Parameter estimation based on the linear concise fractional Fourier transform

Estimating Newton's ring parameters using the Concise Fractional Fourier Transform (CFRFT) faces accuracy and complexity challenges due to its nonlinear quadratic phase term. This paper proposes the Linear Concise Fractional Fourier Transform (LCFRFT), which linearizes the quadratic phase-term coefficients to decouple the fringe coefficients and the lens's curvature radius. Simulations and experimental validations confirm LCFRFT's superiority in various noise environments. In real-world tests on 23 images with a 1.443 m curvature radius, LCFRFT reduced the average estimation error from 2.98% (CFRFT) to 1.71% at a step length of 50. Notably, LCFRFT processed these interferograms in just 29.161 s. To achieve a comparable error level, CFRFT required a step length of 300, extending processing time to 165.956 s. Overall, LCFRFT provides a robust, high-precision and efficient metrology solution for scenarios involving large curvature radii and complex noise environments.