The invention relates particularly, though not exclusively, to laser absorption apparatus and methods.

BACKGROUND OF THE INVENTION One effective way of improving the sensitivity of a laser absorption measurement is to increase the length of the propagation path over which absorption takes place, and this can be accomplished using a multi-reflection cell.

A well known technique based on the use of a multi-reflection cell is cavity ringdown laser absorption spectroscopy (CRLAS). This technique involves measuring the time rate of decay of electromagnetic radiation trapped in a high reflectance resonant optical cavity. An early form of CRLAS, known as continuous wave (CW)-based cavity attenuated phase shift (CAPS) relies on the fact that cavity decay time can be

inferred from a measurement of phase-shift between modulated input and output light of the optical cavity. However, the limiting factor in attaining high sensitivity is fluctuations in and the ability to measure phase angle mainly due to erratic longitudinal mode coupling between the laser light source and the optical cavity.

In another CW-based technique, an optical switch is used to terminate the light source after multiple reflections have become established within the cavity, and the cavity decay time is then measured. This technique has the drawback that it requires ultra- fast timing electronics and an ultra-fast optical switch and these add to complexity and cost.

In another CRLAS approach, known as pulsed cavity ringdown, a laser pulse having a coherence length shorter than the distance for a single pass of the cavity is directed into the cavity and the ringdown decay time (i. e. the time taken for the light intensity to decay by a factor of 1/e) is measured. This technique enables the ringdown absorption to be measured directly, but needs a short pulse laser source and ultra-fast timing electronics.

The afore-mentioned techniques are reviewed in a paper entitled"Cavity Ringdown Laser Absorption Spectroscopy: History, Development and Application to Pulsed Molecular Beams"by J. J. Scherer et al, Chem Rev 1997,97,25-51.

SUMMARY OF THE INVENTION According to one aspect of the invention there is provided an apparatus for analysing electromagnetic radiation comprising a resonant optical cavity including means defining first and second radiation-reflective surfaces, a source of electromagnetic radiation for introducing radiation into said resonant optical cavity whereby the radiation can undergo multiple reflections at said first and second radiation-reflective surfaces, means for varying the optical path length of the cavity as a function of time, means for measuring, as a function of time, intensity of electromagnetic radiation transmitted across one of said radiation-reflective surfaces as said optical path length is varied, and means for transforming the measured intensity of electromagnetic radiation from the time domain to a frequency domain, where frequency is related to a number of reflections p occurring at said one radiation-reflective surface and the coherence length of the measured radiation being at least twice the optical path length of the cavity.

According to another aspect of the invention there is provided an apparatus for measuring decay in intensity of electromagnetic radiation caused by absorption of said radiation by radiation-absorbent sample, comprising a resonant optical cavity for containing said sample and including means defining first and second radiation- reflective surfaces, a source of said electromagnetic radiation for introducing the radiation into said resonant optical cavity whereby said radiation can undergo multiple

reflections at said first and second radiation-reflective surfaces, means for varying the optical path length of the cavity as a function of time, means for measuring, as a function of time, intensity of electromagnetic radiation transmitted across one of said radiation-reflective surfaces as said optical path length is varied, and means for deriving said measure of decay from a variation of the measured intensity as a function of time, the coherence length of the measured radiation being at least twice the optical path length of the cavity.

According to a further aspect of the invention there is provided a method of analysing electromagnetic radiation using a resonant optical cavity including means defining first and second radiation-reflective surfaces, the method comprising the steps of introducing electromagnetic radiation into said resonant optical cavity whereby the radiation can undergo multiple reflections at said first and second radiation-reflective surfaces, varying the optical path length of the cavity as a function of time, measuring as a function of time intensity of electromagnetic radiation transmitted across one of said radiation-reflective surfaces as said optical path length is varied, and transforming the measured intensity of electromagnetic radiation from the time domain to a frequency domain, where frequency is related to a number of reflections p occurring at said one radiation-reflective surface, the coherence length of the measured radiation being at least twice the optical path length of the cavity.

According to a yet further aspect of the invention there is provided a method for

measuring decay in intensity of electromagnetic radiation caused by absorption of said radiation by radiation-absorbent sample, the method using a resonant optical cavity containing said sample and including means defining first and second radiation- reflective surfaces, and the method including the steps of : introducing electromagnetic radiation into said resonant optical cavity whereby the radiation can undergo multiple reflections at said first and second radiation- reflective surfaces, varying the optical path length of the cavity as a function of time, measuring, as a function of time, intensity of electromagnetic radiation transmitted across one of said radiation-reflective surfaces as said optical path length is varied, and deriving said measure of decay from a variation of the measured intensity as a function of time, and the coherence length of the measured radiation being at least twice the optical path length of the cavity.

BRIEF DESCRIPTION OF THE DRAWINGS Embodiments of the invention are now described, by way of example only, with reference to the accompanying drawings, of which : Figure 1 is a diagrammatic illustration of a first embodiment of laser absorption apparatus according to the invention,

Figure 2a shows a drive signal supplied to a piezoelectric ring in the apparatus of Figure 1, Figure 2b shows a plot of measured intensity I (t) of electromagnetic radiation as a function of time t, obtained using the apparatus of Figure 1, Figure 2c is a corresponding plot of measured intensity as a function of frequency f, Figure 3 is a diagrammatic illustration of a second embodiment of laser absorption apparatus according to the invention, Figure 4a shows a more detailed plot of the form shown in Figure 2c, and Figure 4b shows a comparative plot of measured intensity as a function of time obtained using the pulsed cavity ringdown technique.

DESCRIPTION OF PREFERRED EMBODIMENTS Referring now to the drawings, Figure 1 is a diagrammatic illustration of a first embodiment of a laser absorption apparatus according to the invention.

The apparatus comprises a resonant optical cavity 10 containing sample and having

a configuration akin to a Fabry-Perot interferometer. The cavity 10 has end walls defined by a pair of highly reflective mirrors 1,2 having coefficients of reflection rt, r2 typically of the order of 0.995 or higher.

A laser 3 directs a beam B of electromagnetic radiation into the cavity via one of the mirrors 1 (the entrance mirror), and the beam undergoes multiple reflections at the reflective surfaces of both mirrors, passing back and forth across the cavity.

Radiation losses from the beam are attributable to two different effects; that is, some radiation will be absorbed by sample during each pass across the cavity and a small amount of radiation will be transmitted across the reflective surfaces of the mirrors 1,2.

As shown in Figure 1, a photon detector 4 and an associated pre-amplifier 5 are provided to measure the intensity I of radiation transmitted across the reflective surface of mirror 2 (the exit mirror). An optional filter 11 may also be provided in the case of a broadband laser source 3. As will be described in greater detail hereinafter, the measured intensity I can be processed to derive a measure of the decay of intensity of radiation in the cavity due to absorption by the sample, or contamination of the mirrors 1,2 or change in polarisation state of the reflected light beam or coherence length of the beam B.

The measurement of decay is similar to that employed in known cavity ringdown methods; however, in contrast to the aforementioned pulsed cavity ringdown method, the present invention relies upon the interference effect of radiation incident at the surface of the exit mirror 2. Accordingly, in this embodiment, the coherence length CL of the radiation measured by detector 4 is at least 2nNL, where L is the separation of the mirrors 1,2, N is an integer greater than unity, preferably of the order of 100 and n is the refractive index of the sample. By this means, radiation which has already undergone N reflections at the exit mirror 2 can still interfere with radiation which has not undergone any reflections at the exit mirror.

At any particular time t, the intensity of radiation I (t) transmitted across the exit mirror 2 is given by the combined effects of radiation which has undergone different numbers of multiple reflections at the exit mirror 2, which will be assigned an index p for successive pairs of reflections at mirrors 2 and 1. (If p=o the radiation has not undergone any reflection).

The interference effect produced will depend on the relative phases of the radiation incident at the exit mirror 2 and this can be controlled by varying the optical path length Lp of cavity 10, where Lp=nL. In this embodiment, the optical path length of cavity 10 is varied by varying the physical spacing L of the mirrors 1,2. This is accomplished by means of a piezo-electric ring 6 sandwiched between the exit mirror 2 and a fixed support block 7. The piezo-electric ring 6 is supplied via a high voltage

amplifier 8 with a drive signal D having a ramp-type waveform, as shown in Figure 2a. In response, the piezo-electric ring 6 displaces the exit mirror 2 linearly as a function of time through two or more wavelengths A.

Accordingly, the spacing L of the mirrors changes linearly as a function of time, and is given by the expression: where Lo is the nominal spacing of the mirrors (i. e. with mirror 2 centralised) and v is the speed at which the exit mirror 2 is displaced. In this manner, the optical path length Lp of the cavity 10 is swept through a first extreme condition for which the radiation incident at the exit mirror 2 is substantially in-phase and undergoes constructive interference, giving rise to a peak in the measured intensity I (t), and a second extreme condition for which the incident radiation is substantially out-of-phase and undergoes destructive interference, giving a trough in the measured intensity I (t).

Figure 2b shows the variation of I (t) as a function of time t, with the peaks referenced P and the troughs referenced T.

It will be appreciated that radiation which has undergone relatively few reflections (lower values of p) will have suffered relatively fewer losses than radiation which has undergone a larger number of reflections (higher values of p) and will therefore give a greater contribution to the measured output I (t). This can be appreciated by

transforming the measured output I (t) from the time domain to the frequency domain using a Fast Fourier Transform (FFT) 9.

Figure 2c shows the resultant transform, where frequency f is given by the expression: Each spectral line S in the transform corresponds to a respective value of p, and the height of the spectral line represents the contribution made by the respective radiation to the measured intensity I (t).

The coherence length CL of the radiation can be determined from the decay of the spectral lines S.

As will now be explained, it is possible to obtain from the transform a measure of decay of intensity of electromagnetic radiation due to absorption by sample in the cavity 10, and this measure can be used, in turn, to derive a value of the electric field decay (i. e. absorption) coefficient a of the sample.

It can be shown by analysis that the output intensity I (t) is given by the expression: where Io is the intensity of radiation introduced into the cavity,

5 = 2T : nL/R, where n is the sample refractive index and e'n e'+p are the unit vectors of the electric field of radiation that has undergone i and i+p reflections respectively at the exit mirror 2.

The real part of the corresponding Fourier transform I (p) is given by the expression: where frequency f= 2pv/l, p = 0,1,... N.

By further processing equation (2) it can be shown that, If the polarization change between successive reflections is small, the second half of above equation will be near 0. So only, remains. This is exactly related to the intensity of the pth reflection. So in the case of e-2"=1, spectrum intensity can be used to obtain the intensity of pt'reflection by calculating:

Accordingly, the values of the absorption coefficient a can easily be determined by substituting into Eqn4 the values of Io r"r2, L, v which are all known.

Alternatively, a could be determined using a ringdown approach by evaluating the change of frequency f necessary to cause a reduction of the measured intensity by a factor of 1/e.

It can also be shown that provided the polarization state is not changed at each reflection, Eqnl above can be expressed as: From the above analysis, the decay of the frequency domain of output light intensity will depend on the following factors: 1. The absorption coefficient a of the sample.

2. The reflectivity of the mirros r"r2.

3. The coherence length of radiation from the source or as measured by the detector (in case a filter is used).

4. The change of polarization state.

Where any three factors are either controlled or known then the other factor can be derived by analyzing the frequency domain intensity of Eqn2 or Eqn4, or directly the time domain intensity of EqnS.

For example, it will be appreciated that Eqn3 above and Eq"4 above can be used to determine values for r,, r2 in the case when there is no sample present in the cavity (i. e. a=o). This approach provides a way of monitoring the mirror reflectivities to detect for undesirable changes indicative of the presence of surface contamination.

Similarly, these same equations may be used to determined changes of polarisation occurring at different values of p.

In a second embodiment, shown in Figure 3, part of the resonant optical cavity 10 is defined by a single mode optical fibre 12 provided with a self-focusing lens 13 at one end and a highly reflective film 14 at the opposite end, at which multiple reflections can take place. As before, the intensity of radiation I (t) transmitted across film 14 is measured using a photon detector 4 and an associated preamplifier 5 and the measured output is transformed from the time domain to the frequency domain using FFT 9.

Again, an optional filter 11 may be provided.

In this embodiment, the optical path length Lp of the cavity 10 is given by the expression:

where n, and L, are the refractive index and length respectively of a first part 10'of the cavity (i. e. the part between mirror 1 and lens 13) and n2 and L2 are the refractive index and length respectively of a second part 10"of the cavity (i. e. the part defined by the optical fibre 12 and the lens 13).

In this case, the optical path length of the cavity is varied by varying both the refractive index n2 and length L2 of the optical fibre 12, and this is accomplished by applying stress thereto using a piezoelectric tube 15, which may be supplied with a drive signal similar to that described with reference to Figure 2a.

It will be appreciated from the foregoing that the present invention is based on an interference effect and so the measured intensity I (t) contains contributions from radiation which has undergone a range of multiple reflections at the exit mirror.

Accordingly, much higher powers can be attained than has been possible hitherto using the afore-mentioned pulse cavity ringdown technique, for example, and so a much improved sensitivity can be achieved. Furthermore, there is no requirement for ultra fast timing electronics and optical components.

The improvement in sensitivity can be appreciated by comparing Figures 4a and 4b.

Figure 4a shows a plot of intensity as a function of p obtained using an apparatus in

accordance with the present invention, whereas Figure 4b shows a comparable plot of intensity as a function of time obtaining using the known pulsed cavity ringdown technique. Each of these Figures shows two plots; one, represented by a full line, for which absorptivity by the sample is 0.2% per pass through the cavity and another, represented by a broken line, for which absorptivity by the sample is 0.4% per pass through the sample.

It will be noted that the intensity measured using the present invention is very much larger than that obtained using the pulsed decay cavity ringdown technique, giving much improved sensitivity.