Abstract
Lock-in amplification (LIA) is an effective approach for recovery of weak signal buried in noise. Determination of the input signal amplitude in a classical dual-phase LIA is based on incoherent detection which leads to a biased estimation at low signal-to-noise ratio. This article presents, for the first time to our knowledge, a new architecture of LIA involving phase estimation with a linear-circular regression for coherent detection. The proposed phase delay estimate, between the input signal and a reference, is defined as the maximum-likelihood of a set of observations distributed according to a von Mises distribution. In our implementation this maximum is obtained with a Newton Raphson algorithm. We show that the proposed LIA architecture provides an unbiased estimate of the input signal amplitude. Theoretical simulations with synthetic data demonstrate that the classical LIA estimates are biased for SNR of the input signal lower than −20 dB, while the proposed LIA is able to accurately recover the weak signal amplitude. The novel approach is applied to an optical sensor for accurate measurement of NO concentrations at the sub-ppbv level in the atmosphere. Side-by-side intercomparison measurements with a commercial LIA (SR830, Stanford Research Inc., Sunnyvale, CA, USA ) demonstrate that the proposed LIA has an identical performance in terms of measurement accuracy and precision but with simplified hardware architecture.
Highlights
Lock-in amplifier (LIA) is an effective device capable of recovering weak signal buried in high noise level
We introduce in the present work a new dual-phase Lock-In Amplification (LIA) processing for coherent detection
We show with theoretical results and synthetic experimentation that the proposed coherent detection estimate is more accurate than the classical incoherent detection estimate
Summary
Lock-in amplifier (LIA) is an effective device capable of recovering weak signal buried in high noise level. We show that these observations are unbiased even at low SNR This new approach requires, a precise estimate of the phase delay φk. We introduce a linear-circular regression model to accurately estimate phase delays of the input noisy signal [12]. In the present work the circular regression of angular data is used to estimate the phase shift of the input signal [23]. The paper is organized as follows: the Section 2 describes the architecture of the proposed circular regression-based dual-phase digital LIA. The linear-circular model and method used to accurately estimate the phase delay are presented in the Section 3. High-sensitivity measurements of NO2 trace gas in the atmosphere are presented and the performance of the proposed LIA is evaluated in comparison with a commercial LIA (SR830, Stanford Research Inc.)
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