Incoherent broad-band cavity-enhanced absorption spectroscopy

Incoherent broad band cavity enhanced absorption spectroscopy (IBBCEAS), sometimes called broadband cavity enhanced extinction spectroscopy (IBBCEES), measures the transmission of light intensity through a stable optical cavity consisting of high reflectance mirrors (typically R>99.9%). The technique is realized using incoherent sources of radiation e.g. Xenon arc lamps, LEDs or supercontinuum (SC) lasers, hence the name. Typically in IBBCEAS, the wavelength selection of the transmitted light takes place after the cavity by either dispersive or interferometric means. The light is either directly focused onto the entrance slit of a monochromator and imaged onto a charge-coupled device (CCD) array via a dispersive optical element (e.g. a diffraction grating) or imaged onto the entrance aperture of a conventional interferometer. The spectrum is reconstructed taking the Fourier transform of the recorded interferogram. Similar to other cavity enhanced spectroscopic techniques, in IBBCEAS, the transmission signal strength is measured with and without the absorber of interest present inside the cavity ( I(λ) and I0(λ) respectively). From the ratio of the wavelength-dependent transmitted intensities, the effective reflectivity of the mirrors Reff(λ) and the sample path length per pass d inside the cavity, the sample's extinction coefficient α(λ) is calculated as:

α ( λ ) = ( I 0 ( λ ) I ( λ ) − 1 ) 1 − R eff ( λ ) d {\displaystyle \alpha (\lambda )=\left({\frac {I_{0}(\lambda )}{I(\lambda )}}-1\right){\frac {1-R_{\text{eff}}(\lambda )}{d}}}

The sensitivity (smallest achievable α for a given sample) increases for large mirror reflectivities and large path lengths in the cavity, which is maximal, if d equals the cavity length.(1-Reff) includes all unspecified losses per pass (e.g. scattering or diffraction losses) other than the losses due to the limited reflectivity of the cavity mirrors. Note that although the technique is often used for studying absorption, total light extinction, α, is retrieved, and it therefore measures the sum of absorption and scattering. The advantages of IBBCEAS include:

High sensitivity, experimental simplicity High temporal resolution Simultaneous detection of multiple species due to the wide spectral coverage No mode matching involved as in some Cavity Ring Down Spectroscopy applications (CRDS) Applicable to solids, liquids, gases and plasmas. Cost effective The disadvantages include:

Unlike CRDS, the sensitivity is dependent on the light source stability and the measurement accuracy of the transmitted intensity. It requires a reliable calibration procedure to determine baseline optical losses of the system (often performed by calibration of reflectivity as a function of wavelength using known concentrations of sample in the cavity). Lower spectral resolution compared to laser based methods.

Measurement Principle IBBCEAS - Detailed Description

When the optical cavity is illuminated by an incoherent broadband light source like the white light of a lamp or LED, the mode structure of the cavity intensity can be neglected. Consider a cavity of length d formed by two identical high reflectivity mirrors (R1 = R2 = R > 99.9%) with losses L, which is continuously excited with incoherent light of intensity Iin. For an empty resonator with L = 0, the time integrated transmitted intensity I0 is given by

I 0 = I i n 1 − R 1 + R {\displaystyle I_{0}=I_{in}{\frac {1-R}{1+R}}}

The intensity of light transmitted by the cavity, I( = I0 + I1 + I2 + ⋯ ), can be described by the superposition of the light after an odd number of passes, leading to a geometric series:

I = I i n ( 1 − R ) 2 ( 1 − L ) ∑ n = 0 ∞ R 2 n ( 1 − L ) 2 n {\displaystyle I=I_{in}(1-R)^{2}(1-L)\sum _{n=0}^{\infty }R^{2n}(1-L)^{2n}}

Since R < 1 and L < 1 the series converges to:

I = I i n ( 1 − R ) 2 ( 1 − L ) 1 − R 2 ( 1 − L ) 2 {\displaystyle I=I_{in}{\frac {(1-R)^{2}(1-L)}{1-R^{2}(1-L)^{2}}}}

Assuming the losses per pass to be solely due to Lambert-Beer attenuation, i.e. (1 − L) = e(-αd), the extinction coefficient, α can be written as

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