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We present a refractive index measurement method by measuring the longitudinal displacement of the converging rays after passing through a plane-parallel-plate sample. Using the wavefront difference method, the error source from the divergence angle of the beams is eliminated, and an analytical formula for refractive index calculation is derived. With a Fizeau interferometer, an experimental system for plane-parallel-plate sample testing is proposed to verify the principle. Experimental results indicate that the order of its accuracy is 10−4. [ABSTRACT FROM AUTHOR]

The orbital angular momentum (OAM) of light has garnered significant interest in recent years owing to its various applications, and extensive creative research has been conducted to generate OAM. However, the particular helical phase structure of an optical vortex leads to nonsmooth and discontinuous phase profiles and hinders the accurate recovery of the phase distribution of the vortex beam. Significantly, the existence of a wavefront dislocation leads to the failure of the traditional phase unwrapping algorithm. At the same time, it is essential to detect the wavefront of OAM modes in real-time for free-space optical communication and optical precision measurement. Therefore, we designed conformal mappingâ€"spatial phase-shifting interferometry and achieved rapid and high-precision wavefront measurements for the OAM modes. The wavefront of the OAM modes with a topological charge of 1, 2, 4 and 6 were measured, respectively. The results were significantly consistent with the anticipated results based on simulations. This study reveals the mathematical mechanism behind the forked fringe patterns and presents a method for demodulating the helical wavefront from the forked fringe patterns. [ABSTRACT FROM AUTHOR]