cavity ring down spectroscopy

14 February 2012

CE 540

history:• first work in early 1980’s to determine mirror reflectivities in laser applications• operated using red laser line 632nm (e.g. laser gyroscopes)• mirrors were getting so good (>99.99% efficiency) that measuring them was hard• first work Herbelin et al (1980)App. Op. 19, 144• Anderson et al 1984, Appl. Optics 23, 1238 pulsed dye laser (many wavelengths)• development of high quality dielectric dichroic mirrors

CRD Optics

CSU thesis

I(t) = Io exp(-t/o) [assuming index of refraction n = 1], simple exponential decrease

I(t) / Io = exp(-t/o)

for cavity ring down time of t = o time for intensity to drop by 1/e

for an empty cavity, the decay constant is dependent on the loss mechanisms within thecavity = mainly mirror reflectivity. If L is the cavity length and c the speed of light, then

R = = exp{-L/(co)} where (co)/L # cell reflections to 1/e intensity

ln (R) = L/(co)

o = L/(c ln(R))

but ln(R) = 1 – R for R near 1

o = L / {c(1 – R)} [sec]

cavity intensity as a function of time:

L = 50cm, decay time o = 30µs R = 0.99994 and # round trips~10,000 total path length 10km

now add a molecular absorption:

= L / {c(1 – R + L)} [sec]

{ from I(t) / Io = exp(-t/o – ct) and ct = L, total cavity length at time t }

where is the absorption coefficient [/cm] and goes like concentration x cross section

Then the relationship between empty cavity decay time (o) and the decay time with anabsorber present () is:

1/o + c

since c is 1/time added for the absorber

The are a function of wavelength and at each wavelength are fitted with an exponentialdecay curve to get the decay time. Knowing o allows calculation of and from that the concentrations can be determined over a full spectral line using Beer’s law using differential spectroscopy.

O’Keefe et alwww.lgrinc.com/publications/acs.pdf

750 ppm loss 1 – 750 x 10-6 = 0.99925 = 0.0075%

best we can do withthe NASA systemupstairs is about0.015%, about 2xworse

some specs:• mirror reflectivity > 99.995% in near UV/vis are available• fractional absorbance detectable < 10-7/pulse using mirrors at uncertainty in o of 1%

example:• L = 50 cm • decay time ~ 30µsec for reflectivity 99.994%• gives ~ 10,000 round trips during the decay time• a detectable light pulse every 3 nsec = 2 x L/c with laser pulse length < shorterthan cavity round trip

achievable absorbance example:10-7 absorbance. NO2 example with L = 900m = 90000 cm (as in HW problem)

I/Io = 0.9999999 = exp(-L (2.5 x 10-19)N) N = 4.5x106 molecules/cm3 = 0.2 pptv

Advantages of CRDS:• everything is fractional, so not affected by fluctuations in light source intensity – ringdown time does not depend on intensity • very sensitive due to long path length (km) due to multiple mirror reflections• spectral range is usually good since dichroic laser mirrors are somewhat broad

Disadvantages:• laser is nearly monochromatic must build up the spectrum• need particular laser wavelengths for different molecules• high reflectance mirrors (>>99.99% reflectivity)• expensive• absorbances must be < a few % or don’t get enough bounces• source bandwidth must be < absorption bandwidth• frequencies within the laser BW must be reflected equally by the mirrors• excited state lifetime must be < laser roundtrip time in the cavity – so once a photonis absorbed during a particular laser pass, the excited specie has time to relaxbefore the next laser pass• laser scan time limits the time resolution of spectra• dirt in system decreased R. I guess this gets calibrated out when you run the cellw/o the molecule you want to measure in the mixture. But you are sucking outsideair into the cell all the time and it is dirty