Simultaneous measurement with multiple targets via laser feedback interferometry: an algorithm and application in absolute distance sensing

Laser feedback interferometry (LFI) is a compact and highly sensitive technique for non-contact sensing, typically limited to configurations involving a single external target. Extending LFI to simultaneous multi-target measurement remains a significant challenge due to the increased complexity introduced by multiple optical feedback paths. In this work, we present a unified theoretical and computational framework for modeling and solving the excess phase equation in LFI systems with one or more external reflectors. The proposed approach accommodates both weak and moderate/strong optical feedback regimes, enabling robust analysis for diverse operating conditions. To validate the model, we perform experimental measurements of absolute distances to two consecutive targets using a single laser source. The results show a strong agreement between simulation and measured LFI signals across a broad range of optical feedback strengths.