Graduate Thesis Or Dissertation
Superresolved Swept-Wavelength Interferometry: Fundamental Limits and Use in Three-Dimensional Surface Characterization Public Deposited
The high signal-to-noise ratios typical of swept-wavelength interferometry (SWI) enable distance measurements to be superresolved with theoretical 2σ uncertainties as low as 1x10-4 of Fourier transform-limited resolution. This result was obtained by numerically comparing four frequency estimation methods: Local Linear Regression (LLR), Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), Nonlinear Least Squares (NLS), and Candan’s Estimator (CE). For distances greater than 5 to 20 times the SWI system’s transform-limited resolution, it was shown that CE provides the fastest and most accurate results, with precision approaching the Cramér–Rao bound.
Experimentally, the accuracy and precision of superresolved SWI were verified by comparing superresolved distance measurements against a known standard. In an SWI system with 34 μm transform-limited resolution, accuracy was shown to be greater than 2x10-3 of the transform limit, while thermal drift during data collection was shown to degrade the system’s 1σ precision to approximately 9x10-2 of the transform limit.
In combination with superresolution, swept laser sources with long coherence lengths create the possibility for time-multiplexed SWI systems to make high-accuracy, single-shot, non-contact, three-dimensional measurements of arbitrarily shaped surfaces. An algorithm for reconstructing surface shapes from SWI distance measurements was developed, and an 8-channel prototype system was used to characterize the surfaces of an optical flat, a cylindrical lens, and a coin. Resulting accuracies of ±1 m demonstrate that this measurement
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