High-Resolution Real-Time Displacement Measurement for Heterodyne Interferometers Using a Modular Lock-In Amplifier in an FPGA Architecture

Heterodyne interferometry is widely used in science, industry, research, and development. It is mainly applied, but not limited to, displacement measurement, phase difference imaging, vibration measurement, surface quality control, metrology, and lithography. The phase shift between the reference and test beam signals provides information about the path length measurement. Using commercial heterodyne interferometer platforms for real-time applications leads to high costs and a lack of flexibility. To advance in the production of modular and low-cost interferometer systems, we applied a lock-in amplifier (LIA) technique to process heterodyne interferometer signals implemented with a field-programmable gate array (FPGA), providing a trade-off between high resolution and wide bandwidth. The developed method reaches sub-nanometric resolution when tested on simulations and synthetic signals; however, a nanometric resolution is ensured in a real-world test. The actual interferometer has a fundamental optical resolution of L/2, without resorting to the interpolation method. The LIA-FPGA system provides L/45 higher resolution than could be obtained with the fringe counting method, meaning 14~nm with a helium-neon laser of 632.9913774~nm wavelength. In addition, the LIA-FPGA system produces a high-rate measurement at 5200 samples per second, enabling its use in real-time high-speed controllers essential for existing and forefront sophisticated applications. Modular characteristics allow low-cost integration of multiple axes in a single embedded system based on an FPGA.