1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
2. Jinhua Guangfu Hospital, Jinhua 321004, China
Abstract：Time-dependent absorption spectroscopy, such as cavity ring-down spectroscopy (CRDS) and cavity attenuated phase-shift spectroscopy (CAPS), is a new type of absorption spectroscopy technology developed in recent thirty years. It has the advantage of high detection sensitivity, fast response, and not being affected by the fluctuation of light source intensity. Traditional absorption spectroscopy is based on the Lambert-Beer law, such as direct absorption spectroscopy (DAS), wavelength modulation spectroscopy (WMS), cavity enhanced absorption spectroscopy (CEAS) and so on. The weak absorption of material is hard to be measured once the background light signal is strong. And the instability of the light source also brings some limits to the detection. The time dependent absorption spectroscopy can make up for the shortcomings of traditional absorption spectrometry to a large extent because of its characteristics of not being affected by the fluctuation of light source intensity, but it also has its own limitations. First of all, CRDS and CAPS are not theoretically unified. And the existing theory can only apply to Pulse-CRDS with short pulse light where the pulse width is far less than the time constant of the resonant cavity itself. For long pulse-width light source or low reflectivity (less than 99.9%) cavity, the existing theory will no longer apply. As for CAPS, the modulation signal of the light source must be periodically sinusoidal or square-wave modulated signal. And there are no other types of periodic modulation signals and aperiodic signals mentioned. In view of the limitations of the time-dependent absorption spectroscopy mentioned above, we present a novel analytical method on time-dependent spectroscopy in this paper. The resonant cavity is regarded as a first-order sensing system. We use the first-order transfer function to unify the theory of time-dependent absorption spectroscopy and prove the consistency between the existing theoretical results and the derivation results under the novel method on the formula derivation. For Pulse-CRDS, we use Gaussian pulse light to derive the expression of transmitted light intensity under first-order sensing theory and simulate a series of different pulse widths γ, resonant cavity time constants τreal, and fitted time constants τanal. After analysis and comparison, we find the deviation of τanal and τreal is less than 1% when γ<0.3τreal. And the experimental conditions will be no longer sufficient when γ>0.3τreal. In order to make Pulse-CRDS used with long pulse-width light, a correction function is given in this paper. And the error of the corrected ring-down time is less than 1% when the pulse-width is 0.3 times greater than the ring-down time. For CAPS system, we build an experimental platform with LED light source centered at 405nm and square wave modulated. Then we measure the phase difference and the peak value at different frequencies. The time constants τ calculated respectively by the phase-frequency and amplitude-frequency characteristic derived from the first-order transfer function are approximately the same, 7.24 and 7.25 μs with residual ranges of [-0.01, 0.02] and [-0.02, 0.025] respectively. The result shows that the theory of the first-order sensing system is fully applicable to the signal analysis of time-dependent spectroscopy. And the theory of first-order sensing system also makes the theory of time-dependent spectroscopy unified.
Key words：Time-dependent absorption spectroscopy; Cavity ring-down spectroscopy; Phase-shift spectroscopy; First-order transfer function; Time constant
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