Research Of Key Issues In Measuring Cylindricity Error Using Stitching Interferometry

In this dissertation, stitching interferometry for the measurement of cylindricity and its relative techniques have been studied.We have developed a stitching interferometry system for the measurement of cylin-drical surface. A CGH cylinder null is used as wavefront convertor, so that it can diffract a cylindrical test beam from the collimated test beam of the Fizeau interferometer. To measure the form error of the cylindrical lens, the 360-deg form error of a cylinder with high accuracy and high resolution, we have paid more attentions to the relative research fields, and proposed some novel methods as follows,(1) Method of misalignment aberrations removal in null test of cylindrical surfaceIn this technique, all possible aberrations caused by the misalignment errors were analyzed. Based on the first-order approximate principle, the mathematical models, which describe the relationship between the misalignment aberrations and the possible misalignment errors, were deduced. With these mathematical expressions, all possible misalignment errors can be estimated by using the least-squares fitting algorithm, and then the ideal surface deviations can be obtained by subtracting the misalignment aberra-tions from the extracted phase data. Comparing with the existing methods, the proposed method provides a feasible way to estimate the misalignment errors with better accuracy.(2) Compensation of high-order misalignment aberrations in cylindrical interfer-ometry.When the tested cylindrical surface is not perfect or seriously misaligned, a nonze-ro fringe pattern might be obtained. As a result, high-order misalignment aberrations (e.g. coma and spherical aberration) are introduced into the measurement. The sources and types of high-order misalignment aberrations are analyzed by orthogonal Legendre polynomials. Based on the analysis, a mathematical model was proposed to estimate the high-order misalignment aberrations. Then a wavefront difference method was proposed to calibrate the coefficients of this model. With the calibrated coefficients, the high-order misalignment aberrations can be determined and separated from the measurement results. Compared with the lower-order misalignment aberrations removal method, the proposed method can reduce the high-order misalignment aberrations by at least half, and highly accuracy results can be achieved by the proposed method.(3) Stitching interferometry for cylindrical optics with large angular apertureStitching interferometry is an attractive method for measuring optics with large apertures. However, existing stitching algorithms are not suitable for measuring cylindri-cal optics, because the misalignment aberrations in cylindrical interferometry are more complicated than those in plane, spheric, and aspherical measurements. This paper presents a stitching algorithm for measuring cylindrical optics with large angular aper-tures. We use five aberrations (i.e. piston, tilt, tip, defocus and twist) to describe the pos-sible misalignments of the tested cylindrical surface and to build the cylindrical stitching model. Using this model allow us to calculate the relative misalignment aberrations of subapertures from their overlapped areas, so that the full aperture map of a cylindrical surface is obtained by compensating for these misalignment aberrations.(4) Measuring form error of cylinder by stitching interferometryLimited by the f-number of the null corrector (such as computer generated holo-gram, CGH), the 360-deg form error of a cylinder cannot be imaged in one measurement. This paper presents a subaperture stitching method for measuring the form error of cylin-der. The tested cylinder was measured with a cylindrical interferometer to get a set of small subapertures with partially overlapped areas. The stitching algorithm is based on the coordinate mapping from the local frame to the global frame, and the relationship parameters between the adjacent subapertures are calculated from the overlapping areas by virtue of cylindrical coordinate transformation. According to the result parameters, the subaperture measurements are connected to yield the 360-deg form error.The above novel methods being applied in cylindricity error measurement not only can extend the range of application of stitching interferometry, but also can guarantee the result with high accuracy and high resolution. The experimental results show that the full aperture map of cylindrical optics with large angular aperture, the 360-deg form error of a cylinder can be measured and reconstructed based on the proposed methods. Comparing with the existing methods, the proposed measurement system is non-contact, and can provide high accuracy and high resolution result.