution matrices for the slopes of the TIF in the 𝑥 and 𝑦 directions, respectively.…”

“…Instead of building separate R 𝑖 matrices for different TIFs, R 𝑥 and R 𝑦 are utilized, representing the convolution matrices for the slopes of the TIF in the 𝑥 and 𝑦 directions, respectively. It has been discovered that an alternate objective optimization method associated with the LSQR solver can help achieve desired residual height and slope errors simultaneously more efficiently [5].…”

“…Over the past decade, precision machining technologies have rapidly developed, resulting in the increased amount of high-end optics in various applications such as telescopes for space exploration [1,2], extreme ultraviolet (EUV) lithography systems [3,4], synchrotron radiation and freeelectron laser beamlines [5,6], and more. These optics require stringent specifications on surface precision and aspherical surface shapes to better compensate for aberrations [6] and adapt to compact designs [2,7], which has led to the invalidation of conventional mechanical polishing methods and the emergence of computer-controlled optical surfacing (CCOS) technologies [8,9].…”

Ion Beam Figuring System for Synchrotron X-Ray Mirrors Achieving Sub-0.2-µrad and Sub-0.5-nm Root Mean Square

“…With the rapid development of precision technologies, high-precision optics has drastically become in demand for various cutting-edge applications, such as in telescopes for space exploration [1,2], optics in extreme ultraviolet (EVU) lithography [3,4], and X-ray mirrors for synchrotron radiation [5,6]. Stringent requirements on height-and-slope errors have been specified for the requested optical components.…”

“…It removes material from an optical surface at the atomic level by physical sputtering and has many advantages over conventional CCOS processes, such as being highly deterministic, having stable tool influence functions (TIFs), and not producing mechanical load force, minimal surface or subsurface damage, and edge effects. In the past decade, IBF techniques dedicated to synchrotron X-ray mirror fabrication have been greatly advanced in several directions, system design [7,8], dwell time optimization [9][10][11][12][13], slope-oriented or hybrid height-and-slope-figuring models [6,14,15], and process parameter optimization [16]. All of these efforts were directed toward achieving high figuring accuracy and fast convergence to the target surface height-and-slope profiles.…”