Residual Modulation Frequency Induced Phase-Drift Noise in Photoacoustic Ring-Down Spectroscopy

Abstract

Abstract Photoacoustic ringdown spectroscopy (PARS) provides a transient readout route for rapid photoacoustic sensing, but its stability is limited by low-frequency amplitude fluctuations that are not fully explained by conventional laser-power drift, detector noise, or environmental perturbations. Here, we identify residual modulation frequency (RMF) as a deterministic phase-drift source caused by frequency incoherence between sinusoidal modulation and sawtooth wavelength scanning. A phase-walk-off model shows that when the modulation frequency is not an exact integer multiple of the scanning frequency, the modulation phase sampled at the absorption peak changes progressively across successive scan cycles. Controlled detuning experiments demonstrate that the measured oscillation frequency follows the imposed RMF, while synchronized operation at an RMF of 0 Hz markedly improves signal stability, enhances SNR by a factor of 10 to 40, and reduces short-time Allan deviation compared with off-synchronized conditions. An iterative frequency-locking workflow is further developed to keep the modulation frequency near the acoustic optimum while constraining it to the integer-multiple synchronization condition. This work clarifies a synchronization-defined noise mechanism in PARS and provides a practical frequency-design rule for improving the reproducibility and stability of scanned, sinusoidally modulated photoacoustic sensing systems.