Research On Lens Focal Length Detection Method Based On Single Grating Talbot Effect

Medium focal length optics lenses have been widely used in high-power laser controlled nuclear fusion,space optical system and astronomical telescopes optical system.Due to the small numerical aperture of medium focal length optical elements,the focal length measurement is easily affected by external factors such as air disturbances and vibrations.Focal length measurement of medium focal length optical elements has become one of the hotspots and difficulties in the field of optical measurement.Among many focal length measurement methods,the focal length measurement method based on the Talbot effect has been an important way to solve this problem for its simple optical path,stable and reliable performance.In this paper,a focal length measurement method using single grating based on Talbot effect is studied.Firstly,the traditional Talbot effect and the principle of using it to perform focal length measurement is explained.The physical parameter which carrying the information of the focal length value is found to be grating structure period of Talbot image.Secondly,the frequency domain sub-pixel positioning technology is applied to measure grating structure period of Talbot image.The feasibility of the solution is verified by simulation in MATLAB.Three sub-pixel algorithms are compared: centroid algorithm,Gaussian fitting algorithm and spatial moment algorithm.The centroid algorithm is optimized and improved to be iterative centroid algorithm.In addition,the performance of the centroid iterative algorithm is evaluated.The errors of noise,initial phase,and tilt angle of the grating Talbot image are simulated,respectively.The centroid iterative algorithm is found to be more accurate(accuracy reached 0.02 pixels)when the number of fringes is between 100 and 230.Thirdly,the focal length measurement range and its corresponding parameter selection are analyzed.The error analysis of the system is carried out,and the influence of distortion is analyzed.A simple method for measuring distortion is given,and the feasibility of this method is verified by simulation in Zemax.Finally,the focal length measurement system is set up.Two test lenses with focal length design values of 38059.52 mm and 59418.2mm are selected for system accuracy measurement experiments and stability measurement experiments.The experimental results show that system relative error was less than 1%,and relative standard deviation was less than 0.2%,the stability of system is high-quality.