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# Cavity ring down spectroscopy

Cavity Ring Down Spectroscopy (CRDS) can be used to measure the concentration of some light-absorbing substance. Typically, this is a gas. The cavity refers to the space between two mirrors facing each other. A brief pulse of laser light is injected into the cavity, and it bounces back and forth between the mirrors. Some small amount (typically around 0.1% or less) of the laser light leaks out of the cavity and can be measured each time light hits one of the mirrors. Since some light is lost on each reflection, the amount of light hitting the mirror is slightly less each time. Since a percentage leaks through, the amount of light measured also decreases each reflection. If something that absorbs light is placed in the cavity, the light will undergo fewer detections before it is all gone. CRDS essentially measures how long it takes for the light to drop to a certain percentage of its original amount, and this ringdown time can be converted to a concentration.

There are two main advantages to CRDS over other absorption methods:

First, it isn't affected by fluctuations in the laser. In most absorption measurements, the light source must be assumed to remain steady between blank (no analyte), standard (known amount of analyte), and sample (unknown amount of analyte). Any drift (change in the light source) between measurements will introduce errors. In CRDS, the ringdown time does not depend on the brightness of the laser, so fluctuations aren't a problem.

Second, it is very sensitive due to its long pathlength. In absorption measurements, the smallest amount that can be detected depends on the length that the light travels through a sample. Since the light reflects many times between the mirrors, it ends up traveling long distances. For example, a laser pulse making 500 round trips through a 1 meter cavity will effectively have traveled through 1 kilometer of sample.

## Detailed description

Cavity Ring Down Spectroscopy (CRDS) is a form of laser absorption spectroscopy, also known as Cavity Ring-down Laser Absorption Spectroscopy (CRLAS). In CRDS, a laser pulse is trapped in a highly reflective (typically R > 99.9%) detection cavity. The intensity of the trapped pulse will decrease by a fixed percentage during each round trip within the cell due to both absorption by the medium within the cell and reflectivity losses. The intensity of light within the cavity is then determined as an exponential function of time.

$I(t) = I_0 \exp \left (- t / \tau \right)$

The principle of operation is based on the measurement of a decay rate rather than an absolute absorbance. This is one reason for the increased sensitivity over traditional absorption spectroscopy. The decay constant, τ, is called the ring-down time and is dependent on the loss mechanism(s) within the cavity. For an empty cavity, the decay constant is dependent on mirror loss and various optical phenomena like scattering and refraction:

$\tau_0 = \frac{n}{c} \cdot \frac{l}{1-R+X}$

where n is the index of refraction within the cavity, c is the speed of light in vacuum, l is the cavity length, R is the mirror reflectivity, and X is the miscellaneous optical losses. Often, the miscellaneous losses are factored into an effective mirror loss for simplicity. An absorbing species in the cavity will increase losses according to the Beer-Lambert law. Assuming the sample fills the entire cavity,

$\tau = \frac{n}{c} \cdot \frac{l}{1-R+X+ \alpha l }$

where α is the absorption coefficient for a specific analyte concentration. The absorbance, A, due to the analyte can be determined from both ring-down times.

$A = \frac{n}{c} \cdot \frac{l}{2.303} \cdot \left ( \frac{1}{\tau} - \frac{1}{\tau_0} \right)$

Alternately, the molar absorptivity, ε, and analyte concentration, C, can be determined from the ratio of both ring-down times.

$\frac{\tau}{\tau_0} = \frac{ \alpha l }{1-R} = \frac{ \epsilon l C}{2.303(1-R)}$

• High sensitivity due to the multipass nature (i.e. long pathlength) of the detection cell.
• Immunity to shot variations in laser intensity due to the measurement of a rate constant.
• High throughput, individual ring down events occur on the millisecond time scale.
• No need for a fluorophore, which makes it more attractive than LIF or REMPI for some (e.g. rapidly predissociating) systems.