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Maximum-likelihood estimation for frequency-modulated continuous-wave laser ranging using photon-counting detectors.

Baris I Erkmen1, Zeb W Barber, Jason Dahl

  • 1Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA. baris.i.erkmen@jpl.nasa.gov

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Summary
This summary is machine-generated.

This study analyzes photon-counting detectors for frequency-modulated continuous-wave (FMCW) range estimation. The maximum-likelihood estimator approaches the quantum limit under specific conditions, outperforming Fourier transform methods.

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Area of Science:

  • Photon counting detectors
  • Optical metrology
  • Signal processing

Background:

  • Frequency-modulated continuous-wave (FMCW) systems are crucial for high-resolution range estimation.
  • Photon-counting detectors offer enhanced sensitivity but present unique challenges like subunity quantum efficiency, dark counts, and dead time.
  • Understanding the fundamental limits of FMCW range estimation with these detectors is essential for advancing optical sensing technologies.

Purpose of the Study:

  • To determine the minimum achievable mean-square error in FMCW range estimation using photon-counting detectors.
  • To derive and analyze the Cramér-Rao bound for this specific scenario.
  • To develop and evaluate a maximum-likelihood (ML) estimator for FMCW range estimation with photon-counting detectors.

Main Methods:

  • Derivation of the Cramér-Rao bound starting from the probability density function of photon-arrival times.
  • Development of a maximum-likelihood (ML) estimator for arbitrary frequency modulation.
  • Simulation of the ML estimator's performance against the standard quantum limit.
  • Analytic approximation of performance thresholds for linear frequency modulation.
  • Comparison of ML estimator performance with conventional Fourier transform (FT) frequency estimation.

Main Results:

  • The Cramér-Rao bound was derived, revealing three important asymptotic regimes.
  • The ML estimator's performance approaches the standard quantum limit only within specific mean received photon thresholds.
  • Analytic approximations for these thresholds were provided for linear frequency modulation.
  • The ML estimator was shown to be equivalent to the FT estimator when the reference arm is significantly stronger than the target return.
  • In weak reference field scenarios, the FT estimator was found to be suboptimal by approximately a factor of √2 in root-mean-square error.

Conclusions:

  • The derived ML estimator provides a theoretically predicted improvement over conventional FT methods in FMCW range estimation with photon-counting detectors.
  • A proof-of-concept experiment validated the ML estimator's superior performance, achieving the predicted enhancement.
  • The findings establish a benchmark for FMCW range estimation performance with photon-counting detectors, particularly in low-light or weak-signal conditions.