Implementation of a feedback coupling factor and a linewidth enhancement factor estimation method for a self-mixing...

In self-mixing interferometry, a hardware system for accurate estimation of linewidth enhancement factor (α) and optical feedback coupling factor (C) is vital for real-time high-resolution displacement sensing using phase unwrapping methods. To address this problem, this work proposes a novel FPGA implementation of the Modified Newton Method (MNM) for faster and more accurate C and α estimation. After MNM's implementation, it was also integrated into the Hilbert transform-based phase unwrapping method (HT-PUM), producing a novel MNM-HTPUM method. A detailed comparison between MNM-HTPUM, HT-PUM, and the unrolled version of HT-PUM revealed significant improvements. MNM-HTPUM displayed a remarkable 2.6-fold improvement in C estimation and an impressive 3.9-fold enhancement in α estimation compared to HT-PUM. Moreover, it utilized, on average, 1.15 times fewer resources compared to HT-PUM, and 372,000 times fewer resources compared to UHT-PUM. In terms of latency, MNM-HTPUM processed data 712.8 times faster than HT-PUM and 3.5 times faster than UHT-PUM. Operating at a low dynamic power of 0.45W with a clock speed of 10 ns, MNM-HTPUM can measure a maximum target velocity of 2.75 m/s, making it ideal for high-bandwidth applications. This implementation corresponds to a significant advancement in self-mixing interferometry, paving the way for embedded and cost-effective SMI sensors capable of high-resolution displacement sensing.