Noise Limitations in Multi-Fringe Readout of Laser Interferometers and Resonators

Abstract

Laser interferometers that operate over a dynamic range exceeding one wavelength are used as compact displacement sensors for gravitational wave detectors and inertial sensors and in a variety of other high-precision applications. A number of approaches are available to extract the phase from such interferometers by implementing so-called phasemeters, algorithms to provide a linearised phase estimate. While many noise sources have to be considered for any given scheme, they are fundamentally limited by additive noise in the readout, such as electronic readout, digitisation, and shot-noise, which manifest as an effective, white phase noise in the phasemeter output. We calculated and compared the Cramer–Rao lower bound for phasemeters of some state-of-the-art two-beam interferometer schemes and derived their noise limitations for sub-fringe operation and for multi-fringe readout schemes. From this, we derived achievable noise performance levels for one of these interferometer techniques, deep-frequency modulation interferometry. We then applied our analysis to optical resonators and show that frequency scanning techniques can in theory benefit from such resonant enhancement, indicating that the sensitivities can be improved in future sensors.