Yongjian Wan

Absolute calibration of a spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm

Abstract. We present an absolute testing of a spherical reference surface of a Fizeau interferometer with the method of shift-rotation, which relies on the decomposition of the surface deviation into rotationally asymmetric and symmetric components. With a new procedure to measure the rotationally asymmetric component and an iterative algorithm to calculate the symmetric component, the method can calibrate the spherical reference surface with high accuracy. An experiment is presented to verify the validity of the absolute testing method. The reference surface deviation measured with the absolute testing method agrees well with that of random-ball-averaging testing method; the root mean square of the residual figure between them is ∼0.8u2009u2009nm.

Ultra-precision figuring using submerged jet polishing

A new removal optimization method called submerged jet polishing (SJP) is reported. Experiments are conducted to obtain the removal shape. Results of SJP indicate that a Gaussian shape removal function can be obtained and that the removal rate is sensitive to variations in the standoff distance. SJP is applied to the corrective figuring of a BK7 optical glass. The flatness is improved from photovolatic (PV) 0.066 lambda to 0.024 lambda (lambda=632.8 nm) after three iterations, and the root mean square (RMS) value is improved from 0.013 lambda to 0.00395 lambda. The experimental result indicates that SJP has a capability for ultra-precision figuring and can be applied in polishing complex-shaped surfaces.

Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering

This paper presents a novel method to extract the phase shift and phase distribution from two interferograms simultaneously. By employing Hilbert-Huang transform based prefiltering, the background intensities and modulation amplitudes of the two interferograms are suppressed and normalized respectively. With the addition and subtraction operation of the two prefiltered interferograms, two parametric equations are achieved which can be regarded as the complex harmonic motion of the Lissajous figure. The phase of the Lissajous figure can be directly demodulated by the ellipse fitting algorithm. Apart from the advantages of other well-known two-step phase demodulation algorithms, i.e., high accuracy and efficiency of the Gram-Schmidt orthonormalization (GS) method and the less stringent requirement concerning the fringe number in the extreme value of interference (EVI) method, proposed Lissajous figure and ellipse fitting (LEF) approach has another bonus related to its robustness to the fluctuations of the fringe patterns noise, background intensity and modulation amplitude. Simulations demonstrate the outstanding performance of the proposed method, and experiments further corroborate its effectiveness.

Edge effect modeling and experiments on active lap processing.

Edge effect is regarded as one of the most difficult technical issues for fabricating large primary mirrors, especially for large polishing tools. Computer controlled active lap (CCAL) uses a large size pad (e.g., 1/3 to 1/5 workpiece diameters) to grind and polish the primary mirror. Edge effect also exists in the CCAL process in our previous fabrication. In this paper the material removal rules when edge effects happen (i.e. edge tool influence functions (TIFs)) are obtained through experiments, which are carried out on a Φ1090-mm circular flat mirror with a 375-mm-diameter lap. Two methods are proposed to model the edge TIFs for CCAL. One is adopting the pressure distribution which is calculated based on the finite element analysis method. The other is building up a parametric equivalent pressure model to fit the removed material curve directly. Experimental results show that these two methods both effectively model the edge TIF of CCAL.

Optimized absolute testing method of shift-rotation

The absolute testing method of shift-rotation that combines the traditional N-position method and Zernike polynomial fitting has been commonly employed in surface metrology. It preserves the high spatial frequency of the surface deviation with the N-position method to obtain the rotationally asymmetric surface deviation, but it suffers the kNθ order angular terms errors missed by the N-position method when it calculates the rotationally symmetric surface deviation with the Zernike rotationally symmetric polynomial fitting method. An optimized absolute testing method of shift-rotation is presented in this paper. It considers the missing kNθ order errors when the equations of the rotationally symmetric surface deviation are solved. As a result, it is more accurate than the traditional method. Experimental absolute results of spherical surfaces are given.

Simple and rapid data-reduction method with pixel-level spatial frequency of shift-rotation method

Absolute testing methods are commonly employed in surface metrology to calibrate the reference surface deviation and obtain the absolute deviation of the surface under test. A simple and reliable data-reduction method of absolute shift-rotation method with rotational and translational measurements is presented here, which relies on the decomposition of the surface deviation into rotationally asymmetric and symmetric components. The rotationally asymmetric surface deviation can be simply obtained by classical N-position averaging method. After that, the two-dimensional problem of estimating the other rotationally symmetric surface deviation can be simplified to a one-dimensional problem, and it can be directly calculated out with pixel-level spatial frequency based on several measurements of different translations in one same direction. Since that no orthogonal polynomials fitting, such as Zernike polynomials, is required in the calculation, the data reduction of the method is simple and rapid. Experimental absolute results of spherical surfaces are given.

Orthogonal experiment and analysis on process parameters of bowl feed polishing (BFP)

With the development of science and technology, the demand for high-precision product is increasing continuously. Ultra-smooth surface with sub-nanometer roughness has extensive applications in the field of soft X-ray optics, high power laser and laser gyro. Bowl feed polishing (BFP) technology is an effective ultra-smooth surface processing method, but the polishing process of BFP which is affected by a lot of factors is extremely complex and difficult to control. It is important to understand the effect of the process variables such as abrasive particle size, concentration of abrasive particle, speed of polishing pad, acidity and polishing time in the process of BFP. They are very important parameters that must be carefully formulated to achieve desired material removal rates and surface roughness. Using a design of experiment (DOE) approach, this study was performed investigating the main effect of the each parameter during K9 BFP. A better understanding of the interaction behavior between the various parameters and the effect on removal rate and surface roughness is achieved by using the statistical analysis techniques. In the experimental tests, the optimized parameters combination for BFP which were derived from the statistical analysis could be found for material removal rate and better surface roughness through the above experiment results.

A sampling method to measure surface roughness of circular flat

We propose a sampling method to measure surface roughness of circular flat in this paper. The steps of this method are described in following. First, the number of sampling points is determined based on the radius of the circular flat; then the sampling points are selected by a certain angle in helical line; at last we use instrument like white light interferometer to measure the surface roughness of these sample points. The sampling method can effectively use the surface roughness of sampling points to estimate the surface roughness of the overall optical surface. According to mathematic derivation and simulation analysis, this method has a good sampling results, thus it can be widely used to measure the surface roughness of the circular flat.

Neural network based surface shape modeling of stressed lap optical polishing

It is crucially important to establish an accurate model to represent the relationship between the actuator forces and the lap surface changes when polishing a large and highly aspheric optical surface. To facilitate a computer-controlled optical polishing process, a neural network based stressed lap surface shape model was developed. The developed model reflects the dynamic deformation of a stressed lap. The original data from the microdisplacement sensor matrix were used to train the neural network model. The experimental results show that the proposed model can represent the surface shape of the stressed lap accurately and provide an analytical model to be used to polish the stressed lap control system and the active support system for a large mirror.

Grinding and polishing technology by computer controlled active lap for Φ1250mmF/1.5 aspheric mirror

For large aspheric optical elements, Computer Controlled Active Lap(CCAL) manufacturing which developed in IOE (Institute of Optics and Electronics, Chinese Academy of Science), have some advantages such as higher manufacturing efficiency, lower middle-frequency and high-frequency errors comparing the fixed lapping technology and CCOS(Computer Controlled Optical Surface) technology. A paraboloid surface of Φ1250mmF/1.5 was grinded by the active lap bonded with ceramic pills, as well as polished will pitch bonded active lap. During polishing processing a null lens was designed to test the paraboloid surface, the final testing data of RMS with ZYGO interferometer reached to 0.027λ(λ=0.6328μm).