Cavity ring-down spectroscopy (CRDS) is a laser spectroscopy used to measure the decay time of light in an absorbing medium. Owing to its advantages of high precision, high sensitivity, immunity to light intensity fluctuations, and rapid response, it has been widely applied in fields such as greenhouse gas monitoring, aerosol extinction detection, low-loss mirror reflectivity measurement, and analysis of semiconductor material properties. During the detection process, due to the weak intensity of the output light, amplification of the detection signal is necessitated. However, the gain-bandwidth product of the detection system remains constant, resulting in a corresponding reduction in the system’s bandwidth as the amplification factor increases. When the bandwidth is excessively narrow, it can induce distortions in the detected decay curve, reducing the accuracy of ring-down time measurements. To address this issue, this study proposes a cavity decay curve restoration method based on Wiener deconvolution transformation. By using the detector system’s transfer function to restore the decay curve, this method reduces the impact of high-frequency noise on the deconvolution, effectively enhancing the measurement accuracy of cavity ring-down spectroscopy.

The distorted decay curve is restored using Wiener deconvolution. First, the step response curve of the detector is measured to identify the transfer function of the detector system. Subsequently, the decay signal is measured using the cavity ring-down spectrometer, during which the detected signal is distorted compared to the original signal due to the influence of the detector’s response. To facilitate computation, the measured signal is subjected to a Fourier transform, converting the decay curve into a frequency-domain signal. This frequency-domain signal contains the spectrum of the decay curve modulated by the detector system’s transfer function, as well as the noise spectrum. To reduce the impact of high-frequency noise on the deconvolution and accurately restore the decay curve spectrum, Wiener filtering is applied to the frequency-domain signal based on the transfer function of the detector system, resulting in a restored frequency-domain signal. The restored frequency-domain signal is then transformed back into the time-domain using an inverse Fourier transform, yielding a corrected signal closer to a single-exponential decay. Finally, a single-exponential fit is performed to obtain the corrected ring-down time.

To validate the efectiveness of the proposed method, simulations and experiments were conducted. In the simulations, the responses of first-order systems with three different bandwidths to the decay curves were first simulated, as shown in Fig. 2. As the detector bandwidth narrowed, the distortion of the measured decay curves increased, and the measured decay time became longer. Subsequently, simulations were performed to investigate the effect of detector bandwidth on gas concentration measurements. Using the CO₂ absorption spectrum from the HITRAN database, the impacts of different bandwidths on the absorption spectrum measurement were simulated, with the results shown in Fig. 3. As the detector bandwidth narrowed, the measured spectral area decreased, resulting in lower measured gas concentrations. Next, with the detector bandwidth set to 1 MHz, the effects of different ring-down time on the decay curve were simulated (Fig. 5). The results indicate that shorter ring-down time is more significantly affected by the detector bandwidth. Wiener deconvolution was then applied to restore signals with three different ring-down time. The restoration reduced the measurement error of ring-down time to lower than 1/20 of uncorrected result, demonstrating that this method effectively mitigates the influence of detector bandwidth in the simulations. For experimental validation, a frequency-swept continuous-wave cavity ring-down spectroscopy system was constructed to measure decay curves and absorption spectrum. In the experiments, the step response function of the detector was first measured to determine its system transfer function (Fig. 7). The Wiener deconvolution method was then applied to correct the measured cavity ring-down time and the reference CO₂ spectrum (Fig. 13). Experimental results show that the measurement error of the reference CO₂ concentration was reduced to within the nominal range of the reference gas. These results indicate that the deconvolution method effectively corrects decay curve distortions caused by detector responses, thereby improving the measurement accuracy of the cavity ring-down spectroscopy system.

We introduced a ring-down time measurement correction method based on Wiener deconvolution. This method effectively enhances the accuracy of cavity ring-down spectroscopy (CRDS) measurements. Compared to using a broad-bandwidth detection system, this method allows for higher measurement accuracy with a low-cost, narrow-bandwidth system, thereby contributing to a reduction in instrumentation costs. The restoration performance of simulated decay curves demonstrate that for decay curves affected by a 1 MHz bandwidth detector, this method reduced the measurement error of ring-down time to lower than 1/20 of uncorrected result, with the fitting residuals stabilized below 0.009. These results indicate that the method effectively mitigates distortion in the decay curves and restores their original profiles. In the experimental measurement of reference CO₂, the method accurately restored the decay curves and the absorption spectrum. Consequently, the concentration measurement error decreased from 4.99% to 0.25%, well within the nominal uncertainty of ±1%. This demonstrates that the proposed method meets the accuracy requirements of CRDS for precise measurements.