Self-calibration measurement and uncertainty evaluation of lens focal length based on Fabry-Perot Interferometer

This paper proposes a self-calibration method for lens focal length measurement based on a Fabry-Pérot (F-P) etalon, and investigates uncertainty evaluation strategies in scenarios where measurement errors affect the results through indirect propagation. In the measurement method, the relationship between the diameters of interference rings and interference orders in area-array images is utilized, and the relative focal length is calculated using the least squares method. For uncertainty analysis, evaluation models suitable for both the Guide to the Expression of Uncertainty in Measurement (GUM) method and the Monte Carlo method (MCM) are established. In the Monte Carlo method, error propagation approaches are specifically studied for defocus error and pixel pitch error in focal length measurement. The results show that the GUM evaluation method fails to pass validation by MCM, mainly because the distribution of the relative focal length deviates from the t-distribution assumption. Furthermore, this study proposes an uncertainty evaluation process applicable to such indirect measurement models, which provides a valuable reference for complex optical measurement systems.