Research On Measuring Method Of Curvature Radius And Focal Length Of Spherical Optical Element

Spherical optical elements are widely used in laser fusion,photolithography,space observation and medical detection because of their simple structure,low cost and easy assembly.Curvature radius and focal length are the key parameters of spherical(reflection and transmission)optical components.The high precision measurement of curvature radius and focal length has great influence on the machining quality and performance guarantee of spherical optical components.Most of the existing high precision measurement methods have complicated adjustment and analysis process,and the measurement efficiency is difficult to improve.How to achieve fast and high precision measurement of focal length and radius of curvature through low-cost experimental equipment and simple analysis and operation,it has important practical significance for industrial detection and the guarantee of optical system performance.In order to solve the above problems,this thesis carried out the following work:1.An iterative correlation coefficient matching strategy is proposed to achieve high-precision measurement of curvature radius.This method inherits the advantages of low cost and easy operation of Newton’s ring method.The phase introduced by the optical path difference of the measured system is obtained by theoretical derivation.A simple error correction method is given to avoid the complicated error acquisition of the return path,and an interference matching model is established.The interference matching model was used to simulate the interference fringes corresponding to different curvature radius within the search range.The correlation coefficient between each simulated interferogram and the actual collected interferogram was calculated,and the curvature radius corresponding to the maximum correlation coefficient was the output curvature radius.This method only uses a single interferogram throughout the entire measurement process,which will reduce data acquisition requirements and improve measurement efficiency.In the experiment,a Twyman-Green interference measurement optical path was constructed and concave mirrors with curvature radius of 101.6 mm and 1000 mm were tested.The relative errors of the measurement results were 0.013 % and 0.024 %,respectively.2.Although the above iteration correlation coefficient matching strategy achieves high precision measurement in a simple and low-cost way,its iteration calculation process will reduce the measurement efficiency with the increase of the radius of curvature to be measured.In order to ensure the measurement accuracy and greatly improve the measurement efficiency,a fast measurement strategy for large curvature radius is proposed.This method uses a large step length to find a rough solution within a wide search range,and then constructs a small step length refined search range based on this rough solution,which is convenient for quickly determining high-precision measurement results.The simulation and experimental results show that this method can be flexibly applied to different interference systems,greatly improve the measurement efficiency,and the measurement of large curvature radius can be completed in only ten seconds or even a few seconds.In the experiment,the Twyman-Green interference system and the Fizeau interference system were taken as examples,and the concave spherical mirrors with curvature radius of 1000 mm and 41400 mm were tested.The relative errors of the measured results were 0.020 % and 0.076 %,respectively,and the two measurement processes took 7.1 s and 6.7 s,respectively.3.A differential symmetric focal length measurement method is proposed to address the cumbersome theoretical analysis and measurement procedures in existing focal length measurement methods.This method uses a precision displacement table to control the CCD to move once in front of and behind the symmetrical initial acquisition position,and collects three interferograms at equal differential distances.According to the theory,the three interferogram satisfies the equation of differential distance ?L,and the solution corresponding to the minimum value of equation is the focal length of the lens to be measured.This method eliminates the influence of initial position distance error by means of differential symmetry,simplifies the theoretical analysis process,and reduces the influence of environmental factors on the experiment.In the experiment,a convex lens with focal length of 35 mm and 175 mm was measured by Mach-Zehnder interferometric optical path.The relative errors of the measurement results are 0.029 % and 0.04 %,respectively,and the time consuming is 7.3 s and 47.3 s,respectively.For the measurement of long focal length lenses,the idea of " determining coarse solutions with large ranges and large steps,and determining accurate solutions with small ranges and small steps" proposed in the measurement strategy of curvature radius above can be combined to further improve the measurement efficiency.