Maximum - likelihood estimation forfrequency - modulated continuous - wave laser rangingusing photon - counting

We analyze the minimum achievable mean-square error in frequencymodulated continuous-wave (FMCW) range estimation of a single stationary target when photon counting detectors are employed. Starting from the probability density function for the photon arrival times, we derive the Cram ́er-Rao bound (CRB) and highlight three important regimes: the dark-noise-dominated regime wherein the CRB improves quadratically with the mean received photon number, the shot-noise-dominated regime (i.e., the standard quantum limit) in which the improvement is linear, and the dead-time-dominated regime wherein the CRB is constant. We show that if both signal and reference photons cost equal, the shot-noise-limited CRB is minimized when the local field strength is equal to that of the target-return field, and the average frequency-modulation energy determines the performance. Simulation of the maximum-likelihood (ML) estimator shows that its performance approaches the standard quantum limit only when the mean received photons are between two thresholds. We provide analytic approximations to these thresholds for linear frequency modulation. Finally, we report on a proof-of-concept experiment in which ML estimation outperforms conventional beat-frequency estimation. REPORT DOCUMENTATION PAGE (SF298) (Continuation Sheet) Continuation for Block 13 ARO Report Number Maximum-likelihood estimation forfrequency-mo Block 13: Supplementary Note © 2013 . Published in Applied Optics, Vol. Ed. 0 (2013), (Ed. ). DoD Components reserve a royalty-free, nonexclusive and irrevocable right to reproduce, publish, or otherwise use the work for Federal purposes, and to authroize others to do so (DODGARS §32.36). The views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy or decision, unless so designated by other documentation. Approved for public release; distribution is unlimited. ... 61101.1-PH-DRP Maximum-likelihood estimation for frequency-modulated continuous-wave laser ranging using photon-counting detectors Baris I. Erkmen, Zeb W. Barber, Jason R. Dahl 1,∗Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA. Spectrum Lab, Montana State University, Bozeman, MO 59717, USA. ∗Corresponding author: [email protected]