Superresolved swept-wavelength interferometry using frequency estimation methods.

Abstract

The high signal-to-noise ratios typical of swept-wavelength interferometry (SWI) enable distance measurements to be superresolved with 2σ uncertainties as low as 10-4-10-5 of Fourier transform-limited resolution. We compare three methods of superresolving SWI distance measurements: Local Linear Regression (LLR), Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), and Nonlinear Least Squares (NLS). We find that the superresolution method limits both measurement precision and minimum superresolvable distance. Measurement uncertainty is determined by both the superresolution method and the SWI hardware, while SWI hardware alone limits the maximum superresolvable distance. For very short distances, between 2 and 20 times the SWI system's Fourier transform-limited resolution, NLS provides unbiased estimates with the least uncertainty. At longer distances, LLR provides the fastest unbiased estimates. LLR and NLS are more noise tolerant than ESPRIT and are found to operate close to the Cramér-Rao bound. With sufficient SNR, they provide 1σ measurement precision of 10-4 of the transform limit.