Method and apparatus for enhancing the accuracy of CRDS measurements
A method and apparatus for enhancing the accuracy of spectroscopic measurements using a cavity ringdown spectrometer (CRDS) is provided. A first aspect of the invention consists of a novel algorithm for the processing of ring-down data that significantly reduces the amplitude of an exponential fitting artifact, and thereby gives a better estimate of the actual loss. The primary cause of the artifact is the presence of an unwanted backwards-traveling wave that counter-propagates within the ringdown cavity. Scattering due to small imperfections at the cavity mirrors produces this wave and its intensity may be minimized by adjustment of the mirror positions during cavity construction. A second aspect of the invention consists of an apparatus for measuring the backscattered wave within a cavity to allow such cavity mirror adjustments to be made.
1. A method for determining the ringdown time constant τ of the measurement performed by a cavity ringdown spectrometer by fitting the discrete function I F [kT] in accordance with the equation:
I F [kT]=A+B exp(− kT /τ)+ Ck 2 exp(− kT /τ)
wherein T is the sampling time, k is the sequence index, A represents the offset in the ringdown detector electronics, B represents the amplitude of the ringdown waveform and C is the correction which takes account of the mode coupling due to backscattering.
2. A method in accordance with claim 1 for determining the ringdown time constant τ of the measurement performed by a cavity ringdown spectrometer by first fitting the discrete function: I F [kT]=A′+B′ exp(−kT/τ′) which does not include the backscattering term and utilizing the values of A′, B′ and τ′ as initial values for a single iteration fit in the equation:
I F [kT]=A+B exp(− kT /τ)+ Ck 2 exp(− kT /τ).
3. A method in accordance with claim 2 wherein said first fitting is performed using the successive integration method of Matheson.
4. A method in accordance with claim 2 wherein said first fitting is performed using the modified successive integration method of Halmer.
5. A method in accordance with claim 2 wherein said single iteration fit is performed using the non-linear least squares fitting method of Levenberg-Marquardt.