WO2001007878A1

WO2001007878A1 - Apparatus and methods for analysing electromagnetic radiation

Info

Publication number: WO2001007878A1
Application number: PCT/GB2000/001469
Authority: WO
Inventors: Wei Cao
Original assignee: Shimadzu Research Laboratory (Europe) Ltd.
Priority date: 1999-07-23
Filing date: 2000-04-17
Publication date: 2001-02-01
Also published as: AU4418700A; GB9917423D0

Abstract

A laser absorption apparatus comprises a resonant optical cavity having highly reflective mirrors. Laser light undergoes multiple reflections while the spacing of the mirrors is varied as a function of time. The intensity of light transmitted across one of the mirrors is measured as a function of time and the measured intensity is transformed from the time domain to the frequency domain. The absorption coefficient of sample contained within the cavity, or reflectively of the mirrors, or change in polarisation state of the light, or coherence length of the light beam can be determined from the transform or from the intensity itself.

Description

APPARATUS AND METHODS FOR ANALYSING ELECTROMAGNETIC

RADIATION

FTRLD OF THE INVENTION

This invention relates to apparatus and methods for analysing electromagnetic

radiation.

The invention relates particularly, though not exclusively, to laser absoφtion

apparatus and methods.

BACKGROUND OF THE INVENTION

One effective way of improving the sensitivity of a laser absoφtion measurement is

to increase the length of the propagation path over which absoφtion 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 absoφtion 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

absoφtion 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 Absoφtion 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 absoφtion 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

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 absoφtion 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

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 absoφtion

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 absoφtion

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 absoφtion 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 r,,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-amplifϊer 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 absoφtion 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

C_L 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 L_p of cavity 10, where L_p=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 λ.

Accordingly, the spacing L of the mirrors changes linearly as a function of time, and

is given by the expression:

L =L +vt ,

where L₀ 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 L_p 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:

f=^, for p=0,l,2...N.

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 C_L 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 absoφtion 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. absoφtion) coefficient of the sample.

It can be shown by analysis that the output intensity I(t) is given by the expression:

/, = /₀( %-²- (χ( ,_{2 e}--

)^2'- cos(2 K - ^β,₊ )

where I₀ is the intensity of radiation introduced into the cavity, Wⁱ

δ = 2πnL/λ, where n is the sample refractive index and

e I J e l*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:

N-p

I(p) = I₀(^₂)²e-^2aL∑(r_lr₂e-^2aL)²-"i_ι (2)

where frequency f — 2pv/λ, p = 0,1,... N.

By further processing equation (2) it can be shown that,

^₂)²e-^2aL r_lr₂e-^2aLy ₀. _{p +}

I(P) _xr₂e ^')/(/> + !) =

If the polarization change between successive reflections is small, the second half of

above equation will be near 0. So only,

I₀(t,t₁ e-^2aL(r,r₁e^'laLYe₀-e_p (3)

remains. This is exactly related to the intensity of the p^th reflection. So in the case

of e ^~2cL~l, spectrum intensity can be used to obtain the intensity of p^th reflection by

calculating: I(p) - (r r₇ )f(p ₊ \) ^ f₀(t_it₂ γ e-^2al (r_]r₂e-^2aL V (4)

Accordingly, the values of the absoφtion coefficient can easily be determined by

substituting into Eqn4 the values of I₀, r,, r₂, L,v which are all known.

Alternatively, 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 absoφtion coefficient α 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 Eqn5.

For example, it will be appreciated that Eqn3 above and Eqⁿ4 above can be used to

determine values for r,,r₂ in the case when there is no sample present in the cavity (i.e.

α=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 1 1 may be provided.

In this embodiment, the optical path length L_p 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 absoφtivity by the sample is 0.2% per pass through the cavity and another,

represented by a broken line, for which absoφtivity 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.

Claims

1. 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 the 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.

2. An apparatus as claimed in claim 1 wherein said means for varying causes a

variation of the physical spacing of said radiation-reflective surfaces.

3. An apparatus as claimed in claim 1 or claim 2 wherein said means for varying comprises piezoelectric means for causing movement of one of said radiation-

reflective surfaces relative to another of said radiation reflective surfaces.

4. An apparatus as claimed in any one of claims 1 to 3 wherein a part of said

resonant optical cavity is defined by optical fibre, and said means for varying causes

a variation of the optical path length of said optical fibre.

5. An apparatus as claimed in claim 4 wherein said variation as a function of time

of the optical path length of said optical fibre is controlled by application of stress to

said optical fibre.

6. An apparatus as claimed in any one of claims 1 to 5 for measuring decay of

intensity of said electromagnetic radiation caused by absoφtion of radiation by a

radiation-absorbent sample within said resonant optical cavity, including means for

deriving a measure of said decay from a variation of said measured intensity as a

function of said frequency.

7. An apparatus as claimed in any one of claims 1 to 6 wherein said means for

transforming subjects said measured intensity to a Fourier transform.

8. An apparatus as claimed in claim 1 including means for analysing a variation

of said measured intensity as a function of said frequency to evaluate the coherence length of said electromagnetic radiation.

9. An apparatus as claimed in claim 1 including means for analysing a variation

of said measured intensity as a function of said frequency to evaluate the effective

reflectivity of said radiation-reflective surfaces.

10. An apparatus as claimed in claim 9 wherein said means for analysing is

arranged to monitor said effective reflectivity to detect for surface contamination of

said radiation-reflective surfaces.

1 1. An apparatus for measuring decay in intensity of electromagnetic radiation

caused by absoφtion 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, and the coherence length of the measured radiation

being at least twice the optical path length of the cavity.

12. An apparatus as claimed in claim 1 1 wherein said measure of decay is derived

from the shape of a peak in a said variation of measured intensity as a function of

time.

13. An apparatus as claimed in claim 1 1 or claim 12 wherein said means for

varying causes a variation of the physical spacing of said radiation-reflective surfaces.

14. An apparatus as claimed in any one of claims 1 1 to 13 wherein said means for

varying comprises piezoelectric means for causing movement of one of said radiation-

reflective surfaces relative to another of said radiation-reflective surfaces.

15. An apparatus as claimed in any one of claims 1 1 to 14 wherein a part of said

a variation of the optical path length of said optical fibre as a function of time.

16. An apparatus as claimed in claim 15 wherein said variation of the optical path

length of said optical fibre is controlled by application of stress to said optical fibre.

17. An apparatus as claimed in claim 1 including means for analysing a variation of said measured intensity as a function of said frequency to determine a change in

polarisation state of said electromagnetic radiation.

18. 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

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

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, and the coherence length of the

radiation being at least twice the optical path length of the cavity.

19. A method as claimed in claim 18 wherein said varying step causes a variation

of the physical spacing of said radiation-reflective surfaces.

20. A method as claimed in claim 18 or claim 19 wherein a part of said resonant optical cavity is defined by optical fibre, and said varying step causes a variation of

the optical path length of said optical fibre.

21. A method as claimed in claim 20 wherein said varying step comprises varying

as a function of time stress applied to the optical fibre.

22. A method as claimed in claim 18 for measuring decay of said electromagnetic

radiation caused by absoφtion of radiation by a radiation-absorbent sample within

said resonant optical cavity including deriving a measure of said decay from a

variation of said measured intensity as a function of said frequency.

23. A method as claimed in claim 18 including analysing a variation of said

measured intensity as a function of said frequency to evaluate the coherence length

of said electromagnetic radiation.

24. A method as claimed in claim 18 including analysing a variation of said

measured intensity as a function of said frequency to evaluate the effective reflectivity

of said radiation-reflective surfaces.

25. A method as claimed in claim 24 including monitoring said effective

reflectivity to detect for surface contamination of said radiation reflective surfaces.

26. A method for measuring decay in intensity of electromagnetic radiation caused

by absoφtion 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

reflective surfaces,

varying the optical path length as a function of time,

measuring, as a function of time, intensity of electromagnetic radiation

is varied, and

deriving said measure of decay from a variation of the measured intensity as

a function of time, the coherence length of the radiation being at least twice the optical

path length of cavity.

27. A method as claimed in claim 26 including deriving said measure of decay

from the shape of a peak in said variation.

28. A method as claimed in claim 18 including analysing a variation of said

measured intensity as a function of said frequency to determine a change in

polarisation state of said electromagnetic radiation.

29. An apparatus substantially as hereindescribed with reference to the

accompanying drawings.

30. A method substantially as hereindescribed with reference to the accompanying

drawings.