Mengyang Li

Wavefront reconstruction algorithm based on Legendre polynomials for radial shearing interferometry over a square area and error analysis

Based on the Legendre polynomials expressions and its properties, this article proposes a new approach to reconstruct the distorted wavefront under test of a laser beam over square area from the phase difference data obtained by a RSI system. And the result of simulation and experimental results verifies the reliability of the method proposed in this paper. The formula of the error propagation coefficients is deduced when the phase difference data of overlapping area contain noise randomly. The matrix T which can be used to evaluate the impact of high-orders Legendre polynomial terms on the outcomes of the low-order terms due to mode aliasing is proposed, and the magnitude of impact can be estimated by calculating the F norm of the T. In addition, the relationship between ratio shear, sampling points, terms of polynomials and noise propagation coefficients, and the relationship between ratio shear, sampling points and norms of the T matrix are both analyzed, respectively. Those research results can provide an optimization design way for radial shearing interferometry system with the theoretical reference and instruction.

Modal wavefront reconstruction from slope measurements for rectangular apertures.

We present a modal wavefront reconstruction from slope measurements for rectangular optical components of high-power laser systems. Wavefront reconstruction with slope data is an important approach used for wavefront control or correction in high-power systems. In this work, we derive a complete set of orthonormal wavefront slope polynomials for rectangular apertures and describe the modal method for obtaining wavefront representation with the aberration balancing property. Error propagation properties for the modal method are evaluated and compared with the Southwell method. The cross-coupling error is also discussed. Numerical experiments are conducted to illustrate that the modal method can achieve a higher accuracy than the Southwell method. In addition, we also investigate the influence of noise on the modal method compared with that of the Southwell method.

Improved zonal wavefront reconstruction algorithm for Hartmann type test with arbitrary grid patterns

Zonal wavefront reconstruction by use of the well known Southwell algorithm with rectangular grid patterns has been considered in the literature. However, when the grid patterns are nonrectangular, modal wavefront reconstruction has been extensively used. We propose an improved zonal wavefront reconstruction algorithm for Hartmann type test with arbitrary grid patterns. We develop the mathematical expressions to show that the wavefront over arbitrary grid patterns, such as misaligned, partly obscured, and non-square mesh grids, can be estimated well. Both iterative solution and least-square solution for the proposed algorithm are described and compared. Numerical calculation shows that the zonal wavefront reconstruction over nonrectangular profile with the proposed algorithm results in a significant improvement in comparison with the Southwell algorithm.

Phase extraction based on iteration algorithm with crossed fringes in phase measuring deflectometry

In phase measuring deflectometry, two orthogonal sinusoidal fringe patterns are separately projected on the test surface and the distorted fringes reflected by the surface are recorded, each with a sequential phase shift. Then the two components of the local surface gradients are obtained by triangulation. It usually involves some complicated and time-consuming procedures (fringe projection in the orthogonal directions, accurate phase shifting).To avoid the complex process, a novel phase extraction algorithm with crossed fringes is presented in this paper. It is based on a least-squares iterative process. Both a numerical simulation and a preliminary experiment are conducted to verify the validity and performance of this algorithm. Experimental results obtained by our method are shown, and comparisons between our experimental results and those obtained by the traditional phase-shifting algorithm and between our experimental results and those measured by the Fizeau interferometer are made.

A new optical flat surface measurement method based on machine vision and deflectometry

Phase Measuring Deflectometry(PMD) is a non-contact, high dynamic-range and full-field metrology which becomes a serious competitor to interferometry. However, the accuracy of deflectometry metrology is strongly influenced by the level of the calibrations. Our paper presents a calibration-based PMD method to test optical flat surface with a high accuracy. In our method, a pin-hole camera was set next to the LCD screen which is used to project sinusoidal fringes to the test flat. And the test flat was placed parallel to the direction of the LCD screen, which makes the geometry calibration process are simplified. The photogrammetric methods used in computer vision science was used to calibrate the pin-hole camera by using a checker pattern shown on another LCD display at six different orientations, the intrinsic parameters can be obtained by processing the obtained image of checker patterns. Further, by making the last orientation of checker pattern is aligned at the same position as the test optical flat, the algorithms used in this paper can obtain the mapping relationship between the CCD pixels and the subaperture coordinates on the test optical flat. We test a optical flat with a size of 50mm in diameter using our setup and algorithm. Our experimental results of optical flat figure from low to high order aberrations show a good agreement with that from the Fizeau interferometer.

Wavefront reconstruction algorithm based on interpolation coefficients for radial shearing interferometry

A new wavefront reconstruction algorithm for radial shearing interferometer is proposed. Based on the shearing relationship between the expanded wavefront and the test wavefront, the interpolation coefficient matrix are established by the radial shearing ratio and the number of discrete points of test wavefront. Accordingly, the expanded wavefront can be described by an interpolation coefficient matrix and the test wavefront. Then the test wavefront can be calculated from the phase difference wavefront which comes from any radial shearing interferometer. The numerical simulation proves the correctness of the algorithm. The main error source of this algorithm has been analyzed and the error propagation coefficient has been calculated at last. Above results show that the proposed algorithm is an effective and correct algorithm to reconstruct wavefront for radial shearing interferometer.

A calibration method of self-referencing interferometry based on maximum likelihood estimation

Self-referencing interferometry has been widely used in wavefront sensing. However, currently the results of wavefront measurement include two parts, one is the real phase information of wavefront under test and the other is the system error in self-referencing interferometer. In this paper, a method based on maximum likelihood estimation is presented to calibrate the system error in self-referencing interferometer. Firstly, at least three phase difference distributions are obtained by three position measurements of the tested component: one basic position, one rotation and one lateral translation. Then, combining the three phase difference data and using the maximum likelihood method to create a maximum likelihood function, reconstructing the wavefront under test and the system errors by least square estimation and Zernike polynomials. The simulation results show that the proposed method can deal with the issue of calibration of a self-referencing interferometer. The method can be used to reduce the effect of system errors on extracting and reconstructing the wavefront under test, and improve the measurement accuracy of the self-referencing interferometer.