Incoherent broad-band cavity-enhanced absorption spectroscopy

Schematic of light passing an optical cavity. Note that the arrows only illustrate time-dependence of the light intensity and not its spatial distribution inside the cavity. For instance, if injected on-axis, all reflections happen symmetrically distributed around the optical axis.

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.[1] 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 I_in. For an empty resonator with L = 0, the time integrated transmitted intensity I₀ is given by

${\displaystyle I_{0}=I_{in}{\frac {1-R}{1+R}}}$

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:

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

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

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

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

${\displaystyle \alpha ={\frac {1}{d}}\left\vert \ln \left({\frac {1}{2R^{2}}}\left({\sqrt {4R^{2}+\left({\frac {I_{0}}{I}}(R^{2}-1)\right)^{2}}}+{\frac {I_{0}}{I}}(R^{2}-1)\right)\right)\right\vert }$

In case of small losses per pass, L → 0, and high reflectivities of the mirrors, R → 1, α can then be approximated as

${\displaystyle \alpha \approx {\frac {1}{d}}\left({\frac {I_{0}}{I}}-1\right)(1-R)}$

Approximating Δ I / I ₀ ≈ (I ₀ - I) / I ₀ ≈ (I ₀ - I) / I, the minimum absorption coefficient, α_min, can be expressed by the following equation:

${\displaystyle \alpha _{min}={\frac {1}{d}}\left({\frac {\Delta I_{min}}{I_{0}}}\right)(1-R)}$

where Δ I _min is the minimum detectable change in intensity smaller than I_{0}. The maximum sensitivity (for given R and d) is limited by the intensity of the lamp, the dispersion of the monochromator, and the noise of the detector. The above equation demonstrates that the effective path length is (1-R)⁻¹ times longer than that of a conventional single pass experiment. Fiedler et al. have studied in detail the influence of cavity parameters like the cavity length, mirror curvature and reflectivity, different light injection geometries on the IBBCEAS signal.[6]

Fourier Transform Incoherent Broadband Cavity Enhanced Spectroscopy (FT-IBBCEAS) is a variant of IBBCEAS which uses a Fourier transform spectrometer/photodiode instead of the conventional monochromator/CCD in order to establish a spectrum. In this case, the absorption is determined from the Fourier Transform of the intensity of light escaping the cavity. The combination of a Fourier transform spectrometer allows for high spectral resolution to be achievable, however, at the expense of good temporal resolution, making the technique less suitable for kinetic studies. On the other hand, the approach provides an improvement to conventional Fourier Transform spectroscopy for gas applications where small sample volumes are required (e.g. for discharges, combustion plasmas, flames or chemical flow reactors).

The figure above shows the spin forbidden O₂ b-band at ~ 14500 cm⁻¹ (688 nm) measured[7] in ambient air at atmospheric pressure using a xenon arc lamp compared against a calculated HITRAN spectrum. The cavity was formed by two dielectric high reflectivity mirrors (R>0.996 at 662 nm) separated by 89 cm. The characteristic doublets of the O₂ b-band and the bandhead of the R branch are visible in the experimental spectrum. In order to fully exploit the selectivity feature of Fourier transform spectroscopy, the near infrared region is of interest because many overtone spectra of atmospherically relevant gases are located in this part of the spectrum. Some of these studies include the detection of overtone bands of CO₂, OCS,[8] CH₃CN[9] and HD¹⁸O in the near IR.[10]

• Pollution monitoring
• Combustion Diagnostics
• Atmospheric trace gas detection
• Aerosol science
• Breath Analysis
• Fundamental Science and Research
• Chemical Reaction Kinetics

Since its development in 2003, IBBCEAS has been used with a wide variety of incoherent light sources, including arc lamps, LEDs, SLEDs and supercontinnum sources.

• http://www.cfa.harvard.edu/hitran/