GB2541351A

GB2541351A - In-situ pathlength calibration for integrating cavities

Info

Publication number: GB2541351A
Application number: GB1506609.5A
Authority: GB
Inventors: Mary Bergin Sarah; Jane Hodgkinson Elizabeth; Francis Daniel; Peter Tatam Ralph
Original assignee: Cranfield University
Current assignee: Cranfield University
Priority date: 2015-04-19
Filing date: 2015-04-19
Publication date: 2017-02-22
Also published as: GB201506609D0

Abstract

In one aspect, the mean pathlength of an integrated cavity is determined using a light source S1 and two detectors D1, D2. The light from the source to the first detector is not influenced by reflectivity of the cavity, and light from the source to a second detector is influenced by reflectivity. In another aspect there are two light sources S1, S2 and two detectors. The light from the first source to the first detector and the second source to the second detector is not influenced by reflectivity of the cavity, and light from the first source to the second detector and from the second source to the first detector is influenced by reflectivity. In another aspect there are two light sources and a detector wherein light from the first source to the detector is influenced by reflectivity of the cavity and light from the second source to the detector is not influenced by reflectivity. A reference pathlength is determined during a calibration step at a first time using a calibration standard. The pathlength is determined at a second time using the reference pathlength and a comparison of the ratio of light fluxes measured at the first and second times.

Description

Patent Application (Description):

Title: In-situ pathlength calibration for integrating cavities Inventor Details:

Sarah Mary Bergin, Elizabeth Jane Hodgkinson, Daniel Francis and Ralph Peter

Tatam

Engineering Photonics, Cranfield University Cranfield, MK43 OAL, United Kingdom

Description:

Background and Summary of the Invention

Optical absorption sensors are used in the measurement of concentrations of analytes including gases, liquids and solid samples. For example in the case of gas sensing, they offer a high level of specificity to the gas of interest, as well as minimal drift and fast response times. The measurements can be made in-situ and in real time, which is beneficial for processes requiring continuous monitoring.

Quantitative measurements of absorption are based on the Beer Lambert law which can be expressed in terms of radiant flux:

(1)

Where Φε{a) is the radiant flux transmitted through the cell in the presence of an absorbing medium, Φ{0) is the radiant flux incident on the gas cell, a is the absorption coefficient (m1), and L is the optical path length of the cavity (m). The absorption coefficient a is the product of the gas concentration (in atm for example) and the specific absorptivity of the gas ε (in m_1atm_1). At low concentrations this equation becomes approxmately linear, with the concentration of the gas present directly proportional to the absorbance, such that the absorbance A can be written as

(2)

Therefore, it is well known that sample cells with a longer pathlength L will have improved signal to noise ratios for the measurement of a.

For use in understanding the present invention, the following disclosures are referred to: - Berger, E., Griffith, D. W. T., Schuster, G. and Wilson, S. R. (1989), "Spectroscopy of Matrices and Thin Films with an Integrating Sphere", Applied spectroscopy, vol. 43, no. 2, pp. 320-324. - Carr, K. F. (1997), "Integrating sphere theory and applications Part I: Integrating sphere theory and design", Surface Coatings International, vol. 80, no. 8, pp. 380-385. - Chambers, P., Lyons, W. B., Sun, T. and Grattan, K. T. V. (2010), "Analysis of the optical power loss arising from a fibre coupled integrating sphere used as a compact gas sensor", Sensors and Actuators A: Physical, vol. 162, no. 1, pp. 20-23. - Elterman, P. (1970), "Integrating Cavity Spectroscopy", Applied Optics, vol. 9, no. 9, pp. 2140-2142. - Fry, E. S., Kattawar, G. W. and Pope, R. M. (1992), "Integrating cavity absorption meter", Applied Optics, vol. 31, no. 12, pp. 2055-2065. - Fry, E. S., Musser, J., Kattawar, G. W. and Zhai, P. (2006), "Integrating cavities: temporal response", Applied Optics, vol. 45, no. 36, pp. 9053-9065. - Hanssen, L. (2001), "Integrating-sphere system and method for absolute measurement of transmittance, reflectance, and absorptance of specular samples", Applied Optics, vol. 40, pp. 3196-3204. - Hodgkinson, J., Masiyano, D. and Tatam, R. P. (2009), "Using integrating spheres as absorption cells: path-length distribution and application of Beer's law", Applied Optics, vol. 48, no. 30, pp. 5748-5758. - Hodgkinson, J. and Tatam, R. P. (2013), "Optical gas sensing: a review", Measurement Science and Technology, vol. 24, no. 1, 012004. - Johnson, M. (2003), Photodetection and Measurement: maximizing performance in optical systems, 1st ed, McGraw-Hill, New York, pp. 183-200. - K. L. King. (1992) Turbidimeter signal processing circuit using alternating light sources. US Patent no.5140168. - Labsphere (2015). Technical Guide to Integrating Sphere Theory and Applications. Labsphere Inc, North Sutton, NH, USA. Available at - Manojlovic, L. M. and Marinic, A. S. (2011), "On the integrating cavity transfer function and decay time", Measurement Science and Technology, vol. 22, no. 7, pp. 075303. - McManus, J. B., Kebabian, P. L. and Zahniser, M. S. (1995), "Astigmatic mirror multipass absorption cells for long-path-length spectroscopy ", Applied Optics, vol. 34, no. 18, pp. 3336-3348. - McManus, J. B., Zahniser, M. S. and Nelson, D. D. (2011), "Dual quantum cascade laser trace gas instrument with astigmatic Herriott cell at high pass number", Applied Optics, vol. 50, no. 4, pp. 74-75. - Ohno, Y. (2006), "Optical metrology for LEDs and solid state lighting", Rosas, E. and Cardoso, R. (eds.), in: Proceedings of SPIE, Vol. 6046, February 10, Mexico, Fifth Symposium Optics in Industry, pp. 604625. - Tranchart, S., Bachir, I. H. and Destombes, J. -. (1996), "Sensitive trace gas detection with near-infrared laser diodes and an integrating sphere", Applied Optics, vol. 35, no. 36, pp. 7070-7074. - Wheeler, M. D., Newman, S. M., Orr-Ewing, A. J. and Ashfold, Μ. N. R. (1988), "Cavity ring-down spectroscopy ", Journal of the Chemical Society - Faraday Transactions, vol. 94, no. 3, pp. 337-351.

Sensor performance can be enhanced by increasing the interaction of the gas with the light via longer pathlengths using multipass cells [McManus et al., 1995]. Typical multipass cells include the Herriott cell, whereby a single path is created by causing multiple reflections, using spherical or astigmatic mirrors. Herriott cells can have pathlengths of up to 15-100m, dependent on the number of passes achieved through alignment of the mirrors [McManus et al., 2011]. Cavity ringdown spectroscopy (CRDS) likewise creates multiple reflections using highly reflective mirrors and measuring a rate of decay of light with absorption, thus allowing very long (km) average pathlengths [Hodgkinson and Tatam, 2013]. Other cavity-enhanced systems similarly offer very long (km) pathlengths. As the pathlength cannot be accurately determined from the mirror specification, it is obtained experimentally by multiplying the ring down time by the speed of light [Wheeler et al., 1988], The mirrors used in such "cavity enhanced" sensors require very high reflectivity which can be costly to manufacture, typically show optimum performance only over a small wavelength range and require tight alignment tolerances.

Placing a well-defined and laboratory calibrated optical system in an industrial setting subjects the system to a new set of considerations, which may include a dirty sample environment or condensation of a gas analyte within the sample cell, both of which can lead to fouling of the cell and associated reduction of the reflectivity of mirrors or diffuse reflectors.

An integrating cavity is an optical component that consists of a hollow cavity coated on the inside with a highly reflective, typically Lambertian material, used to uniformly scatter and diffuse incident light over a particular wavelength range of interest [Carr, 1997]. A Lambertian surface is an ideal diffuser where the radiance is constant when viewed from any angle. As a result, the incident light undergoes multiple scattering reflections before a proportion of it is incident on a photodetector. Where the cavity is spherical, after the initial launch geometry, the light intensity at the sidewalls is evenly distributed. For practical applications, this property of uniform response, independent of spatial and angular information, makes an integrating sphere ideal for measuring total luminous flux and total spectral radiance of a light source [Ohno, 2006], Other applications include measuring the transmittivity or reflectivity of optical components, even when they partly scatter the light [Hanssen, 2001],

The use of an integrating cavity as an absorption cell has been proposed and investigated for some 40 years. Typical integrating sphere pathlengths of up to 10m are not in the same order as either Herriott cells or cavity-enhanced cells, but offer an advantage in tolerance to misalignment, turbidity within the sample [Berger et al., 1989], a wide wavelength range of operation and relatively robust reflective surface. Previous investigations have taken two approaches, theoretical derivations combining the gas absorption theory with integrating sphere theory to explain how the light acts and interacts with the analyte in the sphere, and practical investigations of performance. A major focus of the field has been to derive the effective pathlength of the cavity from its geometry and the reflectivity of the inner walls at the wavelength of operation. It is known that the pathlength is a sensitive function of the mean reflectivity of the sidewalls, taking into account the reflectivity of the material used as well as the presence of ports to permit the flow of fluid samples, detectors, windows for light entry and exit and other practical requirements. Constraints on the accuracy with which the mean reflectivity can be determined mean that accurate determination of the pathlength must be achieved experimentally rather than via theoretical calculation. Experimental determination of the pathlength has been completed by measuring the absorbance of known calibration standards [Elterman, 1970; Tranchart et al., 1996; Fry et al., 1992; Chambers et al., 2010; Hodgkinson and Tatam, 2009]. These methods have the disadvantage of requiring a supply of known absorbance standards, which can be impractical for sensors located in situ. An alternative means of calibrating an integrating sphere is measuring the temporal decay of measured irradiance following interruption of the source emission [Fry et al., 2006]. This has the disadvantage of requiring high speed electronics and restricts the technique to the use of sources that can be pulsed or modulated over short (nanosecond) timescales.

These bodies of research have demonstrated both experimentally and theoretically that integrating spheres show great promise as multipass gas cells, confirming that long effective pathlengths (e.g. 442cm effective pathlength for a 10cm diameter sphere) are achievable, but also that the pathlength is heavily dependent on the reflectivity of the surface to achieve this. For example, in our work we found that for a 5.04cm diameter sphere giving an effective pathlength of 127cm, covering only 0.44% of the inner surface of the sphere with a highly absorbing (black) film can result in a reduction of effective pathlength to 100cm. Therefore, when introduced to an industrial environment, the long term stability of the sphere's reflectivity (and therefore its pathlength) remains a challenge.

The pathlength of an integrating sphere and its optical throughput are both linked to its mean reflectivity via the well-known integrating sphere relations [Labsphere, 2015], It is known that integrating cavities having alternative geometries, such as cuboid or cylindrical shapes, follow similar laws governing their performance, with the addition of a geometrical factor [Manojlovic and Marinic, 2011], Integrating cavity performance can be expressed as the mean integrating sphere reflectivity, sphere multiplier (which relates to the proportional increase in radiance at the sphere surface with increasing passes of photons across the sphere) or inner sidewall reflectivity and port fraction (the proportion of the sphere inner wall area that is taken up by ports, holes or non-reflecting artefacts). Thus, the measurements made using integrating cavities are sensitive functions of the mean inner reflectivity. That reflectivity typically cannot be determined with sufficient precision to allow calculation of the integrating sphere performance from its materials properties and its geometry. The reflectivity and/or associated properties such as sphere pathlength must be determined experimentally.

Calibration of integrating spheres is therefore also an issue for other integrating sphere applications, including but not limited to measurement of source emission, sample transmission, sample reflectance and detector efficiency. Such measurements typically are performed using transmission or reflectance standards or standard sources, as the means of calibration of the integrating sphere's performance [Labsphere, 2015],

The integrating sphere relations offer an opportunity to measure the pathlength or mean reflectivity by measuring the sphere throughput, or the ratio of the radiant flux leaving the sphere at a port or absorbed by a detector, to the radiant flux entering the sphere from a source or through a window. However, absolute measurements of transmitted optical intensity in industrial systems are complicated by lack of knowledge about emitted intensity, transmittance of windows and detector responsivity. To overcome this problem, we have developed a new ratiometric measurement.

One embodiment of the invention is a novel adaptation of a four beam measurement system, which was originally developed, and is widely used to provide quantitative measurement of turbidity of a fluid [King, 1992], An optical sensor of this design can be used to detect bacterial growth, cleanliness of water, or liquid levels in a fermentation tank.

For absorption measurements, the transmitted power (Φ^) of each path is of the form [Johnson, 2003]:

(3)

(5)

The values of Si, S2, Di and D2 cancel, thus compensating the measurement for any variation in these parameters in use. Equation (5) simplifies to:

(6)

Where Q(0) is the value of Q measured in the absence of the analyte and L*[0) is the pathlength sum equal to (Li2(0)+L2i(0))-(Ln(0)+L22(0)). For small a/.*, this becomes

(7)

This gives an expression with the absorption coefficient (a), and a sum of the pathlengths (L* = (/-12+/-21)-(/-11+/-22))- The source power and detector gain variables have been eliminated, compensating for changes in power output as a result of, for example, degradation of components or certain window fouling situations.

The cited advantages of the four-beam technique were minimization of errors due to signal offset and gain, and accommodating fluids over a wide range of turbidity levels by adjusting gain controls. The method is known to compensate for component variation such as ambient temperature, aging and degradation of component, voltage variations, and sample chamber contamination due to scratching or fouling (either biological or chemical) on the sample chamber body. The technique has also been developed for absorbance measurements [Johnson, 2003].

The present invention comprises a novel adaptation of this compensation scheme for an integrating cavity, so that, as well as the cited above advantages, changes in pathlength due to cell contamination may be compensated and the pathlength may be adjusted accordingly. In this way the gas absorption coefficient may be determined continuously without needing to calibrate the sphere in situ.

Brief Description of the Drawings:

Figure 1 shows a schematic diagram of different preferred embodiments of the invention.

Figure 2 shows a schematic diagram of a conventional system for measurement of the absorption coefficient of a quantity in an integrating sphere, without the compensation for the integrating sphere pathlength described in this disclosure.

Figure 3 shows an illustration of examples of alternative cavity shapes that relate to the invention.

Brief Description of the Drawings:

Figure 4 shows a schematic diagram of the experimental configuration used for testing of the pathlength compensation system in different embodiments. The test configuration used an integrating sphere and made measurement of the absorption coefficient of methane at different dilutions in air, at a wavelength of 1651nm.

Figure 5 shows a schematic diagram to illustrate the data analysis procedure used to determine the measured absorption coefficient of methane at the centre of an absorption line at 1651nm, during the experimental tests.

Figure 6 shows a schematic diagram to illustrate the method used to simulate fouling of the inner walls of the integrating sphere, using a number of fouling tabs, during experimental testing.

Figure 7 shows the results of experimental testing of the first embodiment of the invention, whereby two sources and two detectors were employed to compensate the mean effective pathlength in the presence of sphere wall fouling, compared with a conventional system that employed no such compensation. The results show proportional errors in the measuerd absorption coefficient for an example methane concentration of lOlOppm in air.

Figure 8 shows the results of experimental testing of the second embodiment of the invention, whereby one source and two detectors were employed to compensate the mean effective pathlength in the presence of sphere wall fouling, compared with a conventional system that employed no such compensation. The results show proportional errors in the measuerd absorption coefficient for an example methane concentration of lOlOppm in air.

Details of the Invention:

The invention described in this disclosure is a ratiometric measurement of parameters that allow compensation for changes in the mean effective pathlength of an integrating cavity, and thereby other parameters including but not limited to the mean inner reflectivity, the reflectivity of the sidewall material, the throughput and the sphere multiplier. Note that the term "mean effective pathlength" refers to the equivalent pathlength of a conventional, single pathlength cell that would be required to achieve a comparable magnitude of absorption from the same analyte.

In a preferred embodiment, a typical setup comprises two light sources and two detectors, such that the light source optical axes are arranged such that the first detector measures light in a direct path from the first source and light from a multipass, diffuse path from the second light source. The second detector measures light in a direct path from the second light source and light from a multipass, diffuse path from the first light source. In an example for which we later show experimental verification, the sources are positioned at 90° relative to each other, and therefore by geometry the two detectors are also angled at 90° relative to each other. The two light sources are alternately switched on and off while both detectors make a separate flux measurement for each light source, giving four independent measurements. By forming a ratio of these measurements, it is known that changes in the source intensity, detector responsivity and window transmission can be compensated for. A ratio of measurements made in the absence of the target absorbance is formed that allows compensation for changes in the mean effective pathlength of the sphere since its initial (factory) calibration, and thereby allows more accurate determination of the target absorbance and thereby its concentration. The method compensates for fouling of the integrating sphere sidewalls and, in this preferred embodiment, also for degradation in the source, detector or windows.

The schematic layout of this preferred embodiment is illustrated in Figure 1(a). 1 is the inner wall of an integrating sphere. 2 is a direct optical path from source SI to detector Dl, with a pathlength Ln approximately equal to the diameter of the sphere. The optical beam from source SI is preferably slightly diverging, allowing a proportion of the beam to encounter the active area of the detector and a proportion of the beam to encounter the reflective sphere sidewall in the vicinity of the detector. The proportion of the beam that encounters the sidewall is diffusely scattered around the sphere and, after multiple random passes across the sphere of different individual pathlengths, a proportion of these photons encounters detector D2. 3 represents the multiplicity of reflected paths for photons travelling from source SI to detector D2. The mean effective pathlength for the photons leaving source SI and encountering detector D2 is termed the diffuse path, L12. By similar reasoning, the optical beam from source S2 is also preferably slightly diverging such that a proportion encounters detector D2 and a proportion encounters the sphere sidewall in the vicinity of detector D2. There is thereby a second direct pathlength from source S2 to detector D2, with pathlength l22, and there is a diffuse path i21 from source S2 to detector Dl.

It is preferable to control the divergence of the incoming light as follows. The four paths Ln, L22, L2i and i12 should preferably operate independently from each other i.e. changes to the long path throughput will not be detected at the short path output detector. The proportion of the beams encountering the sidewall in the vicinity of the detector is preferably sufficiently high so as to allow the radiant flux in the diffuse path to be detectable, ie above the noise level of the corresponding detector.

The integrating sphere relations describe how light is diffused around the sphere. Factors governing the extent of diffusion include the reflectivity of the sphere wall, the surface area and the number of port openings in the sphere. The radiance, As, of a general diffuse surface for an input flux, Φ, is given as:

(8)

Where p is the surface reflectivity, B the illuminated area and π the total projected solid angle from the surface.

For an integrating sphere the radiance equation must also consider the reflectivity of the sphere wall as well as losses due to port openings. The port openings are represented by the port fraction,/= (Bap)/Bs), where f is the port fraction, Bap is the sum of the areas of all ports, and Bs is the inner surface area of the sphere. The sphere surface reflectance is given by the reflectivity, p.

Combining these two variables gives a unitless quantity, the sphere multiplier, M:

(9)

This quantity accounts for the increase in radiance at the sidewalls due to multiple reflections.

Therefore for an integrating sphere the surface radiance is given by

(10)

For measurements with a photodetector, the total flux incident on the photodetector is defined as:

(11)

Where Bd is the active detector area (m2) and 0 is the projected solid angle (sr) of the detector field of view.

Now we consider the absorption of light by an analyte, as described by equations (1) and (2).

For a conventional, single pathlength gas cell, in the absence of gas, assuming that there are no other components in the beam path that absorb, reflect or scatter the light, the transmitted light is equal to the incident light.

(12)

When using an integrating sphere as a gas cell, in the absence of gas the transmitted light will not equal the incident light as with conventional gas cells. Rather it is described in terms of the incident flux and equations (10) and (11) to give:

(13)

Here, <E>d is the radiant flux measured at a detector whose field of view includes a proportion of the sidewall of the integrating sphere. As the values of Bd, Bs and Ω are fixed and can be known, a constant, k, is used to represent these. A ratio Q is formed of the measurements of radiant flux made by detectors D1 and D2 when the sources SI and S2 are turned on independently. This ratio is used in the well-known four beam technique for measurement of turbidity and absorption, as previously described.

(14)

Where Φάη is the radiant flux measured by detector D2 when source SI is turned on, Φ^ι is the radiant flux measured by detector D1 when source S2 is turned on, Φ^η is the radiant flux measured by detector D1 when source SI is turned on, and Φ*22 is the radiant flux measured by detector D2 when source S2 is turned on. The radiant flux measurements corresponding to the direct paths across the sphere, Φ,η and Φ,·22, are described by equations (1), (2) and (12). The radiant flux measurements corresponding to the diffuse paths across the sphere, Φ^ι2 and Φ^2ι, are described by equation (13). In this manner, the formation of Q differs from its use in the previously discussed four beam technique for measurement of absorbance, where Φ^12 and Φ^21 would instead correspond to direct path measurements.

For each gas measurement made, a zero measurement (i.e. no analyte present) is derived by measuring the radiant flux at one or a number of wavelengths where the analyte does not absorb light (a baseline measurement) and inferring the value of the measurement in

the absence of the analyte at the absorbing wavelength(s). Alternatively, the measurement at zero analyte could be made at the absorbing wavelength(s) by introducing a clean, analyte free sample to the integrating sphere.

This gives an expression for Q(0), in the absence of the analyte of interest.

(15)

When fouling on the sphere wall occurs, it changes the mean reflectivity of the sidewalls and the throughput of each diffuse path changes. For example, if the reflectivity reduces, the radiant fluxes Φ^ and Φ^ι might also reduce according to equation (13).

The result of a change in the sphere mean reflectivity, and therefore its pathlength, can be measured using the values of Q(0) in the following manner.

An initial calibration stage is performed, whereby the value of Q(0) is determined for the initial (unfouled) state and the mean effective pathlength L of the sphere is determined using standard reference analytes whose absorbance is known. These value are termed Q(0)ca| and Lca\, respectively. Alternatively, other parameters of interest for the sphere might be determined, including but not limited to the sphere multiplier M, the mean inner reflectivity, the sidewall reflectivity p and the sphere throughput.

Because the optical beams in the direct paths do not encounter the sidewalls, it is reasonably assumed that changes to the direct paths Ln and l2i are negligible.

When the integrating sphere is used in situ, as previously described it may not be practical to complete the initial calibration and instead it becomes necessary to compensate for fouling-induced changes to the sphere parameter of interest, which in this example is its mean effective pathlength. The value of Q(0) in the in situ, potentially fouled state is determined from radiant flux measurements and termed Q(0)fOUi. A ratio of Q(0) in the fouled and initial calibration states is formed as follows.

(16)

Substituting the values for the transmitted flux, the expression becomes

(17)

As changes to the direct paths are negligible, the flux values cancel for all direct paths. The k constants likewise cancel leaving an expression in terms of the sphere multiplier only

(18)

This expression may be used to compensate for changes in sphere performance that are related, via the integrating sphere relations, to the sphere multiplier M. In this example, we use equation (18) to determine changes to the mean effective pathlength of the sphere.

It is known from the integrating sphere relations that the sphere multiplier M can be related to the mean effective pathlength of the sphere, Leff, as follows.

(19)

Where d is the diameter of the sphere.

Substituting this into equation (18) for each value of M, the expression becomes

(20)

For simplicity in this example, it is assuming that the paths have been set up symmetrically, i.e. /.12=/.21=1, and so the expression becomes

(21)

Thus the new pathlength /.(0)foui can be calculated by rearranging equation (21) to become

(22)

The pathlength can be used to determine the true concentration of the analyte in the potentially fouled state as follows. The ratio Q is formed using flux measurements at a wavelength or range of wavelengths absorbed by the target analyte, and termed Q[a).

In the potentially fouled state, Q(a) becomes:

(23)

The value of the absorbance at the wavelength of operation, and therefore the concentration of the analyte, can be determined by a simple rearrangement of equation (23), making use of flux measurements made in situ and made during an initial calibration stage when the sphere was in a clean, unfouled state.

It can be advantageous in some applications to be able to reduce the number of components in a sensor, for reasons of cost, complexity or ease of manufacturing. In a second embodiment of the invention, the number of components is reduced to one source SI and two detectors D1 and D2. This embodiment is described mathematically by reference to the above analysis for the embodiment that uses two sources and two detectors and by reference to Figure lb, which shows a schematic layout of the embodiment whose source and detector location is similar to those in Figure la.

The value of Q in equation (14) is now given by

(24)

And equation (17) becomes

(25)

In this embodiment, any potential degradation of the source, detector and associated windows is not cancelled and therefore these quantities must be taken into account. In the case of zero analyte, we know that

(26)

Substitution into equation (25) gives the following, where the k factors and direct path fluxes cancel but the detector efficiencies D and sphere multipliers, M, do not, leading to

(27)

In this embodiment it may be assumed that the detectors degrade in a similar manner to one another, which could be a valid assumption in some environments, and therefore the second term in equation (27) can be neglected. Substituting equation (19) gives

(28)

And the value of the new pathlength can be determined by rearrangement of equation (28).

(29)

Expansion of equation (24) yields

(30)

For the fouled state, the value of L12(0)foul can be determined by reference to equation (28).

In a third embodiment, it is advantageous to reduce the number of components to include two sources SI and S2 and one detector Dl. This embodiment is described by reference to Figure lc, which shows a schematic layout of the embodiment whose source and detector location is similar to those in Figure la. By a similar analysis, it can be shown that the new pathlength can be determined by

(31)

Which is rearranged to give

(32)

In this embodiment it may be assumed that the two sources degrade in a similar manner to one another, which includes the effects of any windows over the sources. It can also be shown that the absorbance of the analyte can be determined via rearrangement of the following equation:

(33)

For the fouled state, the value of L2i(0)foui can be determined by reference to equation (29).

In a general analysis, an embodiment may be arranged so as to provide n direct paths and m diffuse paths between multiple sources and detectors. For example, if there are j sources and k detectors, the parameter Q is generally defined as

(34)

By a similar analysis to the above, it can be shown that the mean effective pathlength for an integrating cavity also takes a general form. For the sake of simplification, we illustrate this with an example whereby the diffuse pathlengths are all identical and termed L, in which case the following expression applies.

(35)

We can compare the mathematical compensation of the pathlength described above with the conventional use of an integrating cavity employing no pathlength compensation. An example of an uncompensated system is shown in Figure 2. In this figure, 1 is again the inner wall of the integrating cavity, 2 is a direct path from source to detector and 3 is a diffuse path from source to detector.

By reference to equation (1), the absorption coefficient is measured as follows.

(36)

It is known that for integrating cavities, a modification of this expression may be required for high values of aLca\ where equation (36) becomes nonlinear. Such modifications employ an alteration to the pathlength that is a function of the absorption coefficient [Tranchart et a I, 1996] or an equivalent alteration to the form of equation (36) that is based on the Beer-Lambert law [Hodgkinson et al, 2009], However, it will be understood that such modifications do not relate directly to this invention since they can be applied similarly to both the calibrated and fouled states of the system, ie to equations (23), (30) or (33) as well as equation (36).

We now make reference to the above analysis in a description of the embodiments. A first embodiment comprises a system consisting of an integrating cavity, at least two sources and at least two detectors, arranged such that each detector encounters a proportion of light from one source that takes a direct path from the source to the detector without encountering the cavity sidewalls, and encounters a proportion of light from the other source that takes a diffuse path, ie that has been multiply reflected by the sidewalls. The first detector encounters the direct path from the first source and the diffuse path from the second source, and the second detector encounters the direct path

from the second source and the diffuse path from the first source. An example of such a system is shown schematically in Figure la.

In this embodiment, the mean effective pathlength of the cavity is initially determined during a calibration using known techniques, which for example may include the use of standard absorbers. At a separate time, the mean effective pathlength of the cavity is determined via a ratiometric measurement of the light power at both the first and second detectors, for each of the first and second sources independently. The ratiometric measurement to determine the mean effective pathlength of the cavity takes the form of equation (22) above. This embodiment is able to compensate the integrating sphere pathlength for changes in fouling of the sidewalls, degradation in the sources and degradation in the detectors, including changes in the transmission of the windows over the sources or detectors. A second embodiment comprises a system consisting of an integrating cavity, at least one source and at least two detectors, arranged such that a first detector encounters a proportion of light from the source that takes a direct path from the source to the detector without encountering the cavity sidewalls, and a second detector that encounters a proportion of light from the source that takes a diffuse path from the source, ie that has been multiply reflected by the sidewalls. An example of such a system is shown schematically in in Figure lb.

In this embodiment, the mean effective pathlength of the cavity is initially determined during a calibration using known techniques, which for example may include the use of standard absorbers. At a separate time, the mean effective pathlength of the cavity is determined via a ratiometric measurement of the light flux at both the first and second detectors from the source. The ratiometric measurement to determine the mean effective pathlength of the cavity takes the form of equation (29) above. This embodiment is able to compensate the integrating sphere pathlength for changes in fouling of the sidewalls and degradation in the source, including changes in the transmission of the window over the source. A further aspect of this embodiment is that the first detector may be positioned inside the cavity, at the cavity sidewall, or outside the cavity. A third embodiment comprises a system consisting of an integrating cavity, at least two sources and at least one detector, arranged such that the detector encounters a proportion of light from the first source that takes a direct path from a first source to the detector without encountering the cavity sidewalls, and encounters a proportion of light from the second source that takes a diffuse path, ie that has been multiply reflected by the sidewalls. An example of such a system is shown schematically in in Figure lc.

In this embodiment, the mean effective pathlength of the cavity is initially determined during a calibration using known techniques, which for example may include the use of standard absorbers. During use of the system, the mean effective pathlength of the cavity is determined via a ratiometric measurement of the light power at both the first and second detectors, for each of the first and second sources independently. The ratiometric measurement to determine the mean effective pathlength of the cavity takes the form of equation (32) above. This embodiment is able to compensate the integrating sphere pathlength for changes in fouling of the sidewalls, degradation in the sources and degradation in the detectors, including changes in the transmission of the window over the detector.

It is known that the properties of an integrating cavity including the inner wall surface reflectivity, the mean inner wall reflectivity (taking into account the port fraction), the cavity multiplier and the mean effective pathlength are all mathematically related to one another. Therefore a further aspect of the invention is to make a ratiometric measurement as described above that compensates for in situ changes in any of the said properties of the integrating cavity. A further aspect of the invention according to the above embodiments is a system, whereby the ratiometric measurement of the in situ mean effective pathlength is used to determine the absorption coefficient of an analyte contained or partially contained within the cavity. A further aspect of the invention according to the above embodiments is a system, whereby the measurement of absorption coefficient of the analyte is used to determine the quantity or concentration of a substance. The substance may be a gas, liquid, solid or a quantity dissolved in a gas, liquid or solid.

It is also provided a method of calibrating an integrating sphere, whereby measurements are made of the light flux by at least two detectors from at least two sources, arranged such that each detector encounters a proportion of light from one source that takes a direct path from the source to the detector without encountering the cavity sidewalls, and encounters a proportion of light from another source that takes a diffuse path, ie that has been multiply reflected by the sidewalls. The first detector encounters the direct path from the first source and the diffuse path from the second source, and the second detector encounters the direct path from the second source and the diffuse path from the first source, according to the arrangement shown schematically in Figure la.

In this method, the mean effective pathlength of the cavity is initially determined during a calibration using known techniques, which for example may include the use of standard absorbers. At a separate time, the mean effective pathlength of the cavity is determined via a ratiometric measurement of the light power at both the first and second detectors, for each of the first and second sources independently. The ratiometric measurement to determine the mean effective pathlength of the cavity takes the form of equation (22) above. A further aspect of this method is that the first detector may be positioned inside the cavity, at the cavity sidewall, or outside the cavity.

It is also provided a second method, whereby measurements are made of the light flux on at least two detectors from at least one source, arranged such that a first detector encounters a proportion of light from the source that takes a direct path from the source to the detector without encountering the cavity sidewalls, and a second detector that encounters a proportion of light from the source that takes a diffuse path, ie that has been multiply reflected by the sidewalls. An example of such an arrangement is shown schematically in in Figure lb.

In this method, the mean effective pathlength of the cavity is initially determined during a calibration using known techniques, which for example may include the use of standard absorbers. During use of the system, the mean effective pathlength of the cavity is determined via a ratiometric measurement of the light flux at both the first and second detectors from the source. The ratiometric measurement to determine the mean effective pathlength of the cavity takes the form of equation (29) above.

It is also provided a third method, whereby measurements are made of light flux on at least one detector from at least two sources, arranged such that the detector encounters a proportion of light from a first source that takes a direct path from the source to the detector without encountering the cavity sidewalls, and encounters a proportion of light from a second source that takes a diffuse path, ie that has been multiply reflected by the sidewalls. An example of such an arrangement is shown schematically in in Figure lc.

In this method, the mean effective pathlength of the cavity is initially determined during a calibration using known techniques, which for example may include the use of standard absorbers. During use of the system, the mean effective pathlength of the cavity is determined via a ratiometric measurement of the light power at the detector for each of the first and second sources independently. The ratiometric measurement to determine the mean effective pathlength of the cavity takes the form of equation (32) above.

It is known that the properties of an integrating cavity including the inner wall surface reflectivity, the mean inner wall reflectivity taking into account the port fraction, the multiplier and the mean effective pathlength are all mathematically related to one another. Therefore it is also provided a method according to the above embodiments whereby a ratiometric measurement is made as described above that compensates for in situ changes in any of the said properties of the integrating cavity.

It is further provided a method according to the above embodiments, whereby the ratiometric measurement of the in situ mean effective pathlength is used to determine the absorption coefficient of an analyte contained or partially contained within the cavity.

It is further provided a method according to the above embodiments, whereby the measurement of absorption coefficient of the analyte is used to determine the quantity or concentration of a substance. The substance may be a gas, liquid, solid or a quantity dissolved in a gas, liquid or solid.

In the above embodiments and methods, the term source can be taken to mean any object from which light is emitted, which could include a laser, LED or incandescent bulb mounted against the cavity, the end of an optical fibre or waveguide or free space optical beam, via which light has been directed from a remotely located source, or a window or lens through which light has been directed from a remote source. Similarly, the term detector can be taken to mean any object via which light is transmitted to a photodetector, which could include a photodetector mounted against the cavity, the end of an optical fibre or waveguide or free space optical beam, via which light is been directed towards a remotely located photodetector, or a window or lens through which light is been directed towards a remotely located photodetector.

Embodiments making use of at least two sources may provide independent measurements of each source by turning the sources one at different times, by turning them on and off alternately, by modulating the sources with different frequencies or by modulating the sources with different amplitude signatures.

In a further aspect of those embodiments using at least two sources, the sources preferably both emit light over overlapping wavelength ranges.

In a further aspect of those embodiments using at least two detectors, the detectors preferably both respond to light over overlapping wavelength ranges.

It is known that in conventional use of integrating cavities, a detector used to measure light taking a diffuse path from a source is preferably positioned so as to have no direct line of sight from said source to said detector, which may be achieved by means of a baffle or by limiting the detector's field of view [Labsphere, 2015; Hodgkinson et al, 2009]. A further aspect of the invention is therefore that detectors positioned inside the integrating cavity and encountering a proportion of the light in a direct path from a source, may be placed within the so-called "first strike spot" where the beam of light from the source first encounters the cavity sidewall, which is contrary to typical conventional configurations.

The cavity in the above embodiments and methods may comprise a sphere, a cuboid or other arbitrarily shaped volume. This is shown schematically in Figure 3. In this figure, 1 is again the inner wall of the integrating cavity, 2 is a direct path from source to detector and 3 is a diffuse path from source to detector.

We now illustrate two of the embodiments with an experimental example. The experiments employ the well-known technique of tunable diode laser spectroscopy (TDLS). A typical TDLS setup employs a tunable diode laser, with the output wavelength tuned to scan over the gas absorption line of interest at very high resolution. The tuning of the laser is achieved by controlling its temperature and electrical current.

In a technique termed direct absorption spectroscopy the laser diode emitting in the region of 1651nm was scanned across one or more gas lines by ramping the injection current with a sawtooth waveform of known frequency. The light was directed through an analyte, in this case a gas (methane), which has an absorption line at 1651nm. The resulting measured transmission consisted of the ramped waveform, corresponding to an increase in the intensity of the output as the current is increased. In the presence of a gas analyte, a dip in the signal corresponds to the gas absorption line when the scanned laser wavelength matched the gas absorption wavelength.

The components used in these experiments are now described. - Two tunable laser sources (DFB, VCSEL, External cavity) at an appropriate wavelength for the gas absorption line being used. This work used two NEL DFB lasers, NLK 1U5EAAA, which were pigtailed to optical fibre. - Two aspheric lens (Lightpath 350230-D and Thorlabs C280TM), used to optimise the divergence of the light from the sources into the sphere. - An integrating sphere (Thorlabs IS200-4) with a diameter of 50.8mm and modified to have 6 port openings, four for component exit and entry, spaced at 90° intervals around the sphere and two are for gas input and output. - Two variable gain detectors (Thorlabs PDA 10CS-EC) and switchable gain. - A signal generator (HP 33120A) to supply a sawtooth waveform with a frequency of 1kHz to the laser controller to allow tuning of the laser emission wavelength. - Two laser current controller (Profile LDC202) used to control the current of each laser to a set DC level with an additional modulation waveform supplied by the signal generator. - Two laser temperature controllers (Profile TED200), used to control each of the lasers' temperatures to setpoints that provided an emission wavelength at 1651nm. - Data acquisition system using the Labview software environment, to capture the detector across the whole sawtooth waveform and permit averaging of multiple waveforms. - Gas handling system: test gases were fed to the sphere from two certified cylinders (Scott Specialty Gases), one containing hydrocarbon (HC) free air, and the other containing 2.5%vol methane in HC free air. A bank of mass flow controllers (Teledyne Hastings HFC-302 with THPS-400 controller) was used to control flow rates from the two cylinders, with downstream mixing generating a series of mixtures of different concentrations in the range 0-0.625% vol.

Figure 4 shows a schematic diagram of the experimental arrangement. 4 is an integrating sphere, 5 and 6 are separate photodetector / amplifiers, 7 and 8 are two optical fibre pigtailed DFB laser diodes, 9 is a signal generator, 10 and 11 are laser current drivers, and 12 is computer based data acquisition system. For test purposes, two gas cylinders 13 were connected to a bank of mass flow controllers 14 in order to provide a series of dilutions of methane in air at known concentrations. 15 represents a repositioned light source, either 7 or 8 separately, for the purpose of evaluating the absorbance of the target gas using 16, an optical transmission cell with a known pathlength and 8, a photodetector / amplifier of the same type as 4 and 5, used to measure the flux transmitted through the optical cell 16.

The outputs from two fibre-coupled 1651nm distributed feedback lasers were placed at 90° intervals from each other and the emitted light divergence controlled with aspheric lenses to have a beam diameter of approx 5.5mm at the opposite exit port. Two variable gain detector / amplifiers (Thorlabs PDA10CS) were used with a gain of OdB to measure the flux in the direct paths and 50dB to measure the flux in the diffuse paths. These were placed at the two opposite ports, recessed from the sphere port so that baffles were not required. The detectors were recessed from the sphere so as to avoid a direct line of sight with the input source positioned at 90°. The ports were made from Spectralon with a thickness of 10mm to maximise reflectivity.

The interrogation system used was a simple form of direct spectroscopy, in which the emitted wavelength from a tunable diode laser was scanned across a methane line at 1651nm. A sawtooth waveform was provided by a signal generator and used to modulate the current into a laser controller between a minimum of 90mA and a maximum of 130mA for each laser diode. The laser diodes were operated independently, at different time intervals.

In the absence of gas, a reference measurement showed a rising output intensity with current, as expected. In the presence of methane, a dip corresponding to a gas line is observed, at a wavelength specific to the molecule of interest, thus allowing identification and quantification of the molecule of interest. The outputs were sampled using a data acquisition card and transferred to a PC for data processing. See Figure 5 for a schematic representation of the data analysis.

For initial calibration of the sphere pathlength, the output from each laser was first coupled into a 114.5cm single pass gas cell with AR coated wedged windows, and then coupled into the integrating sphere at the respective port. The gas inlet and outlet pipes were connected so that the two cells were filled with the same concentration of gas, in series. The flow rate was controlled by mass flow controllers so as to control the concentration of methane in air.

Using direct absorption, the transmitted signal was recorded for each of the cells with gas (lOlOppm concentration), corresponding to Φθ(α), and without gas, corresponding to Φθ(0). This was noted for cell and sphere for both lasers to give relative absorbances. Using equation 14, an effective pathlength could be calculated.

(37)

Where Lsphere was the pathlength of the sphere, being equal to Ln or /.21 depending on which detectors and sources were being used to perform the calibration. Z.cen =114.5cm, Asphere is the absorbance of the analyte in the sphere and >4ceii is the absorbance of the analyte in the 114.5cm gas cell.

The detectors were both set to a gain of OdB, and measurements of light flux for direct paths, Ln and L22 were made by turning on the sources alternately at different times. The gains were then switched to 50dB and fluxes measured for the diffuse paths, Ln and i21· The four paths were first measured for zero gas (HC free air), then for gas at varying concentrations.

The following tests were then performed to simulate degradation in the optical components.

To simulate fouling of the internal walls of the integrating sphere, up to 7 tabs of black tape of approximate size 5mmx7mm were placed at different locations around the inner walls of the sphere, one by one. When each new fouling tab was added, flux values were recorded for each concentration of gas as described above. This experiment is shown schematically in Figure 6.

To simulate source intensity variation, the laser output intensity was reduced. The laser current for laser 1 (SI) was reduced from 110mA to 105mA. To ensure that the 1651nm gas line was still centred as the current was ramped, the temperature was adjusted from 16.16°C to 16.35°C. This had the effect of reducing the emitted intensity by 4.2%.

To determine the light fluxes at the wavelength corresponding to the gas absorption line, measurements from a scan across the line centre were averaged over the 30 data points closest to the line centre, corresponding to a wavelength rage of 0.67pm around the gas line centre. Figure 5 shows a schematic illustrating the analysis of the waveforms.

Using the measured flux values, calculations were performed of the values of Q(a) and Q(0) for the calibration and fouled states, for the various concentrations of gas according to equation (15). The mean effective pathlength of the sphere was calculated for each of the fouled states according to equation (22) and used to calculate the absorption coefficient of the gas at the line centre according to equation (23). For the purpose of comparison, this was compared with a calculation of the absorption coefficient performed according to equation (23) without the use of our invention, ie using the original calibrated pathlength Lca\ without any modification.

An example of the results is shown in Figure 7 for determination of gas absorption coefficient for different levels of sphere wall fouling. The example shows analysis of the results of compensating the pathlength using the first embodiment of the invention, with two sources and two detectors as shown in Figure 6. A comparison was made with use of the same setup without the invention, ie uncompensated measurements according to equation (36) and Figure 2.

The result demonstrate that if the optical pathlength at calibration, Lca\, is wrongly assumed to be correct, then errors of over 50% were observed for the use of 5 fouling tabs, corresponding to a tab area of approximately 3.2% of the inner area of the sphere. Using the invention to compensate for associated changes in the optical pathlength, errors remained within ±3% for the use of up to 5 fouling tabs. Errors increased for higher levels of fouling, which we attribute to an overall loss of integrating performance of the cavity when the mean internal reflectivity drops substantially.

The second experiment considered source degradation, in the absence of wall fouling as well as with sphere wall fouling. This experiment was used to test the first embodiment of the invention, with two sources and two detectors as shown in Figure 6.

The system was tested with clean air only (not gas) so that differences in output values would be solely attributable to component variation or sphere wall fouling. As with the previous experiment, fouling tabs were placed at various locations around the sphere wall, taking measurements of the four paths each time a new tab was placed inside the sphere. For each tab addition, a component "degradation" measurement was taken for source 1 direct and diffuse paths.

To demonstrate the compensation scheme, the Q(0) values for calibrated source and "degraded" source were compared for different levels of fouling, rather than with the calibrated value. For the uncompensated scheme, the direct path flux values for calibrated source and "degraded" source were used. This meant that differences in the measurements were solely a result of component degradation and not sphere wall fouling. With a drop in laser current from 110mA to 105mA, one would expect a percentage difference in output power of approximately 4.2%.

Table 1: Measurement error for uncompensated and compensated system for a 4.2% reduction in source power for a methane concentration of lOlOppm.

As seen in Table 1, the uncompensated system produced errors of a similar magnitude to the reduction in source power, as expected, with an average proportional difference of 4.04%. Whereas using the compensated system of this invention, this percentage difference dropped to 0.18% on average.

In a further experiment, results were analysed according to the second embodiment of the invention, with one source and two detectors. The experimental setup was identical to the previous experiments, as shown in Figure 6, however the second laser, corresponding to source S2, was not used. In this case, the pathlength for the integrating sphere was determined using equation (29) and used to compensate the measurements. A comparison was again made with an uncompensated system.

In this experiment, the second embodiment of the invention was able to compensate the mean effective pathlength of the integrating sphere so as to give errors that were within ±8% compared with up to over 70% for the uncompensated system.

Claims

Patent Application (Claims): Title: ln-situ pathlength calibration for integrating cavities Claims What is claimed is

1. A method of determining the mean effective pathlength of an integrating cavity, using at least one light source and at least two detectors, whereby the at least one light source comprises light emitted by a laser, a light emitting diode or an incandescent filament, or light exiting an optical fibre, lens or window, such that light traversing from the at least one source to the first detector is substantially not influenced by the reflectivity of the cavity and the light traversing from the at least one light source to the second detector is substantially influenced by the reflectivity of the cavity, a reference mean effective pathlength of the cavity being determined during a calibration step at a first time using a calibration standard, and then the actual mean effective pathlength of the cavity being determined at a second time by reference to the reference mean effective pathlength and to the ratio of light fluxes measured at the second time by the first and second detectors from the at least one light source, and to the ratio of light fluxes measured at the first time by the first and second detectors from the at least one light source.

2. The method of claim 1, whereby the at least one light source comprises at least one wavelength range that is substantially not absorbed by an analyte and at least one wavelength range that is substantially absorbed by an analyte.

3. The method of any of the preceding claims, whereby the calibration step involves determination of a reference value Q0cai equal to the ratio of the light fluxes measured at the first time at the non-absorbed wavelength from the at least one light source by the second detector to the light flux measured at the first time at the non-absorbed wavelength from the at least one light source by the first detector, and the actual pathlength is determined by calculating the value of the reference pathlength multiplied by a value Qoact, formed by the ratio of the light fluxes measured at the second time at the non-absorbed wavelength from the at least one light source by the second detector to the light flux measured at the second time at the non-absorbed wavelength from the at least one light source by the first detector, divided by Qoca|.

4. A method of determining a characteristic of an integrating cavity, using at least two light sources and at least two detectors, whereby the at least two light sources each comprise light emitted by a laser, a light emitting diode or an incandescent filament, or light exiting an optical fibre, lens or window, arranged such that light traversing from the first source to the first detector is substantially not influenced by the reflectivity of the cavity, light traversing from the first source to the second detector is substantially influenced by the reflectivity of the cavity, light traversing from the second light source to the second detector is substantially not influenced by the reflectivity of the cavity, light traversing from the second light source to the first detector is substantially influenced by the reflectivity of the cavity and light traversing from the second light source to the second detector is substantially influenced by the reflectivity of the cavity, a reference characteristic of the cavity being determined during a calibration step at a first time using a calibration standard, and then the actual characteristic of the cavity being determined at a second time by reference to the reference mean effective pathlength and to the light fluxes measured at the second time by the first detector from the first light source and by the first detector from the second light source and by the second detector from the second light source and by the second detector from the first light source, and to the light fluxes measured at the first time by the first detector from the first light source and by the first detector from the second light source and by the second detector from the second light source and by the second detector from the first light source.

5. The method of claim 4, whereby the at least two light sources each comprise at least one wavelength range that is substantially not absorbed by an analyte and at least one wavelength range that is substantially absorbed by an analyte.

6. The method of either of claims 4 or 5, whereby the calibration step involves determination of a reference value Q0cai equal to the product of the light fluxes measured at the first time at the non-absorbed wavelength from the first light source by the second detector and from the second light source by the first detector, divided by the product of the light fluxes measured at the first time at the non-absorbed wavelength from the first source by the first detector from the second source by the second detector, and a second value Q0fOUi is formed by the product of the light fluxes measured at the second time at the non-absorbed wavelength from the first source by the second detector from the second source by the first detector, divided by the product of the light fluxes measured at the second time at the non-absorbed wavelength from the first source by the first detector from the second source by the second detector, and then the actual characteristic is determined by calculating the value of the reference characteristic multiplied by the square root of (Qofoui divided by Qocal)·

7. The method of any of claims 4, 5 or 6, whereby the characteristic of the integrating sphere that is determined is its mean effective pathlength.

8. A method of determining the mean effective pathlength of an integrating cavity, using at least two light sources and at least one detector, whereby the at least two light sources each comprise light emitted by a laser, a light emitting diode or an incandescent filament, or light exiting an optical fibre, lens or window, such that light traversing from the first light source to the at least one detector is substantially not influenced by the reflectivity of the cavity and the light traversing from the second light source to the at least one detector is substantially influenced by the reflectivity of the cavity, a reference mean effective pathlength of the cavity being determined during a calibration step at a first time using a calibration standard, and then the actual mean effective pathlength of the cavity being determined at a second time by reference to the reference mean effective pathlength and to the ratio of light fluxes measured at the second time by the at least one detector from the first and second light sources, and to the ratio of light fluxes measured at the first time by the at least one detector from the first and second light sources.

9. The method of claim 8, whereby the at least two light sources each comprise at least one wavelength range that is substantially not absorbed by an analyte and at least one wavelength range that is substantially absorbed by an analyte.

10. The method of either of claims 8 or 9, whereby the calibration step involves determination of a reference value Qocai equal to the ratio of the light flux measured at the first time at the non-absorbed wavelength by the at least one detector from the first and second light sources, and the actual pathlength is determined by calculating the value of the reference pathlength multiplied by a value Q0act, formed by the ratio of the light flux measured at the second time at the non-absorbed wavelength by the at least one detector from the first and second light sources, divided by Qocai·

11. The method of any of claims 1 - 3 or claims 7 - 10, whereby the mean effective pathlength is used to determine the light absorbance for the integrating cavity.

12. The method of any of claims 1 - 3 or claims 7 - 10, whereby the mean effective pathlength is used to determine the quantity of an analyte contained within the integrating cavity.

13. An instrument for determining the mean effective pathlength of an integrating cavity, the instrument comprising at least one light source and at least two detectors, whereby the at least one light source comprises light emitted by a laser, a light emitting diode or an incandescent filament, or light exiting an optical fibre, lens or window, arranged such that light traversing from the at least one light source to the first detector is substantially not influenced by the reflectivity of the cavity and the light traversing from the at least one light source to the second detector is substantially influenced by the reflectivity of the cavity, the instrument establishing a reference mean effective pathlength at a first time during a calibration step and establishing an actual mean effective pathlength by making reference to the light fluxes measured by the first and second detectors from the at least one light source at the first and second times.

14. The instrument of claim IB, whereby the at least one light source comprises at least one wavelength range that is substantially not absorbed by an analyte and at least one wavelength range that is partly absorbed by an analyte.

15. An instrument for determining a characteristic of an integrating cavity, the instrument comprising at least two light sources and at least two detectors, whereby the at least two light sources each comprise light emitted by a laser, a light emitting diode or an incandescent filament, or light exiting an optical fibre, lens or window, arranged such that light traversing from the first light source to the first detector is substantially not influenced by the reflectivity of the cavity, light traversing from the first light source to the second detector is substantially influenced by the reflectivity of the cavity, light traversing from the second light source to the second detector is substantially not influenced by the reflectivity of the cavity, and light traversing from the second light source to the first detector is substantially influenced by the reflectivity of the cavity, the instrument establishing a reference characteristic at a first time during a calibration step and establishing an actual characteristic by making reference to the light fluxes measured by the first and second detectors from the first and second light sources at the first and second times.

16. An instrument for determining a characteristic of an integrating cavity, the instrument comprising at least two light sources and at least one detector, whereby the at least two light sources each comprise light emitted by a laser, a light emitting diode or an incandescent filament, or light exiting an optical fibre, lens or window, arranged such that light traversing from the first light source to the at least one detector is substantially not influenced by the reflectivity of the cavity and light traversing from the second light source to the at least one detector is substantially influenced by the reflectivity of the cavity, the instrument establishing a reference characteristic at a first time during a calibration step and establishing an actual characteristic by making reference to the light fluxes measured by the at least one detector from the first and second light sources at the first and second times.

17. The instrument of any of claims 15 - 16, whereby the characteristic of the integrating sphere is its mean effective pathlength.

18. The instrument of any of claims 15 - 17, whereby the at least two light sources each comprise at least one wavelength range that is substantially not absorbed by an analyte and at least one wavelength range that is partly absorbed by an analyte.