Enhanced performance of self-mixing interferometry for piezoelectric material displacement measurement using the data fusion method

Piezoelectric materials play a pivotal role in enabling nano-positioning. However, their precision control is hindered by hysteresis, creating a need for a low-cost, non-contact displacement sensor capable of achieving high-precision control. While hysteresis models and self-mixing interferometry (SMI) with phase unwrapping methods offer cost-effective solutions for monitoring the displacement of piezoelectric materials, their versatility is often limited in complex scenarios. This study proposes a fusion method that combines the piezoelectric material drive voltage with SMI displacement measurements using the fringe counting method. This approach provides a balanced trade-off among cost, accuracy, and versatility for displacement monitoring. Compared to SMI alone, the proposed method reduces the root mean square error (RMSE) by 30.1 % and the maximum error by 45.5 %, achieving an accuracy of 120.7 nm and an RMSE of 45 nm. These improvements make the method particularly well-suited for cost-sensitive applications requiring high precision.