Xuhui Xie

Algorithm for ion beam figuring of low-gradient mirrors

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100 λ.

Microscopic morphology evolution during ion beam smoothing of Zerodur® surfaces.

Ion sputtering of Zerodur material often results in the formation of nanoscale microstructures on the surfaces, which seriously influences optical surface quality. In this paper, we describe the microscopic morphology evolution during ion sputtering of Zerodur surfaces through experimental researches and theoretical analysis, which shows that preferential sputtering together with curvature-dependent sputtering overcomes ion-induced smoothing mechanisms leading to granular nanopatterns formation in morphology and the coarsening of the surface. Consequently, we propose a new method for ion beam smoothing (IBS) of Zerodur optics assisted by deterministic ion beam material adding (IBA) technology. With this method, Zerodur optics with surface roughness down to 0.15 nm root mean square (RMS) level is obtained through the experimental investigation, which demonstrates the feasibility of our proposed method.

Corrective capability analysis and machining error control in ion beam figuring of high-precision optical mirrors

In deterministic ion beam figuring (IBF) technology, the application of small ion beam enhances the corrective capability for mid-to-high spatial frequency errors on the optical surface, which directly determines the surface accuracy of the figuring process. But when the diameter of the ion beam becomes smaller, the machining errors will have a stronger influence on the final figuring result, so these errors must be controlled through corresponding methods. We investigate the corrective principle in IBF for surface errors of different spatial frequencies and establish the selection criterion for removal function in different figuring stages to realize the rapid convergence of surface accuracy. Then, through analyzing and controlling the machining errors in the figuring process, high-precision mirrors can be rapidly obtained. Finally, experiments on fused silica planar and spherical samples are conducted on our self-developed IBF system, and their final surface accuracy are both smaller than 1.1 nm RMS (root-mean-square) and 12.0 nm PV (Peak-to-Valley) after several iterations within 20 min.

Ion beam figuring of high-slope surfaces based on figure error compensation algorithm.

In a deterministic figuring process, it is critical to guarantee high stability of the removal function as well as the accuracy of the dwell time solution, which directly influence the convergence of the figuring process. Hence, when figuring steep optics, the ion beam is required to keep a perpendicular incidence, and a five-axis figuring machine is typically utilized. In this paper, however, a method for high-precision figuring of high-slope optics is proposed with a linear three-axis machine, allowing for inclined beam incidence. First, the changing rule of the removal function and the normal removal rate with the incidence angle is analyzed according to the removal characteristics of ion beam figuring (IBF). Then, we propose to reduce the influence of varying removal function and projection distortion on the dwell time solution by means of figure error compensation. Consequently, the incident ion beam is allowed to keep parallel to the optical axis. Simulations and experiments are given to verify the removal analysis. Finally, a figuring experiment is conducted on a linear three-axis IBF machine, which proves the validity of the method for high-slope surfaces. It takes two iterations and about 9 min to successfully figure a fused silica sample, whose aperture is 21.3 mm and radius of curvature is 16 mm. The root-mean-square figure error of the convex surface is reduced from 13.13 to 5.86 nm.

Mathematical modeling and application of removal functions during deterministic ion beam figuring of optical surfaces. Part 1: Mathematical modeling.

Ion beam figuring (IBF) is established for the final precision figuring of high-performance optical components, where the figuring accuracy is guaranteed by the stability of the removal function and the solution accuracy of the dwell time. In this deterministic method, the figuring process can be represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time. However, we have found that the current 2D convolution operation cannot factually describe the IBF process of curved surfaces, which neglects the influences of the projection distortion and the workpiece geometry on the removal function. Consequently, the current 2D convolution algorithm would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, based on the material removal characteristics of IBF, a mathematical model of the removal function is developed theoretically and verified experimentally. Research results show that the removal function during IBF of a curved surface is actually a dynamic function in the 2D convolution algorithm. The mathematical modeling of the dynamic removal function provides theoretical foundations for our proposed new algorithm in the next part, and final verification experiments indicate that this algorithm can effectively improve the accuracy of the dwell time solution for the IBF of curved surfaces.

Morphology evolution of fused silica surface during ion beam figuring of high-slope optical components.

Ultra-precision and ultra-smooth surfaces are vitally important for some high performance optical systems. Ion beam figuring (IBF) is a well-established, highly deterministic method for the final precision figuring of extremely high quality optical surfaces, whereas ion sputtering induced smoothing, or roughening for nanoscale surface morphology, strongly depends on the processing conditions. Usually, an improper machining method would arouse the production of nanoscale patterns leading to the coarsening of the optical surface. In this paper, the morphology evolution mechanism on a fused silica surface during IBF of high-slope optical components has been investigated by means of atomic force microscopy. Figuring experiments are implemented on two convex spherical surfaces by using different IBF methods. Both of their surface errors are rapidly reduced to 1.2 nm root mean square (RMS) after removing similar deep material, but their surfaces are characterized with obviously different nanoscale morphologies. The experimental results indicate that the ion incidence angle dominates the microscopic morphology during the IBF process. At near-normal incidence, fused silica achieves an ultra-smooth surface with an RMS roughness value R(q) down to 0.1 nm, whereas nanoscale ripple patterns are observed at a large incidence angle with an R(q) value increasing to more than 0.9 nm. Additionally, the difference of incidence angles on various machined areas would influence the uniformity of surface quality, resulting from the interplay between the smoothing and roughening effects induced by ion sputtering.

Mathematical modeling and application of removal functions during deterministic ion beam figuring of optical surfaces. Part 2: application

Ion beam figuring (IBF) is established for the final precision figuring of optical components. In this deterministic method, the figuring process is represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time, where the figuring precision is guaranteed by the stability of the removal function as well as the solution accuracy of the dwell time. However, the current 2D convolution equation cannot factually reflect the IBF process of curved surfaces, which neglects the influence of the projection distortion and the workpiece geometry. Consequently, the current convolution algorithm for the IBF process would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, we propose an improved algorithm based on the mathematical modeling of the dynamic removal function in Part A, which provides a more accurate dwell time for IBF of a curved surface. Additionally, simulation analysis and figuring experiments are carried out to verify the feasibility of our proposed algorithm. The final experimental results indicate that the figuring precision and efficiency can be simultaneously improved by this method.

Structure optimization and fabricating capability analysis of an ion-beam machine for a subnanometer optical surface

Ultraprecise and ultrasmooth surfaces become critical requirements for some high-performance optical systems. Ion-beam figuring (IBF) is a good and highly deterministic method for the final precision optical figuring. However, the uniform convergences of all spatial frequency surface errors are strongly dependent on the dynamic performance and ion-beam stability of the IBF machine. In this paper, only the dynamic performance is discussed, which is limited by the acceleration and velocity of the motion system. So we discuss these problems and their influences on figuring optical surfaces in detail. The structure optimization principle is based on the fabricating capability of ultraprecise surface errors in all spatial frequency ranges. With this requirement, the structure optimization of a quick-response platform is performed to improve its dynamic performance. Manufacturing experiments on a fused silica spherical concave surface (Φ135.7  mm, radius of curvature 340.5 mm) are accomplished, and the IBF machine can effectively correct the figure errors and improve the surface quality simultaneously. The IBF process realizes the uniform convergence of surface errors in all spatial frequency ranges, which is reduced down to 0.368 nm RMS, 0.204 nm RMS, and 0.087 nm RMS, respectively. The final results indicate that the performance of the new designed IBF machine meets the requirements well for the fabrication of a subnanometer optical surface.

Ion beam machining error control and correction for small scale optics.

Ion beam figuring (IBF) technology for small scale optical components is discussed. Since the small removal function can be obtained in IBF, it makes computer-controlled optical surfacing technology possible to machine precision centimeter- or millimeter-scale optical components deterministically. Using a small ion beam to machine small optical components, there are some key problems, such as small ion beam positioning on the optical surface, material removal rate, ion beam scanning pitch control on the optical surface, and so on, that must be seriously considered. The main reasons for the problems are that it is more sensitive to the above problems than a big ion beam because of its small beam diameter and lower material ratio. In this paper, we discuss these problems and their influences in machining small optical components in detail. Based on the identification-compensation principle, an iterative machining compensation method is deduced for correcting the positioning error of an ion beam with the material removal rate estimated by a selected optimal scanning pitch. Experiments on ϕ10 mm Zerodur planar and spherical samples are made, and the final surface errors are both smaller than λ/100 measured by a Zygo GPI interferometer.

Research on temperature field of KDP crystal under ion beam cleaning.

KH2PO4 (KDP) crystal is a kind of excellent nonlinear optical component used as a laser frequency conversion unit in a high-power laser system. However, KDP crystal has raised a huge challenge in regards to its fabrication for high precision: KDP crystal has special physical and chemical characteristics. Abrasive-free water-dissolution magnetorheological finishing is used in KDP figuring in our lab. But the iron powders of MRF fluid are easily embedded into the soft surface of KDP crystal, which will greatly decrease the laser-induced damage resistance. This paper proposes to utilize ion beam figuring (IBF) technology to figure and clean the surface of a KDP component. Although IBF has many good performances, the thermal effect control is a headachy problem for the KDP process. To solve this problem, we have established its thermal effect models, which are used to calculate a components surface temperature and thermal gradient in the whole process. By this way, we can understand how to control a temperature map and its gradient in the IBF process. Many experiments have been done to validate and optimize this method. Finally, a KDP component with the size of 200×200×12  mm is successfully processed by this method.