Wenlin Liao

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.

Self-calibrated subaperture stitching test of hyper-hemispheres using latitude and longitude coordinates

Limited by the f-number of the transmission sphere, it is impossible to test the whole surface of a hyper-hemisphere using a standard interferometer directly. This paper presents an extension of the subaperture stitching test method to hyper hemispheres. The stitching algorithm is based on the coordinate mapping from local measurement frame to a global frame, and overlapping correspondence is calculated by virtue of coordinates of latitude and longitude. The reference surface error is represented by Zernike polynomials and self-calibrated during the stitching to achieve higher accuracy. Then the stitched surface error distribution is presented by map projection. To realize accessibility to the whole surface of a hyper-hemisphere, we also propose a design for the subaperture test platform, according to the subaperture lattice design. Finally, a hemisphere and a full sphere are tested and figured, respectively, to validate the method and the experimental setup.

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 Technology: Figuring, Adding and Smoothing for High-precision Optics

Besides conventional ion beam figuring process, ion beam adding has been proposed and applied in optical fabrication. Ion beam smoothing processes, especially on fuse silica and Zerodur are discussed, and ultra-smooth surfaces are achieved.

Rapid fabrication technique for nanometer-precision aspherical surfaces

High-precision aspherical optics are widely used in modern optical systems with the capability of providing high image quality, but an aspherical surface is more challenging to fabricate because of its more complex shape compared with other surfaces. Ion beam figuring (IBF) provides a highly deterministic technology for ultra-precision fabrication of aspherical surfaces. However, the convergent efficiency and final accuracy are strongly dependent on the original surface state, where the topography and distribution of the surface errors generated during the pre-processing should be taken into account. Consequently, we propose a combined technique that includes magnetorheological finishing, smoothing polishing, and IBF. This technique can effectively control different surface errors during the polishing process, and then rapidly impart nanometer-precision fabrication. Comparative figuring experiments are performed on a parabolic surface, and the original surfaces before IBF are pre-processed by manual polishing and our combined technique, respectively. The results indicate that abundant high-slope and middle-to-high frequency surface errors exist on the surface after conventional polishing, and this surface state limits the final fabrication accuracy. Nevertheless, a smooth surface is prepared by our combined technique and a nanometer-precision aspherical surface is rapidly obtained, which demonstrates the feasibility of our proposed method.