Hardware implementation and comparison of displacement retrieval algorithms for a laser diode-based optical feedback interferometric sensor

Abstract

Optical feedback interferometer (OFI) lasers, also called self-mixing (SM) lasers, have been widely explored over the last couple of decades due to their low cost, compactness, and self-aligned nature and they provide a very good solution for measurements of displacement, vibration, distance, velocity, etc. The SM effect takes place when a part of the laser beam is fed back to the active laser cavity after reflecting from the target. The reflected beam interferes with the emitted beam and hence the optical and spectral characteristics of the laser get changed. To retrieve the vibration or displacement signal of the target from the SM signal, different postprocessing algorithms have been proposed, such as the phase unwrapping method (PUM). The first step of the PUM leads to the coarse estimation of the laser phase and the final step is an iterative joint estimation of 2 parameters, namely laser coupling coefficient $C$ and linewidth enhancement factor $\alpha $. To make this algorithm applicable for real-time measurements, parallel joint estimation for a wide range of $C$ and $\alpha $ values needs to be done. In this research, 3 algorithms, namely PUM, direct fringe unwrapping (DFU), and improved DFU (IDFU) were tested for FPGA implementation by using Verilog HDL (hardware description language) so that more precise and real-time vibration and displacement signals of targets could be extracted from the SM sensor in an embedded systems environment. These algorithms were developed using Verilog HDL for implementation on the Xilinx Spartan-3 Xcs400-FG320 development board. Our designed IDFU algorithm performed $0.492\, $times better than the parallel PUM algorithm in maximum clock frequency and $1.53$ and $1.21$ times better than the PUM in slice registers and LUT utilization of hardware resources, respectively. The designed DFU algorithm can operate $1.355$ times better than IDFU in maximum clock frequency and $25.34$ and $14.25$ times better than IDFU in slice registers and LUT utilization of hardware resources, respectively.