| Since Allen of Leiden University established the basic theory of vortex beam in 1992,the generation,detection and application of vortex beam has become a research hotspot all over the world.The applications based on vortex beam mainly involve communication,imaging,optical tweezers,detection and other fields.Among them,scholars have done a lot of research in the fields of communication,imaging and optical tweezers,established a complete theory and developed mature technology.However,the application of vortex beam in optical precision measurement is still in the development stage,and there are still many novel applications waiting for people to study.Aiming at the technical gap of vortex beam in radius of curvature(ROC)measurement,a set of ROC measurement scheme is established,which has high precision and large measuring range,by means of theoretical analysis,simulation analysis and experimental verification.At the same time,considering that the helical wavefront distortion of vortex beam will cause the measurement error of the ROC,this paper further proposes a helical wavefront detection method of the vortex beam.The failure of the traditional four-steps phaseshifting method in helical wavefront detection is theoretically studied,the corresponding solutions are given,which lays a foundation for the high-precision dynamic measurement of helical wavefront of vortex beam.The main works of this thesis are as follows:1.In this thesis,a ROC of spherical wave measurement method based on the interference between vortex beam and spherical wave is proposed.And the measurement principle and method of ROC of spherical wave is given,the measurable range is calculated,and the fitting accuracy of Fermat’s spiral coefficient by least square regression fitting method and robust M regression fitting method is simulated and compared,also the influence of wavefront error and random noise on the measurement accuracy of ROC is simulated.The Mach-Zehnder interferometer optical path is set up.And the measurement experiments of convex lens and concave mirror with nominal ROC of 60mm and 900mm verify the correctness of this method.2.A good wavefront is the key to achieve high-precision measurement.To avoid the influence of the wavefront distortion on the measurement accuracy of the ROC.A wavefront detection method for vortex beams based on conformal mapping-spatial phase-shifting interferometry is proposed.Using the basic mathematical principles of conformal mapping,the interferogram in log-polar coordinate is mapped to Cartesian coordinate.The traditional fourstep phase-shifting method is used to obtain the wrapping phase,and then the transverse shear least square method is used to expand the wrapping phase.Through inverse conformal mapping,the helical phase in log-polar coordinate is obtained,which overcomes the failure of the traditional four-step phase-shifting method in helical wavefront detection,and achieved fast and efficient helical wavefront measurement of vortex beam. |
