Flat Mirror Stitching Measurement Study Based On Structured Light Reflection

According to the optical diffraction imaging principle, the angular resolution of an optical system is defined by 1.22λ/D. Larger telescope diameter improves telescope condenser capacity as well as telescope angular resolution. Along with the development of space science and technology, increasing observing demand has been requiring higher and higher resolution on the telescopes, which results in the increasing telescope’s primary mirror. Considering the factors such as primary mirror material, processing, testing, deformation, costs, transportation and so on, the largest primary mirror diameter of telescope can be 8m. US astronomers have proposed the method of stitching several small mirrors together to make a large primary mirror, which is combining a series of secondary mirrors to realize the same optical properties as a single primary mirror. The technology of mirror stitching of the primary mirror breaks the restrictions of telescope primary mirror diameter, and ha s been widely used in the researching and manufacturing of modern large telescopes. In the process of segmented mirror fabrication and assembly, the stitching measurement technology has become a difficult and hot point, and has been developing rapidly in recent years. Existing methods of secondary mirror stitching measurement can reach a high level on accuracy. However, most of them are complex in principle, they often requires harsh on detection conditions, which restrictive much in practical applications.Although the existed telescopes usually use spherical or aspheric mirrors as primary mirror, large flat mirrors can be used as second mirror of space telescopes, to serve as reflecting correctors. Further, in the broader sense, flat mirrors can be treated as free form surfaces, spherical or aspheric mirrors with special properties. Thus the study and theories of flat mirror stitching can not only be used in large flat mirror stitching, but also be extended for mirrors with other shapes.Based on structured light reflection and camera calibration, this paper mainly researches on secondary flat mirror stitching measurement, to provide a simple structure, high efficiency, appropriate accuracy, and high environment adaptability detection method for segmented mirror confocal adjustment stage. By studying the characteristic points extraction algorithms of camera calibration patterns, we present a new characteristic points extraction algorithm with high accuracy, anti-noise and anti-defocus feature. Then we propose a method on flat mirror tilt and displacement measurement, prove the feasibility of the method with a series of experiments, and use the method in the flat secondary mirror real-time stitching measurement experiments. The main contents of this paper are as follows:1. Researching the existing large-diameter telescope stitching detection methods around the world and future research trends, we select five representative methods to analyze their characteristics and difficulties, namely Shack-Hartmann sensor method, Broadband & Narrowband co-phasing algorithm, Pyramid sensing technology, Michelson interferometer detection method and white light detection method based on the principle of the Michelson interferometer. And we research existing flat mirror tilt angle and displacement detection method, analyzes and compares the accuracy and applicability of the existing methods.2. Based on the comparison of camera calibration pattern and corresponding characteristic point extraction algorithms, we choose three commonly used calibration patterns: checkerboard pattern, Gaussian point matrix pattern, and 2D sinusoidal fringe pattern. We compare their characteristics point extraction algorithms and calibration accuracy used in the camera intrinsic parameters calibration. Through simulation and intrinsic parameters calibration experiments, we conclude that when affected by noise and defocus, the 2D sinusoidal fringe method based on Fourier phase analysis method has better performance than checkerboard method and Gaussian point matrix method, and has the lowest reprojection error of intrinsic parameter calibration, which proves that 2D sinusoidal fringe method has the highest accuracy in characteristic point extraction.3. In the characteristic point extraction of 2D sinusoidal fringe pattern based on Fourier phase analysis, the characteristic points should not contain edge points due to the inherent property of the Fourier transform; otherwise it would significantly increase the extraction error. To solve this problem, we propose the use of phase shifting method to replace the Fourier method in extracting phase. The difference is that each point phase value calculated from Fourier method is affected by adjacent points, but the phase shifting method can calculate the phase of each point independently. Phase extraction using the phase shifting method increases the application scope of the 2D sinusoidal fringe in extracting characteristic points. When handling with characteristic points including edge points, the extraction accuracy can maintain in a good value.4. Flat mirror tilt and displacement measurement principle based on structured light reflection and camera calibration is proposed in this paper. Through the introduction of the virtual image plane coordinate system, we convert the flat mirror tilt and displacement measurements into virtual image plane tilt and displacement measurements of calibration points, which is a reverse application of structured light reflection technology. The measuring principle is simple and easy; measuring equipments are widely used experimental equipments, which can save much cost. Experimental results prove that the flat mirror tilt measurement accuracy using this method is around 1″, the displacement measurement accuracy is under 1μm, and the measurement dynamic range is large up to mm level. Flat mirror pose measurement based on structured light reflection has relatively low demands on the environment. It does not require darkroom conditions, and tolerant with air turbulence, temperature, humidity changes and so on.5. We set a virtual reference plane target at first, and then use the method of this paper to measure and adjust a flat mirror, make it as close as possible to the target plane. Online adjustment experiments show the tilt angle and displacement have reached optimum accuracy, which proves that our method can be used to adjust a mirror to a specified location.6. Experiments of two flat mirror adjustment stitching have been taken out. We use two flat mirrors; one is fixed while another can be adjusted. We measure the tilt and displacement differences between the two mirrors using structured light reflection method, until the second mirror is coplanar with the first one. After a series of online real-time adjustments, we get numerical stitching results that the tilt error of about 6", and the displacement measurement error of about 0.5μm. The precision is expected to be higher if the resolution of experiment equipments is higher.7. The uncertainty of intrinsic parameters and the different chosen point matrix can affect the flat mirror stitching results. Through analysis and experiments, we found that the main source of error that affects 2D sinusoidal fringe structured light reflection measurement of flat mirror tilt and displacement is the camera calibration error, which including intrinsic parameters calibration error and error introduced by mirror surface, the synthetic performance is external parameter error. Further, we propose some measures to reduce or avoid those errors.