Surface Parameter Error Measurement Of Aspheric Surface Based On The Nearest Sphere With Partial Compensation Interferometry

With the wide application and in-depth study of aspheric surfaces,the manufacture and metrology of high-precision aspheric surfaces are playing the key roles in the field of optics.And high-precision metrology technology is the prerequisite for manufacturing qualified optical elements.Generally,optical metrology systems should measure the surface figure error(SFE)and the surface parameter errors(SPEs)precisely.Among them,SPEs affect the focal length and classification basis for the aspheric surface,which mainly include vertex radius of curvature error and conic constant error.Currently,SPEs can be measured by profilometry,ray tracing method and null interferometry method.And to our knowledge,there is still lack of research on the measurement of SPEs with partial compensation interferometry(PCI).Hence,this dissertation focus on the measurement of SPEs in PCI system.The SPEs measurement of aspheric surface is required to have high precision,large dynamic range and certain generalities.The proposed SPE measurement of aspheric surface based on the nearest sphere with PCI could achieve the above requirements.And the content of this dissertation includes as follows:1.The existing SPEs measurement methods of aspheric surface are reviewed.Then we summarize the following three key problems to be solved in this field based on further survey:(1)the system modeling in PCI system;(2)the SPEs measurement of aspheric surface based on PCI method;(3)the coupling of errors.2.For the lack of system modeling in PCI system,the dissertation proposes the mathematical model of best compensation distance(BCD),based on which,the relative position of partial compensator,aspheric surface under test(SUT)and nearest sphere can be determined quickly.3.The dissertation proposes the basic SPEs measurement method of aspheric surface.Based on thegeometrical relationship between SPEs and BCD,theoretical equations are established to measure the SPEs.The calculation process can be simplified and the universality of measurement can be increased,and can also be extended to the measurement of high-order aspheric surfaces.4.For the coupling of errors,the dissertation proposes the principle of position compensation in PCI system,the elimination method of the influence of SFE,the elimination method of the influence of transfer coefficient,and the correction method of theoretical equations.Thus,the SPEs measurement system of aspheric surface with PCI can be established.Besides,the Fizeau interference locating method is adopted to exactly locate the position of aspheric surface in real PCI system.On this basis,the dissertation proposes a self-positioning PCI system based on deformable mirror or spatial light modulator.5.The experiment system is established to measure actual aspheric surfaces.The average relative measurement accuracy of the proposed method could be better than 0.02%for the vertex radius of curvature error and 2.00% for the conic constant error.The error analysis is conducted to evaluate the whole measurement system.Through the work of the dissertation,the SPEs measurement method of aspheric surface based on the nearest sphere with PCI is established,which is an effective method for the SPEs measurement of aspheric surface with simple calculation process,wide measurement universality and high measurement accuracy.