Optimization of air refractive index based on dispersive interferometry

Abstract

This study discusses the limitations of the multi-color method for air refractive index compensation and introduces the nonlinear objective refractivity optimization (NORO) to address these shortcomings. Utilizing a nonlinear objective function and the Davidon-Fletcher-Powel (DFP) optimization method, NORO provides precise, self-corrected geometric distance without the need for extensive environmental sensing or broad spectral coverage. Compared to the multi-color method, the NORO method reduces the minimum usable spectral range from 600 nm to 40 nm, achieving consistency with the empirical formula within 2.5 ppm using a 90 nm spectral range, significantly decreasing the dependence of algorithm accuracy on the spectral range. During a 4.5-hour long-term compensation, the relative residual compared to the empirical formula remains within 3 ppm, with a standard deviation of σ E  = 9.4 × 10−7. Additionally, in long-distance measurements compared with the empirical formula, the NORO method demonstrates an agreement within 1.89 × 10−7 m for distances up to 12 m, without requiring environmental parameter sensing.