Novel applications and stabilisation for widely wavelength modulated laser interferometry for precision dimensional metrology.

The need for precision dimensional metrological techniques is always increasing, including high precision displacement measuring metrology used to precisely and accurately position stages, components and machines. Laser interferometry is widely considered the most precise technique available for single dimensional displacement measurements, however extending this to multiple dimensions typically involves complex and costly interrogation systems. In this thesis, a series of novel multi-dimensional stage encoder designs and experimental results are presented as an application of a state-of-the- art metrological technique, that uses sinusoidal wavelength modulation and range-dependant signal processing to multiplex the signals from multiple interferometers into a single interferometric signal. Using range-resolved interferometry (RRI), a series of interferometers comprising measurements in multiple dimensions are multiplexed onto a single photodetector, which are then are independently and concurrently demodulated and evaluated. This technique is applied to novel designs for a 2-dimensional displacement encoder, a 3-dimensional displacement encoder and a dual-beam angle encoder, where unlike prior work which has typically required complex optical setups involving polarisation-sensitive optical components and detectors, uses only minimal, simple bulk optic components to evaluate multiple dimensions simultaneously. In this work, nonlinearities below 1 nm along with typical displacement noise levels below 0.4 nm/√Hz are presented for experimental results of ±50 µm controlled stage motions, showing results which are highly comparable to existing techniques. Further to this, in order to make high precision results with confidence, high-stability lasers are required. In non-modulated and weakly modulated wavelength regimes, there are a significant number of techniques available for laser stabilisation, for both short-term and long-term requirements and linked to highly stable references. However, for widely-wavelength modulated techniques such as RRI, where the modulation depth is several orders of magnitude greater than standard reference widths, the vast majority of existing techniques are either unsuitable or significantly less-effective. In this thesis, a novel technique for long-term stabilisation of a widely wavelength modulated laser to a high stability reference standard is presented. Introduced as "swept absorption line locking", the principle behind this technique, in addition to experiments to test the efficacy of this technique are presented. Included in this, is comparison to a highly-stabilised helium-neon laser, which is often considered a "gold-standard" for stability, where co-linear displacement measurements of a Michelson interferometer are performed and compared to determine the RRI evaluation wavelength. The results presented here show fractional stabilities as low as 6×10−⁸ over timescales of ∼1000 seconds using this novel stabilisation technique, and the comparison to the HeNe laser interferometer shows good agreement between the calculated RRI evaluation wavelength and the expected stabilised value within calculated uncertainties.