Research On Subaperture Stitching Interferometry

Interferometry is a widespread precise testing technology for optical metrology. Since interference pattern is determined by the phase difference between the reference wavefront and the testing wavefront, it is required a standard lens with the same aperture as the surface under test or even larger. Obviously, it will increase weight, installation difficulty and price as the aperture of the standard lens enlarging. Nevertheless, subaperture stitching interferometry is a high precision surface metrology, which can test an optical element with large aperture utilizing interferometer with small aperture, effectively cut down the cost and reserve the medium-high frequency information cut by the large aperture interferometer. Additionally, subaperture stitching interferometry can decrease the fringes number to expand the transverse and longitudinal dynamic range of the apherical surface measurement. Because the accuracy of the subaperture stitching interferometry depends on the positioning system, the range of the apherical surface measurement is limited by the resolution of the detector, this thesis is dedicated to study a mechanical error compensation algorithm, stitching test with an auxiliary location method using artificial mark, and the design of a new variable non-null compensator to expand the range of the asphere stitching interferometry. The major research efforts are summarized as the following points.1. To improve the accuracy of stitching interferometry, it is importante to solve the mechanical errors caused by the relative movement between the interferometer and the surface under test, and to subtract the reference surface figure. The mechanical errors of different movement mode were analyzed, and a mechanical error compensation algorithm was proposed based on constrained optimization theory. Compensators for flat, sphere elements were discussed. We especially analyzed mechanical errors in the asphere surface measurement based on wavefront aberration theory, from which we deduced mechanical error compensators for annular subaperture stitching interferometry. Aiming at decreasing the effect of an unknown reference surface, the reference surface was fitting by Zernike polynomials using maximum likelihood estimation.2. The mechanical error compensation algorithm was deduced with a hypothesis that the positioning system had a high accuracy, so the precision of the stitching measurement would decrease as the positioning accuracy decreasing. The influence of positioning accuracy on the stitching measurement was analyzed and the result showed the algorithm was more robust than the general stitching algorithm. Iteration is a common method to improve the precision of the stitching algorithm, which can improve the precision and multiply increase the compute time simultaneously. In order to select proper algorithm balancing accuracy and time, we analyzed iteration algorithm by simulation. Finally, we did subaperture stitching test with a flat, a sphere and a rotation symmetrical asphere respectively. Compared with the full-aperture measurement, the results verified the validity of the stitching algorithm experimentally.3. For the measurement with low positioning accuracy, we applied artificial circular marks to find the subaperture positions and used mark centers automatic detection to improve efficiency. In the polishing of a 468 mm flat surface, we used the precise data offered by subaperture stitching test, which ensured that the surface error converged quickly to final RMS 14.54 nm. The experimental results showed this positioning method relaxed the requirement of a precise location, and accumulated experience for the actual applies of the subaperture stitching interferometry.4. In order to expand the range of the asphere stitching interferometry, we took a deformable mirror as the variable non-null compensator. Analyzing the feasibility of this compensator, it was concluded that a deformable mirror only need produce low order aberrations to test asphere, avoiding the complicated production of high order aberrations. Based on elasticity theory, we designed an actuator pattern to deform the mirror by generating bending moments. Utilizing finite element method software to simulate deformable mirror, the results showed that the actuator forces were minor, and the fitting errors of the aberrations were less than 5%.