Understanding the sensitivity of cavity-enhanced absorption spectroscopy: pathlength enhancement versus noise suppression

Abstract

Cavity-enhanced absorption spectroscopy is now widely used as an ultrasensitive technique in observing weak spectroscopic absorptions. Photons inside the cavity are reflected back and forth between the mirrors with reflectivities R close to one and thus (on average) exploit an absorption pathlength L that is 1/(1 − R) longer than a single pass measurement. As suggested by the Beer-Lambert law, this increase in L results in enhanced absorbance A (given by αL with α being the absorption coefficient) which in turn favours the detection of weak absorptions. At the same time, however, only (1 − R) of the incident light can enter the cavity [assuming that mirror transmission T is equal to (1 − R)], so that the reduction in transmitted light intensity ΔI caused by molecular absorption equates to that would be obtained if in fact no cavity were present. The enhancement in A = ΔI/I, where I is the total transmitted light intensity, achievable from CEAS therefore comes not from an increase in ΔI, but a sharp decrease in I. In this paper, we calculate the magnitudes of these two terms before and after a cavity is introduced, and aim at interpreting the sensitivity improvement offered by cavity-enhanced absorption spectroscopy from this observable-oriented (i.e. ΔI and I) perspective. It is first shown that photon energy stored in the cavity is at best as intense as the input light source, implying that any absorbing sample within the cavity is exposed to the same or even lower light intensity after the cavity is formed. As a consequence, the intensity of the light absorbed or scattered by the sample, which corresponds to the ΔI term aforementioned, is never greater than would be the case in a single pass measurement. It is then shown that while this “numerator” term is not improved, the “denominator” term, I, is reduced considerably; therefore, the increase in contrast ratio ΔI/I is solely contributed by the attenuation of transmitted background light I and is ultimately down to the suppression of any measurement noise that is associated with it. The noise component that is most effectively suppressed is the type whose magnitude scales linearly with light intensity I, as is typical of noise caused by environmental instabilities, followed by the shot noise which scales as square root of I. No suppression is achievable for noise sources that are independent of I, a notable example being the thermal noise of a detector or of detection electronics. The usefulness of this “noise suppression” argument is that it links the sensitivity gain offered by a cavity with the property of measurement noise present in the system, and clearly suggests that the achievable sensitivity is dependent on how efficient the various noise components are “suppressed” by the cavity.