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The accurate measurement of spatial angle is the key technology for the plane flatness and guide rail straightness detections. This paper presents a lens-array-based optical system and an analytical model for micro spatial angle measurement. In this system, a collimated light beam passes through a fourarray-lenses arranged in pyramid shape and forms a regular array spots on CCD (Charge Coupled Device) sensor. The angels with respect to the axes of X, Y are calculated by analyzing the distance of these spots on the CCD, the distance between adjacent apertures on the lens array and the inclination angle between the lens array and the CCD. Using the Coordinate value of array spots on CCD, the angle around Z axis also can be calculated simultaneously. Finally, the accuracy of the proposed method is verified by comparing the measured results with the autocollimator, and it is shown that the proposed approach enabled to achieve RMS≤0.1″. Additionally, this measurement system which is consists of a laser source, lens arrays and CCD, compared with other methods, is smaller in volume and more convenient to carry.INDEX TERMS Image edge detection, Measurement by laser beam, Optical arrays.
The accurate measurement of spatial angle is the key technology for the plane flatness and guide rail straightness detections. This paper presents a lens-array-based optical system and an analytical model for micro spatial angle measurement. In this system, a collimated light beam passes through a fourarray-lenses arranged in pyramid shape and forms a regular array spots on CCD (Charge Coupled Device) sensor. The angels with respect to the axes of X, Y are calculated by analyzing the distance of these spots on the CCD, the distance between adjacent apertures on the lens array and the inclination angle between the lens array and the CCD. Using the Coordinate value of array spots on CCD, the angle around Z axis also can be calculated simultaneously. Finally, the accuracy of the proposed method is verified by comparing the measured results with the autocollimator, and it is shown that the proposed approach enabled to achieve RMS≤0.1″. Additionally, this measurement system which is consists of a laser source, lens arrays and CCD, compared with other methods, is smaller in volume and more convenient to carry.INDEX TERMS Image edge detection, Measurement by laser beam, Optical arrays.
In space-based gravitational wave detection, establishing ultra-long-distance and ultra-high-precision laser links between satellites is achieved through the laser acquisition and tracking system. The laser spot centroid positioning method, which offers low computational complexity and strong adaptability to beam shape, is currently the core measurement method during the laser acquisition phase. However, due to various interference factors encountered in practical tests, this algorithm often falls short of meeting the extremely high requirements. To address this challenge, this paper first defines the specific performance criteria for the centroid positioning method based on the needs of laser acquisition in gravitational wave detection. It then comprehensively analyzes how detector noise, window truncation effects, and beam wavefront aberrations impact the accuracy of angular measurements. Using derived analytical expressions, an improved centroiding algorithm is proposed to mitigate the effects of detector noise and wavefront aberrations simultaneously. Numerical simulations are conducted to design the specific parameters for the algorithm and the system, resulting in the ability to achieve an angular measurement accuracy of 60 nrad at the telescope front end.
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