Laser dispersion spectrometer

Abstract

A laser dispersion spectrometer is described which comprises: a laser source arranged to form a laser beam, an electro-optic phase modulator arranged to add a plurality of sidebands to the laser beam responsive to an RF modulation signal, optics arranged to transmit the laser beam including the plurality of sidebands through a sample, a photodetector arranged to receive the laser beam from the optics following transmission through the sample, and to generate a corresponding electrical photodetector output, a DC / RF splitter arranged to split the photodetector output into a DC component and an RF modulated component, an IQ demodulator arranged to demodulate the RF modulated component to form demodulated quadrature components, and a calculation element arranged to calculate a phase parameter which is related to optical phase of the laser beam following transmission of the laser beam through the sample using the DC and demodulated quadrature components.

Description

[0001] Laser dispersion spectrometer

[0002] The present invention relates to a laser dispersion spectrometer, and to a method of determining a phase parameter which is related to, or a measure of, optical phase of a laser beam following transmission through a sample for example using such a spectrometer. Embodiments of the invention may in particular use a near or mid infrared laser beam, and may be used to detect one or more species in a gaseous sample, for example over an extended atmospheric “open-path”. Detection of methane in the atmosphere is one such area of application.

[0003] Introduction

[0004] Tunable laser dispersion spectroscopy (LDS) exploits the anomalous optical dispersion occurring when the laser field interacts with a molecular resonance giving rise to a corresponding spectral feature. Upon interaction, not only the amplitude of the field is affected (absorption) but also the phase, and the full properties of the light field may hence be recovered. The phase change spectrum carried by the field can be used to infer molecular concentration, with the benefit of linearity, and increased immunity to intensity fluctuations. Although these advantages apply to a wide variety of spectroscopic situations, these are also prime advantages for open-path field measurements of fugitive gas emissions.

[0005] The LDS phase spectrum may be measured by heterodyne detection of coherent fields offset in frequency to create an optical dispersion contrast. For example, controlled sidebands of a source laser field can be used. In the mid infrared (MIR), particularly in the 3-5 pm and 8-12 pm atmospheric transparency windows where molecules exhibit fundamental ro-vibrational transitions, acousto-optic modulators (AOM) have been used to generate dual-frequency coherent laser beams without intensity modulation. Using AOMs is straightforward but limited in terms of the allowable frequency offset between sidebands (typically <200 MHz). Yet, to maximize the dispersion contrast between the two sidebands, an offset on the order of the molecular linewidth to be probed is desirable. At atmospheric pressure, molecular ro-vibrational transitions are collisionally broadened to few gigahertz. Alternatively, at the cost of increased complexity, direct semiconductor laser current modulation has been demonstrated, as well as MIR difference frequency generation to push the sideband frequency separation to the GHz range.

[0006] In the near infrared (NIR), ro-vibrational molecular transitions are harmonics and much weaker than in the MIR (for example 100 times weaker for methane), but a wealth of mature, commercially available photonics technologies are available, particularly for radiofrequency (RF) sideband creation. Waveguide-based electro-optic modulators (EOMs) allow modulation frequencies up to a few tens of GHz, even suited for broadband absorbers. NIR LDS based on a type of EOM known as an intensity modulator (IM) have been reported, for example see W. Ding et aL, Applied Optics, 55, 31 , 2016, “Dualsideband heterodyne of dispersion spectroscopy based on phase-sensitive detection”. IMs allow control on the output sideband pattern and therefore enable the most straightforward implementation of NIR LDS, but they require precise control for the long-term stable suppression of specific sidebands to mitigate temperature and charge build up effects.

[0007] The invention addresses these and other issues of the related prior art.

[0008] Summary of the invention

[0009] The invention provides a laser dispersion spectrometer, and a method of carrying out laser dispersion spectroscopy, with improved robustness, cost- and power-efficiency, which can be used for a variety of spectroscopic tasks such as atmospheric open-path continuous monitoring, and particularly for dispersion spectroscopy tasks in the near infrared, where the benefits of the maturity and cost effectiveness of NIR photonics is retained. Rather than using a Mach-Zender interferometer-based electro-optic intensity modulator requiring active stabilization, a simpler, low-power consumption electro-optic phase modulator (PM) is used for sideband creation. The greater simplicity and economy of the architecture comes at the cost of far more complex sideband patterns, which is addressed through signal analysis to recover the benefits of molecular dispersion spectroscopy.

[0010] Some embodiments of the invention provide an open-path, fibre-based spectrometer, and corresponding methods, that operates in the near infrared, which enables the use of cheap and modular optics components largely developed for the telecoms industry. The spectrometer uses phase modulation (as opposed to intensity modulation) to spread the optical power over a plurality of sidebands (for example around ten, and typically less than around thirty). Phase modulators are less sensitive to changes in ambient conditions and are simpler to operate than intensity modulators. However, this hardware implementation requires novel signal analysis to calculate a suitable phase parameter which is immune to optical power variation in the laser beam received at the photodetector following transmission through the sample.

[0011] In particular, therefore, the invention provides a method of determining a phase parameter which is a measure or estimate of, or is related to, the or an optical phase of a laser beam following transmission of the laser beam through a sample, the method comprising: passing the laser beam through an electro-optic phase modulator driven by an RF modulation signal so as to add a plurality of frequency sidebands to the principal frequency of the laser beam; passing or transmitting the laser beam including the plurality of sidebands through the sample; receiving the laser beam following passage through the sample at a photodetector to generate an electrical photodetector output; splitting the photodetector output into a DC component and an RF modulated component; demodulating the RF modulated component to form demodulated quadrature components; measuring the DC component and demodulated quadrature components; and calculating the phase parameter of the laser beam following transmission of the laser beam through the sample using the measured DC and demodulated quadrature components.

[0012] The determined phase parameter may for example be described as a measure of the phase or phase change of the overall beat-note generated by nearest-neighbour pairs of the plurality of frequency sidebands. The determined phase parameter may in particular have advantageous properties in being essentially immune to variations in the power of the laser beam received at the photodetector.

[0013] Typically, the laser beam will be in the near infrared, but could be in the mid infrared or some other wavelength range. The sample will typically be a gaseous sample, but could be a liquid or in some other phase or mixture of phases, and may be contained in sample chamber or be present in an open-path, for example where the sample is the open atmosphere.

[0014] The phase parameter may be calculated using a ratio of: a first weighted sum of the measured DC component and a first of the measured demodulated quadrature components, and a second weighted sum of the measured DC component and the second of the measured demodulated quadrature components. The phase parameter may be expressed as an arctangent of this ratio, or in various other forms. An example of a suitable calculation of the phase parameter is provided in equation (5) below. Each weighted sum may combine the measured DC component and one of the measured demodulated quadrature components in the same ratio of 1 : / r.The parameter k may lie within a range of possible values such as -1000 <= k<= +1000, or rmay be equal to 1. The possible or useful values of fcmay in particular be limited by singularities in the arctangent function seen in equation (5) below.

[0015] The RF component may be demodulated using an IQ demodulator, by providing the IQ demodulator with an input of the same RF modulation signal as used to drive the phase modulator. The photodetector output may be split into a DC component and an RF modulated component using a bias-tee or similar component. The electro-optic phase modulator may add at least two, at least four, at least six, or at least eight, and optionally ten or more, and optionally less than thirty sidebands to the laser beam, for example where each such added sideband has at least 2% or 5% of the intensity or power of the principal laser frequency.

[0016] Although the laser spectrometer may in principle operate at a single principal laser frequency, more commonly the laser beam will be frequency scanned along with the sidebands, either continuously or in discrete steps, across a spectral feature of a component species of the sample. The DC and the demodulated quadrature components may then be measured as a function of the scanned frequency, and the phase parameter may also be calculated as a function of the scanned laser beam frequency. A concentration of the component species of the sample may then be determined using the phase parameter calculated as a function of the scanned laser beam frequency.

[0017] Operating parameters of the spectrometer, such as the number and / or spacing of the sidebands, the frequency of the RF modulation signal, the k parameter and so forth may be modified or adjusted so as to help optimize the determined phase parameter for example depending on the spectral width of the target spectral feature. For example, the spectral features of most common atmospheric molecular species have linewidths in the range of a few gigahertz, but there may also be interest in detecting more complex molecules, which can have spectral features with much greater linewidths (such as detection of molecules for air quality monitoring purposes, or detection of toxic molecules intended for malicious purposes).

[0018] Various data conditioning steps may be applied to the demodulated quadrature components before using them to calculate the phase parameter, for example one or more of: fitting a curve to each demodulated quadrature component as a function of scanned laser frequency and subtracting the respective fitted curve from the corresponding demodulated quadrature component to effect a baseline correction to each demodulated quadrature component; and carrying out one or more polar coordinate system rotation operations on the demodulated quadrature components.

[0019] The method may particularly be applied to open-path atmospheric measurements for example where the component species of the sample is methane, and the spectral feature is a near-IR absorption feature of methane.

[0020] The concentration of the component species may be calculated by using a parameterised forward model of the spectrometer or the above described method aspects to derive synthetic values of the phase parameter, and an optimization process (which may for example be implemented as an optimal estimation process) to adjust one or more parameters of the forward model so as to fit the synthetic values of the phase parameter to the calculated values of the phase parameter. As part of this calculation one or more of: an a priori chirp rate of the scanned laser beam, a spectrum noise of the calculated values of the phase parameter, and an initial signal to noise ratio of the calculated values of the phase parameter, may be calculated and provided to the optimization process.

[0021] The optimization process may output both the determined concentration of the component species of the sample, and one or more quality assurance or control parameters relating to the determined concentration.

[0022] The invention also provides apparatus corresponding to the methods described above and elsewhere in this document, for example a laser dispersion spectrometer comprising: a laser source arranged to form a laser beam; an electro-optic phase modulator arranged to add a plurality of frequency sidebands to the laser beam responsive to an RF modulation signal, for example around ten such sidebands; optics arranged to transmit the laser beam including the plurality of sidebands through a sample; a photodetector arranged to receive the laser beam from the optics following transmission through the sample, and to generate a corresponding electrical photodetector output; a DC / RF splitter arranged to split the photodetector output into a DC component and an RF modulated component; an IQ demodulator arranged to demodulate the RF modulated component to form demodulated quadrature components; and a calculation element arranged to calculate a phase parameter which is a measure or estimate of, or is related to, optical phase of the laser beam following transmission of the laser beam through the sample, using the DC and demodulated quadrature components.

[0023] As noted above, the calculation element may be arranged to calculate the phase parameter using a ratio of: a first weighted sum of a measurements of the DC and a first of the demodulated quadrature components; and a second weighted sum of measurements of the DC and a second of the demodulated quadrature components, and in various other ways as described herein.

[0024] The laser dispersion spectrometer may further comprise a suitable signal conditioning element arranged to apply data conditioning to the demodulated quadrature components, optionally comprising one or more of: fitting a curve to each demodulated quadrature component and subtracting the respective fitted curve from the corresponding demodulated quadrature component to effect a baseline correction to each demodulated quadrature component; and carrying out one or more polar coordinate system rotation operations on the demodulated quadrature components. The laser dispersion spectrometer may further comprise a laser driver arranged to frequency scan the laser beam across a spectral feature of a component species of the sample. The calculation element may then be arranged to calculate the phase parameter as a function of the scanned laser beam frequency.

[0025] The laser dispersion spectrometer may further comprise an analyser arranged to determine a concentration of the component species of the sample using the phase parameter calculated as a function of the scanned laser beam frequency. The analyser may be arranged to determine a concentration of the component species using a parameterised forward model of the laser dispersion spectrometer to derive synthetic values of the phase parameter, and an optimization process (which may be implemented using an optimal estimation method) to adjust one or more parameters of the forward model so as to fit the synthetic values of the phase parameter to the calculated values of the phase parameter.

[0026] Various aspects of the described apparatus and methods, for example any or all of the signal conditioning element, the calculation element and the analyser may be implemented using computer software on one or more suitable computer systems. Such computer systems may form part of a main spectrometer unit, or could be provided separately either locally or remotely. Each such computer system will typically comprise one or more microprocessors, memory for storing and executing the computer software and for storing related data, and suitable input / output mechanisms as required by the application such as one or more network ports, visual display units, keyboards or other controls, and so forth.

[0027] The invention then may also provide computer implemented methods, computer software or programs arranged to implement such methods, one or more computer readable media carrying such software or computer programs, and computer apparatus arranged to carry out such methods. For example, the invention also provides a computer implemented method of calculating a phase parameter which is a measure of, or is related to, the or an optical phase of a laser beam following transmission through a sample, the method comprising: receiving a DC component and demodulated quadrature components of an RF component of an output signal from a photodetector detecting the laser beam; and calculating the phase parameter from the received DC and demodulated quadrature components, for example using a ratio of: a first weighted sum of the measured DC and a first of the measured demodulated quadrature components, and a second weighted sum of the measured DC and the second of the measured demodulated quadrature components, and optionally as an arctangent of such a ratio. The invention then also provides a computer program arranged to carry out this method, one or more computer readable media carrying computer program code arranged to carry out the method, and computer apparatus arranged to carry out the method.

[0028] Brief description of the drawings

[0029] Embodiments of the invention will now be described, with reference to the drawings, of which:

[0030] Figure 1 schematically shows a laser dispersion spectrometer, arranged to sample the atmosphere along an open path, and including sideband generation using an electrooptic phase modulator;

[0031] Figure 2 provides further details regarding how an optical subsystem of the spectrometer of figure 1 may be constructed;

[0032] Figure 3 provides further details regarding how a radiofrequency (RF) subsystem of the spectrometer of figure 1 may be constructed;

[0033] Figure 4 illustrates how the spectrometer may be used to scan a laser beam with multiple sidebands created using the electro-optic phase modulator;

[0034] Figure 5 show graphs of both measured (points) and modelled (lines) of the following signals / components: top panel - quadrature I and Q components output by the IQ demodulator; middle panel - RMS magnitude of the / and Q components as ( l2+ Q2), which is proportional to the RF power; and lower panel - the calculated phase parameter;

[0035] Figure 6 illustrates stages of signal conditioning of the raw quadrature I and Q components before use in calculation of the phase parameter;

[0036] Figure 7 shows how the analyser of figure 1 can be implemented using a forward model of the spectrometer and an optimization or optimal estimation process; and

[0037] Figure 8 provides a flow chart of methods of laser dispersion spectrometry using a spectrometer such as that of figures 1 to 3 and 7.

[0038] Detailed description of embodiments

[0039] Referring to figure 1 there is shown schematically a spectrometer 10 for detecting one or more component species of a sample 20 using a laser beam 25, and in particular for determining concentration of such component species within the sample. In particular, the sample may be a gaseous sample, and in the arrangement of figure 1 the sample is probed in an open path configuration in which the laser beam is directed across an extended external and typically atmospheric path which may typically be of tens to hundreds of meters in length. In such configurations the laser beam could be reflected back to the spectrometer by means of a distant retroreflector 30. Such an arrangement may be used for atmospheric monitoring, for example monitoring for greenhouse gases such as methane.

[0040] However, in other configurations the sample may be probed within a closed sample cell or chamber, typically using a multi-path cell having opposing mirrors to increase the path length and therefore the sensitivity of the spectrometer, or provided in other ways. Although the sample may be gaseous, liquid or other fluid samples, or even solid samples or samples of mixed phase may instead be used.

[0041] The laser beam is preferably a near infrared laser beam, for example within a wavelength band from about 700 to 2500 nm. However, the laser beam could instead be in the mid infrared, for example within a wavelength band from about 2 to 20 pm.

[0042] The spectrometer comprises a laser source 100 for generating the laser beam 25. The laser beam is typically scanned in frequency using a suitable laser driver 105. The frequency scanned laser beam is then passed through an electro-optic modulator 110, and in particular an electro-optic phase modulator rather than an electro-optic intensity modulator. The phase modulator is driven by an RF modulation signal 115 provided by an RF source 120. The phase modulator 110 adds a plurality of sidebands 35 to the laser beam 25, the optical frequency spacings of which correspond to or, are the same as, the frequency of the RF modulation signal.

[0043] The frequency scanned laser beam 25 including the sidebands 35 added by the phase modulator 110 is then directed into the sample 20 using optics 40, for example into an open atmospheric path containing the sample using a telescope forming part of the optics 40, before being received back (in figure 1 again using the telescope or optics 40 following reflection from the distant retroreflector 30) and directed to a photodetector 130 which generates a corresponding electrical photodetector output 135.

[0044] In order to detect or determine concentration of a component species of the sample, the laser beam is typically scanned in frequency across a spectral feature such as an infrared or near infrared absorption line or some other molecular resonance spectral feature of the component species. Because the refractive index of the sample changes slightly as a function of optical frequency across the absorption line or other spectral feature, change in phase of the laser beam as received at the photodetector, as a function of scanned frequency, can be used to determine concentration of the component species. Such techniques are generally referred to in the prior art as phase sensitive laser dispersion spectroscopy. In some prior art arrangements, such as that of W. Ding et al., Applied Optics, 55, 31 , 2016, “Dual-sideband heterodyne of dispersion spectroscopy based on phase-sensitive detection", an electro-optic intensity* modulator is used to generate a very limited number of sidebands of significant intensity (for example of at least 2% or at least 5% of the intensity or power of the central frequency), and typically just two such sidebands. Electrooptic intensity modulators are typically constructed to incorporate a Mach-Zehnder interferometer arrangement to suppress further sidebands. This makes determination of phase change of the laser beam due to passage through the sample relatively straightforward.

[0045] However, an electro-optic *phase* modulator 110 as used in embodiments of the present invention is typically of less complex construction, lacking any such Mach Zehnder arrangement, and therefore typically gives rise to a larger number of sidebands of significant intensity or power (for example of at least 2% or at least 5% of the intensity or power of the central laser frequency), typically at least four, six, eight, ten or more such sidebands. This larger number of sidebands 35 makes it much more difficult to determine changes in phase of the laser beam due to passage through the sample 20, from which concentration of one or more component species with the sample can be determined as discussed above. The spectrometer 10 described herein therefore uses particular signal processing and analysis techniques as described below to determine a modified phase parameter representing, or which is a measure of, the or an optical phase of the laser beam following passage through the sample.

[0046] The spectrometer may be arranged to generate and use a particular number of sidebands, and / or the frequency of the RF modulation signal may be set, depending for example on the spectral width of the spectral feature to be measured. For example, if the spectral feature arises from a complex molecule with a very broad spectral response, a higher frequency RF modulation signal and / or a larger number of sidebands may be required to effectively measure properties of that spectral feature than if the spectral feature is of smaller spectral width.

[0047] Note that a complete optical phase description of the laser beam would need to take account of all of the sidebands each with their own phase. The modified phase parameter described herein may be considered instead to be a measure of the phase change of the overall beat-note generated by nearest-neighbour sidebands.

[0048] Typically, the phase modulator 110 may comprise a waveguide formed of a nonlinear crystal, for example of lithium niobate, which has a refractive index which is a function of an applied electric field, in this case as a function of the RF modulation signal 115 applied to the phase modulator.

[0049] The photodetector output 135 is passed to a DC / RF splitter 140, such as a bias tee, which separates a DC component or signal of the photodetector output 135, and passes the remaining RF component or signal 145 to an IQ demodulator 150. The IQ demodulator also receives the RF signal 115 used to drive the phase modulator 110, and uses this RF signal to demodulate the RF component 145 into quadrature baseband components or signals / and Q.

[0050] As described in more detail below, a phase parameter which is measure of, is related to, or is a close approximation to, the or an optical phase of the laser beam 25 as received at the detector following transmission through the sample, is calculated from the DC component and the / and Q demodulated quadrature components, and in figure 1 this is carried out by calculation element of unit 170. More particularly, the phase parameter V7may be calculated using a ratio of a first weighted sum of the measured DC with a first of the measured quadrature components (for example / ), and a second a weighted sum of the measured DC with the second of the measured quadrature components (for example Q). Further details of this calculation are provided below. Optionally, the phase parameter may be expressed as an arctangent of that ratio in order to correspond closely to optical phase of the detected laser beam, and for the variations in the phase parameter as the laser is scanned in frequency across the spectral feature of interest to be of most direct relevance in determining concentration of the species. However, the phase parameter can be usefully expressed as other functions of the ratio.

[0051] Each of the first and second weighted sums may combine the measured DC and one of the measured demodulated quadrature components in the same ratio of 1 k, where k may typically be k = 1 , or could take other values such as in the range -1000 <= k <= +1000. A suitable value of k maybe established experimentally during test or calibration stages to determine a value of k which provides an optimum mapping and / or minimum noise for example in a mapping between the variation of the phase parameter across a spectral feature and the concentration of a species giving rise to that spectral feature.

[0052] Before the DC and the / and Q demodulated quadrature components can be used to calculate the phase parameter < / an analogue to digital converter 155 is first used to measure the DC and quadrature components, and a signal conditioning element or unit 160 is used to filter and / or otherwise condition at least the / and Q measurements, in particular as functions of the scanned frequency of the laser beam. The measured values of the DC and quadrature / and Q components following any such conditioning are then used to calculate the phase parameter V, typically as a function of scanned frequency vof the laser beam determined using the output of the laser driver 105, which can also be measured using the analogue to digital converter 155 as shown in figure 1.

[0053] The output phase parameter can then be used by an analyser 180 or similar unit or element to calculate one or more properties of the sample, such as concentration Csof species s from the phase parameter as a function of scanned laser frequency. Concentration of a species can be calculated in various ways from the phase parameter, for example by a simple measurement of the peak to peak amplitude of the phase parameter signal as the laser frequency scans across the spectral feature and using this amplitude to determine the concentration from a lookup table or calibration function already defined through a calibration phase of the same or a similar spectrometer, or defined using a mathematical model of the system.

[0054] Other ways of obtaining relevant properties of the sample from the calculated phase parameter as a function of laser frequency include fitting the output of such a forward model of the system to the phase parameter spectrum.

[0055] Note that although we refer to scanning the laser beam, frequency across a spectral feature, in principle this could involve setting the laser beam frequency to just two or a small number of different frequencies, and determining the phase parameter at those frequencies. In some embodiments the phase parameter may be calculated for just a single beam frequency, especially if laser frequency can be sufficiently accurately controlled, and useful properties of the sample such as concentration of a target species obtained from the phase parameter calculated for that single frequency.

[0056] Note that typically, the signal conditioning element 160, the calculation element 170 and the analyser 180 will be implemented in software executing on one or more suitable computer systems. In practice, such computer systems could be located within the spectrometer 10 itself, or could be wholly or partly located elsewhere, for example in local or remote computer system.

[0057] A more detailed example of how the spectrometer 10 of figure 1 may be implemented will now be set out, in particular with reference to figure 2 which illustrates an optical subsystem 200 of the spectrometer, and figure 3 which illustrates an RF subsystem 300 of the spectrometer. A further subsystem not shown explicitly in the figures is a data acquisition subsystem which implements at least the analogue to digital converter 155, signal conditioning element 170 and calculation element 170 of figure 1 , although details of the functionality implemented by the data acquisition subsystem will be described below. In the optical subsystem of figure 2, the laser source 100 is a tunable fibre-coupled butterfly-packaged diode that emits at 1651 nm (an Eblana Photonics EP1651 -0-DM-B01- FM laser may be used). A 1 metre long polarization maintaining fibre 202 from the laser source is coupled to the input of the electro-optic phase modulator 110 (a lithium niobate waveguide phase modulator such as an iXblue MPZ-LN-01 may be used). The phase modulator 110 generates frequency sidebands 35 with an interval corresponding to the frequency of the RF modulation signal 115, in this case 1 .5 GHz, generated by the RF source 120 of the RF subsystem as illustrated in figure 3.

[0058] In the arrangement of figure 2, the optics 40 of figure 1 may be taken to comprise all of the optical components downstream of the phase modulator. These include an aspheric lens 210 (f = 18:8 mm) mounted on a translation stage 215 which collimates the output from the phase modulator 110 to free space, and for open-path measurements, a monostatic arrangement in which the laser beam 25 is directed through a 5 mm diameter hole through the centre of a 50.8 mm-diameter gold coated off-axis parabolic mirror 220, which forms the receiving optics. A pair of beam-steering mirrors 225 is used to align the laser beam 25 through the centre of the 5 mm-diameter hole, after which it is launched to open space by a square gold coated turning mirror 230 (side 50.8 mm) to a corner cube retroreflector 30 located outside, some 90 metres away from the spectrometer instrument 10. Part of the reflected light is captured by the OAPM 220 and focused onto the active area (80 mm diameter) of a 5 GHz-bandwidth InGaAs photodetector 130 (in this example a Thorlabs DET08C / M). An alignment laser 218 may also be provided for alignments of the optical path through optics 40.

[0059] The tunable laser source 100 can be set to scan across any particular spectral feature of interest. In this example, a laser current of 75 mA, temperature of 25 C, and optical power leaving laser source of 2.3 mW were used to probe transitions of methane at 6057.1 cm1. The spectral feature probed comprised four unresolved features centred on 6057.080 cm'1, 6057.092 cm-1, 6057.100 cm1, and 6057.127 cm'1(the first transition being the 2n3 overtone, the others being unknown). This group of transitions is a strong feature, well isolated from possible interfering features from other atmospheric species.

[0060] In the present example the laser source 100 was tuned over this spectral feature by a symmetric triangular modulation voltage (-1 V to +1 V, 1 kHz) generated using the laser driver 105 implemented using a function generator (in this case a Tektronix AFG3102), resulting in a 3.3 cm1laser frequency scanning range, and an associated ±54 % power modulation. The RF subsystem illustrated in figure 3 is interfaced to the optical subsystem of figure 2 through the phase modulator 110 for sideband creation and the photodetector for RF baseband demodulation of optical heterodyne beat notes. The frequency of the RF modulation carrier signal in this example is set to 1 .5 GHz, chosen to give an optimum range of the phase parameter < for the particular spectral features being probed in this case. The inventors’ modelling of the phase signal found that for frequencies below 1 .5 GHz the frequency interval between adjacent sidebands was small compared with the linewidth of the spectral feature, leading to a weak beat-note. For frequencies greater than 1 .5 GHz, the sideband interval was great enough that at any given moment only a few sidebands were interacting with the molecular resonances, which restricted the beat-note power and resulted in a broad phase signal which was modulated by the carrier signal. The choice of 1 .5 GHz not only gave the greatest amplitude for the spectral feature being scanned, but also the ‘cleanest’ dispersion-like spectrum of the phase parameter V7. More generally, however, the frequency of the modulation carrier signal might fall within a range of 1 .0 to 2.0 GHz, or some other suitable range.

[0061] The RF source 120 was implemented using a phase-locked dielectric resonator oscillator and amplified by a low-noise amplifier 310 (gain 11.1 dB) before being split by a directional coupler 315. Most of the power of the RF modulation signal 115 (20.4 dBm out of 21 .1 dBm) was used to drive the phase modulator 110. The remaining power of the RF modulation signal 115 was attenuated (by 6 dB down to 5.7 dBm), filtered (band-pass filter 320 with pass region 1 .48 GHz - 1 .57 GHz) and used as the reference RF local oscillator (LO) for the demodulation of the photodetector signal 135 by the IQ demodulator 150. An in-phase quadrature (IQ) demodulation was performed by the IQ demodulator 150 to recover both amplitude and phase of the RF component 145 of the photodetector signal 135.

[0062] On the photodetector side, the RF component 145 of the photodetector signal 135 resulting from optical heterodyning between sidebands was separated from the constant, DC component using the DC / RF splitter 140 implemented using a bias tee. The RF component 145 of the photodetector signal was then amplified by a chain of three LNAs 330 (total gain 42.6 dB), and propagated to the RF input of the IQ demodulator through a DC block 340. Filtering within the demodulator ensures that only the beating of the ‘nearest neighbour’ sidebands contributes to the demodulated signal.

[0063] The IQ demodulator output was filtered to pass only the baseband differencefrequency component produced by the RF mixing. The DC signal from the photodetector 130 was amplified by a transimpedance amplifier 350 (gain GDC = 104 V / A). The quadrature ( / and Q) and DC signals were acquired synchronously to the laser tuning signal from laser driver 105, at a rate of 250 kilosamples / s. The laser driver 105 was implemented using a ramp generator 360 providing the triangular waveform mentioned above to a current driver 370 for generating a current for driving the laser source 100.

[0064] The expression for the electric field, Eft), describing the laser radiation transmitted through an electro-optic phase modulator 110 operated with an RF modulation signal 115 having an angular frequency Q, and modulation depth d is given by equation 1 , where E, is the field incident on the modulator, w is the angular frequency of the light field, <p is the phase of the light field, Jnare Bessel functions of the first kind of order n. The insertion loss of the modulator is neglected:

[0065] The sideband amplitude structure is always symmetric, solely controlled by the modulation depth. The relative phase of the sidebands is affected by the sign of Jn, which is governed by the relation J.n(6) = (-1 )nJn(5). At low modulation depth, few sidebands are significantly excited and the carrier retains most of the power. To generate optical beatnotes of reasonable power, the modulation depth must be great enough to spread the optical power over several sidebands, with typically at least four, but often six, eight, ten or more being present. The phase of the beat-note is hence more complex than for a dualfrequency laser dispersion spectrometer for example implemented using an electro-optic intensity modulator, and depends on the relative phases and strength of the nearest neighbour sidebands.

[0066] After interaction with a molecular dilute medium such as the sample 20 of figure 1 , the transmittance of the amplitude of the nth sideband component is characterized by the coefficient rn, and the sideband accrues a phase shift q>n. The resulting field on the photodetector, after passing through the dilute medium is given by equation 2:

[0067] After optical heterodyning of the sidebands (by optical detection at the photodetector 130), conditioning by the RF back-end system and RF baseband demodulation, the quadrature I and Q signals provided by V, and Vqare given in equations 3 and 4:

[0068] Owing to a polar coordinate transformation, the / and Q signals can also be expressed in terms of magnitude voltage 14- and phase a, where a = arctan (Vq / Vi).

[0069] In order to provide an effective implementation of laser dispersion spectroscopy by spectrometer 10, calculation of a parameter V related to, or which is a measure of, the or a phase of the laser beam received back at the photodetector 130 following transmission through the sample 20, but independent of its amplitude variations is desired. The phase of the demodulated RF signal can be derived from the / and Q quadrature outputs of the IQ demodulator. However, in doing the transformation, when the / and Q signals are close to zero, the calculated phase is extremely noisy due to a singularity (division by a term close to zero). This is a fairly systemic problem as / and / or Q are close to zero away from any molecular resonance and exactly equal to zero at resonance. To obviate this issue, and make the proposed electro-optic phase modulator-based laser dispersion spectrometer viable, the proportionality of 14 and Vqwith Vdcas described in equations 3 and 4 above may be exploited, by also measuring and using Vdc.

[0070] A "modified” phase parameter as defined in equation 5 which is a measure of, or is related to, the or a phase of the laser beam arriving at the detector following transmission through the sample is therefore calculated by the calculation element 170 of figure 1 and used as the final conditioned spectrometer output or used by analyser 180 in determining properties of the sample 20 such as a concentration of a particular species. The calculated phase parameter may for example be described as a measure of the phase or phase change of the overall beat-note generated by nearest-neighbour pairs of the plurality of frequency sidebands. The calculated phase parameter may in particular have advantageous properties in being essentially immune to variations in the power of the laser beam received at the photodetector.

[0071] All the terms in equation 5 have been described above except for k, which is a scaling parameter that can be adjusted to avoid any singularity in the calculation of< / / . For many situations, rcan be simply set to k = 1 , although effects of varying k will be discussed later. b

[0072] Equation 5 therefore, in summary, indicates that a phase parameter V7representing optical phase of the laser beam following transmission through the sample can be calculated using a ratio of a first weighted sum of the measured DC signal VDc and a first of the measured quadrature components Vqor Vi, and a second a weighted sum of the measured DC signal VDC and the second of the measured quadrature components Vqor Vi. In particular, to obtain a phase parameter V which is close to the actual phase, an arctangent of this ratio can be calculated. Each weighted sum is such as to add the DC signal and the corresponding quadrature signal in a particular ratio, expressed using the parameter k in equation 5, and this ratio is preferably the same for both weighted sums.

[0073] By way of example of operation of embodiments of the invention, the three panels of figure 4 plot the near infrared absorption line spectral feature of methane at about 6057.1 cm1discussed above, additionally taking into account the effects of water vapour and CO2 concentrations, as they contribute to the spectrum, with relative humidity taken as 60% and the CO2 concentration taken to be 413 ppm. Figure 4 then also shows the described laser frequency sidebands 35 used in embodiments of the invention, relative to the methane spectral feature as the laser frequency is scanned across the feature. The top panel shows the sidebands mostly away from the spectral feature, the middle panel with the sidebands starting to overlap, and the bottom panel with the sidebands being centred on the spectral feature. For clarity, the panels show the sideband pattern up to \n\ = 3, although in the model results presented below in figure 5 many more sidebands, up to \n\ = 75 were used.

[0074] Figure 5 shows results both from mathematically modelling the spectrometer and its interaction with the above methane spectral feature, and actual experimental results using the experimental configuration shown in figures 2 and 3, except that rather than using a long open path sample, a gas cell of length 55 mm containing 9.5% methane at atmospheric pressure was used. The top panel shows the quadrature / and Q signals, or more particularly V / and Vqabove, as the laser is scanned in frequency across the spectral feature, with the mathematical model results shown as solid lines and the experimental results as solid points. The mathematically modelled and experimentally measured modulus of the I and Q signals (which is proportional to the amplitude of RF component 145 of the photodetector signal 135) is similarly shown in the middle panel, and the phase parameter < calculated from the quadrature signals and the DC signal is similarly shown in the bottom panel. The vertical dashed lines indicate the three instances of the laser frequency scan illustrated in the three panels of figure 4.

[0075] Owing to the antisymmetric nature of the phase shift between the beat-notes (in the absence of a perturbation from the spectral feature, the beat note generated by the mixing of the sidebands n and n+1 is out of phase with that from -n and -(n+1), so when the laser is far from a spectral feature the RF component 145 of the photodetector signal 135 is very small. As the laser frequency approaches the spectral feature as marked as (1 ) in figure 5, a few weak sidebands interact with the main resonance of the spectral feature, and there is a small amount of power in the RF component 145 and therefore V starts to become significant. When the laser frequency is close to the point of maximum gradient of the spectral feature as marked by (2) in figure 5, the sideband pattern is maximally asymmetrically perturbed by the spectral feature, leading to turning points in I, Q, beat note amplitude, and the phase parameter < < When the n = 0 sideband (central laser frequency) is resonant with the centre of the spectral feature at (3) in figure 5, the sideband structure is symmetrically perturbed spectral feature: the beat notes from the respective sideband pairs cancel out and there is no RF component 145 of the photodetector signal 135.

[0076] As mentioned above in connection with the signal conditioning element 160 of figure 1 , to calculate an optimal value for the phase parameter V, several steps of data conditioning are preferably carried out, including to remove unwanted potential bias in subsequent determinations of concentration of a sample species, for example using analyser 180. Figure 6 illustrates various steps which may be taken as part of this conditioning. In panels (a) and (b) a curve such as a third order polynomial (plotted as smooth lines) is fitted to each of the spectra of / and Q respectively, as measured by the analogue to digital converter 155. The fitted curves are then subtracted from the measured data, partly to remove offset voltage introduced by the IQ demodulator 150 and partly to remove an etalon fringe that originated from the window in front of the photodetector in the experimental arrangement shown in figure 2. Panel (c) shows the / and Q components (as functions of time within the laser frequency scan, so effectively as functions of frequency) after this baseline correction, in which some residual fringing remains.

[0077] Following the baseline corrections, two rotation operations are then performed on the / and Q components (which being orthogonal can be expressed in terms of polar coordinates using a magnitude and phase so can be rotated together in that coordinate system): the first rotation to maximise the amplitude of the / component, and the second rotation by TT / 4 to balance the amplitudes of the / and Q components. These rotations correct for any drift in the phase of the RF modulation signal 115.The calculation element 170 then uses the resulting conditioned I and Q components together with the DC component to calculate the phase parameter representing optical phase using the left side of equation 5. This calculated phase parameter is then represented at panel (e) of figure 6. It can be seen that much of the residual fringing has been removed by the rotation steps. Analysis of a range of datasets recorded with a gas cell indicate that this fringe removal is a consistent and reliable outcome of the described signal conditioning.

[0078] A number of spectra of the phase parameter are then averaged together to result in the white noise reduction shown in the final phase parameter as plotted in panel (f), which may conveniently be passed to the analyser 180 for use in calculating properties of the sample such as concentration of the species giving rise to the spectral feature.

[0079] As noted above in discussion of figure 1 , concentration Csof a component species of the sample can be calculated in various ways from spectra of the phase parameter V7, for example by a simple measurement of the peak to peak amplitude of the phase parameter signal as the laser frequency scans across the spectral feature and using this amplitude to determine the concentration from a lookup table or calibration function already defined through a calibration phase of the same or a similar spectrometer, or defined using a mathematical model of the system.

[0080] However, in particular embodiments, concentration Csof a component species of the sample can be determined by fitting the output of a parameterised forward model of the spectrometer to calculated spectra of the phase parameter. Figure 7 illustrates some ways in which the analyser 180 of figure 1 can be used to carry out such processes, by incorporating a pre-calculation module 505 and a forward model module 510.

[0081] A set of data conditioned spectra of the phase parameter V7based on output of the photodetector 130 are provided by the calculation unit 170 of figure 1 to the analysis unit 180. These spectra will typically already have been data conditioned, for example as discussed above in connection with figure 6, to reduce white noise and in other ways. Each such phase parameter spectrum received by the analysis unit 180 may therefore be a data conditioned average of some tens, hundreds or thousands of raw spectra calculated by the calculation unit from I, Q and DC data collected over a time period for example of the order of a second, and a set of such data conditioned spectra, for example tens or hundreds of such spectra, may be used by the analyser 180 to determine a single value of a concentration Csof a component species. In the arrangement of figure 7 a pre-calculation module 505 of the analyser 180 uses the data conditioned spectra to calculate a number of intermediate parameters Ai ... An. These intermediate parameters may in particular include: an a priori estimate of the chirp rate of the laser beam, that is the rate of change of optical frequency of the laser beam as it is scanned in frequency across the one or more spectral features of interest; a measure of the spectrum noise in the set of data conditioned spectra, which can be calculated using the covariance matrix of all the spectra in the set, so as to provide a standard deviation of every spectral data point; and an initial signal to noise ratio of the set of data conditioned spectra. For this purpose the signal is a peak-to-peak amplitude of < , and the noise is calculated from difference spectra which are differences between successive data conditioned spectra, which for small averaging times should contain only the modified phase random noise. The standard deviation of each difference spectrum is calculated and used as the noise input for calculating the initial signal to noise ratio. This calculation of noise might include potential sources of bias (such as actual changes in the concentration of a component species of the sample between successive spectra), and so this initial signal to noise ratio is only an initial quality metric, which can be refined further by the forward model module as discussed below.

[0082] Some or all of the intermediate parameters Ai ... Anmay be passed as shown in figure 7 to the forward model module 510, which also receives sets of the data conditioned spectra of the phase parameter V derived from output of the photodetector 130 and uses these in combination to calculate a concentration Csof a component species of the sample and one or more further final parameters Bi ... Bnfor output. In particular, the forward model module 510 comprises a forward model 515 of the spectrometer which generates a synthetic phase spectrum V’ based on fixed and floating parameters, discussed below, and the forward model module 510 then compares the set of the spectra of the phase parameter received from the calculation module 170 with the synthetic phase spectrum V’ using an optimization process or module 520 which could for example use an optimal estimation method.

[0083] Fixed parameters which may be used by the forward model 515 are listed below: L Optical path length (m) of the laser beam through the sample;

[0084] NsNumber of sidebands to use in the calculations;

[0085] Q Modulation angular frequency (rad / s) applied by the EOPM;

[0086] 5 Modulation depth of the RF modulation signal; F Scaling factor;

[0087] T Demodulator response parameter;

[0088] K k scaling parameter used by the calculation module;

[0089] T Temperature (K) of the sample;

[0090] P Pressure (torr) of the sample.

[0091] In addition to these fixed parameters, the forward model 515 also takes spectroscopic parameters from a spectral database as inputs, for example from the HITRAN database (see https: / / hitran.org ), and the optimization process 520 in combination with the forward model 515 then generates at least the following fitted parameters:

[0092] CsConcentrations of one or more component species of the sample;

[0093] S(t) Laser frequency chirp rate (rad / s2); ct Laser frequency offset (rad / s).

[0094] The optimisation process 520 in combination with the forward model 515 also generates uncertainties associated with the above fitted parameters, and parameters that can be used for quality assurance and control as well as spectral diagnosis, including a final signal to noise ratio, chi-squared, along with degrees of freedom (which quantifies the sensitivity of the fit to each of the fit parameters), and the residuals. The final signal to noise ratio is calculated in the same way as the initial signal to noise ratio, except the noise is calculated from the standard deviation of the residuals.

[0095] The above fitted parameters, related uncertainties and quality assurance and control parameters are then output as represented in figure 7 as Csand Bi ... Bn.

[0096] Use of a forward model 515 and optimization process 520 (for example using an optimal estimation method or approach) to determine concentration of one or more component species of the sample brings important advantages, for example relative to a more basic look-up table approach, including: the described spectrometer provides a relatively simple optical architecture but produces convoluted spectra (resulting from multiple sidebands) that cannot be directly interpreted. The forward model and optimization process then obviates the complexity of the convoluted spectra, leading to simple, yet robust, determination of species concentration in a sample; the optimization process and forward model fitting produces trustable uncertainties on the fit parameters derived from robust error propagation from the pre-calculation module through the forward model module. The confidence in the determined species concentrations is therefore enhanced; as well as the uncertainties, the forward model module produces further quality assurance / control parameters, including the final signal to noise ratio, degrees of freedom, and chi-squared. These can readily be used to implement data quality flagging; the forward model module produces residuals that can be used for spectral diagnosis and improvement of the forward model, again enhancing the data quality flagging; whereas the look-up table approach uses only two points in a spectrum of the phase parameter < / (for example maximum and minimum values of < ), the forward model and optimization approach can use values of across the full spectrum, leading to substantial reductions in uncertainty of the final concentration measures; the forward model and optimization approach does not rely on a prior calculation, and thus allows a much wider validity range of measurement conditions; the forward model and optimization approach allows spectral scanning across multiple spectral features or spectral regions with other complexities, for example involving multiple component species within the sample and / or overlapping spectral features arising from these. The look-up table approach is difficult to implement in a way which takes account of such complexities.

[0097] Although figures 1 to 3 and 7 largely describe embodiments of the invention in terms of apparatus aspects, embodiments of the invention also provide corresponding methods and steps, and figure 8 is a flow chart showing some such steps as would typically be carried out by a laser dispersion spectrometer such as that of figures 1 to 3 and 7, and referring also to the operations illustrated in figures 4 to 6. Following generation of a suitable laser beam 25 for example by laser source 100, in step 410, the laser beam is passed through an electro-optic phase modulator 110 which is driven by an RF modulation signal 115 so as to add a plurality of sidebands to the laser beam, for example see the sidebands 35 shown in figures 1 and 4. At step 420, the laser beam 25, including the plurality of sidebands 35, is transmitted or passed through a sample 20, for example using optics 40 to direct the beam through an open atmospheric path. At step 430 the transmitted laser beam is then received back at a photodetector 130 to generate a corresponding electrical photodetector output.

[0098] In order to determine or calculate a phase parameter which is a measure of, or is related to the or an optical phase of the laser beam following transmission through the sample, which can be used to detect or determine properties of the sample, at step 440 the photodetector output is split into a DC component and an RF modulated component, for example using the bias-tee of figure 3. At step 450 the RF modulated component is then demodulated, for example by using the RF modulation signal 115 as an additional signal to an IQ demodulator 150, to form / and © demodulated quadrature components. At step 460 the DC component and demodulated quadrature components are measured, for example using one or more analogue to digital converters 155 of figures 1 or 3, and signal conditioning may be applied to the quadrature components as discussed above and illustrated in figure 6.

[0099] At step 470 the phase parameter is calculated from the measured DC and demodulated quadrature components as variously discussed above.

[0100] Once the phase parameter has been calculated, typically as a function of scanned frequency of the laser beam across a spectral feature of a species in the sample, one or more properties of the sample such as a concentration of that species may be determined in step 480, using any of the techniques described above such as a suitable look-up table approach, or using an arrangement such as that of figure 7 in which a forward model 515 of the spectrometer is combined with an optimal estimation process 520, optionally with a precalculation module 505 carrying out pre-calculation of parameters to be used by the forward model and optimal estimation process such as an a priori chirp rate and an initial signal to noise ratio.

[0101] One of the key features of the described spectrometer apparatus and methods is independence of the phase parameter from the laser beam power received at the photodetector 130, which can vary significantly especially in open path atmospheric arrangements. Measurements were therefore conducted using the arrangement of figures 2 and 3 but with the received laser power being varied using attenuating Mylar films and using a 55 mm gas cell containing a 9.5% methane at atmospheric pressure. With each measurement using a different received laser power corresponding to an average of 32 seconds of data and normalized to the phase amplitude of the data-point recorded with the mid-range power of 71 mW, there was no clear variation in the calculated phase parameter as the laser power was varied over two orders of magnitude, implying that the calculated phase parameter is essentially immune to variations in laser power.

[0102] The effect of the variations in received laser power was also investigated using the same spectrometer configuration but over an extended atmospheric open path. The retro- reflected beam received at the photodetector 130 displayed large power fluctuations (around a factor of 2), owing to the refractive index variations in the air (caused on a short timescale by turbulence) and the retroreflector moving slightly in the wind. Despite this, no strong correlation between the concentration measurements of methane and the associated photodetector DC component signal was found (Pearson correlation coefficient -0.19), consistent with the above laboratory measurements.

[0103] The precision of the described spectrometer 10 and related methods was also investigated in the laboratory using methane as the target species, contained in a gas cell. To determine species concentration, for example using analyser 180 of figure 1 , values for the phase parameter as a function of laser beam frequency need to be transformed into species concentration measurements. This can be achieved in various ways, but in the present investigation a straightforward look-up table approach was used owing to the linearity of optical dispersion and therefore also the phase parameter with concentration of the target species, at least in the case of the 6057 cm-1methane absorption line being probed. The model calculations previously described were used to generate a look-up table that linked the peak-to-peak amplitude of the phase parameter signal to the methane concentration, for a given laser path length.

[0104] In forming the lookup table, methane concentration values ranging from 1 .0 ppm to 5.0 ppm in steps of 0.5 ppm, and temperature values ranging from 273 K to 293K in steps of 0.1 K were used. For each temperature, a linear fit can be performed on the concentration as a function of phase parameter amplitude data from the look-up table, which provides the conversion from the phase parameter to methane concentration for measurements made at a given temperature (within the above ranges).

[0105] In order to assess the precision of the determined phase parameter, the Allan standard deviation (ASD) of data recorded with the gas cell was calculated, focussing on quantifying the noise on the phase parameter by calculating the ASD away from the target spectral feature. Analysis of the data revealed etalon fringing in the phase parameter data, and so two ASD calculations were performed: one at a frequency on the minimum of a fringe, and the other at a frequency on the side of the fringe. Both calculations find a minimum of ASD with an averaging time close to 2 s, with a corresponding ASD of 1 .3 millirad (minimum of fringe) and 2.6 millirad (side of fringe). The greater ASD value for the side of fringe data is likely to be a result of laser frequency noise.

[0106] The look-up table was used to transform some of the phase data into concentrations using different averaging times, and the ASD of these data was calculated. For very short averaging times the ASD data showed a white noise statistic. As the averaging time was increased, the ASD statistic departed from white noise, reaching a local maximum at an averaging time of around 600 ms. For longer averaging times the ASD decreases, following a white noise statistic again, until reaching a minimum of 3.5 ppb over a 100 m optical path with an averaging time of 2 s. The effect of the k parameter in equation (5) was also investigated using similar gas cell measurements, finding that for a given data-set rcan be varied to give a maximum of the signal-to-noise ratio of the phase parameter, but that the optimal rvalue varies for different data-sets (for example depending on the amplitude of the / and Q signals). Typically, the value of k maybe optimised for particular applications, measurement types, and scenarios, but a value of k= 1 may generally be suitable, and values broadly in the range of -1000 <= k<= +1000 may also be found to optimal in different situations, with such values of k being determined experimentally or during calibration. Although in equation 5 the same value of k is used in both the weighted sum vdc+ k.vqand vdc+ k.v, in principle different values of k could be used in these two weighted sums, so for example the phase parameter could be calculated as some function of a ratio of arbitrary weighted sums of the DC and / and the DC and Q components. Although the phase parameter may be expressed as the arctangent of such a ratio, various other expressions could equally well be used.

[0107] It will be apparent to the skilled person that a number of modifications and variations can be made to the described embodiments without departing from the scope of the invention for example as defined in the appended claims. For example, although embodiments of the invention have largely been described in the context of using a near infrared laser beam, where phase modulator technology is more mature, power efficient and compact, the laser beam could instead be in the mid infrared for example within a range of 2 to 20pm, with use of a suitable phase modulator capable of operation within this spectral range.

Claims

CLAIMS:1 . A method of determining a phase parameter related to optical phase of a laser beam following transmission through a sample, comprising: passing the laser beam through an electro-optic phase modulator driven by an RF modulation signal so as to add a plurality of sidebands to the laser beam; transmitting the laser beam including the plurality of sidebands through the sample; receiving the laser beam following passage through the sample at a photodetector to generate a photodetector output; splitting the photodetector output into a DC component and an RF modulated component; demodulating the RF modulated component to form demodulated quadrature components; measuring the DC component and demodulated quadrature components; and calculating the phase parameter which is related to optical phase of the laser beam following transmission of the laser beam through the sample from the measured DC and demodulated quadrature components.

2. The method of claim 1 wherein the phase parameter is calculated using a ratio of: a first weighted sum of the measured DC and a first of the measured demodulated quadrature components, and a second weighted sum of the measured DC and the second of the measured demodulated quadrature components, and optionally as an arctangent of that ratio.

3. The method of claim 2 where each weighted sum combines the measured DC and one of the measured demodulated quadrature components in the same ratio of 1 k, where k is optionally one of: -1000 <= k <= +1000; and k = 1 .

4. The method of any preceding claim wherein the RF component is demodulated using the RF modulation signal.

5. The method of any preceding claim wherein the photodetector output is split into a DC component and an RF modulated component using a bias-tee.

6. The method of any preceding claim wherein the electro-optic phase modulator adds at least four, and optionally at least six or at least eight sidebands to the laser beam.

7. The method of any preceding claim wherein passing the laser beam including the plurality of sidebands through the sample comprises passing the laser beam along an open path through the atmosphere.

8. The method of any preceding claim wherein the laser beam is a near infrared laser beam.

9. The method of any preceding claim further comprising frequency scanning the laser beam across a spectral feature of a component species of the sample, and both measuring the DC and the demodulated quadrature components, and calculating the phase parameter, as a function of the scanned laser beam frequency.

10. The method of claim 9 further comprising determining a concentration of the component species of the sample using the phase parameter calculated as a function of the scanned laser beam frequency.11 . The method of claim 9 or 10 wherein data conditioning is applied to the demodulated quadrature components as functions of scanned laser beam frequency before using them to calculate the phase parameter as a function of the scanned laser beam frequency.

12. The method of claim 11 wherein the data conditioning comprises one or more of: fitting a curve to each demodulated quadrature component and subtracting the respective fitted curve from the corresponding demodulated quadrature component to effect a baseline correction to each demodulated quadrature component; and carrying out one or more polar coordinate system rotation operations on the demodulated quadrature components.

13. The method of any of claims 9 to 12 wherein the component species of the sample is methane and the spectral feature is an absorption feature of methane.

14. The method of any claims 8 wherein the concentration of the component species is calculated by using a parameterised forward model of the steps of any of claims 1 to 8 to derive synthetic values of the phase parameter, and an optimization process to adjust one or more parameters of the forward model so as to fit the synthetic values of the phase parameter to the calculated values of the phase parameter.

15. The method of claim 14 further comprising generating and providing to the optimization process one or more of: an a priori chirp rate of the scanned laser beam, a spectrum noise of the calculated values of the phase parameter, and an initial signal to noise ratio of the calculated values of the phase parameter.

16. The method of claim 14 or 15 wherein the optimization process outputs both the determined concentration of the component species of the sample, and one or more quality assurance or control parameters relating to the determined concentration.

17. A laser dispersion spectrometer comprising : a laser source arranged to form a laser beam; an electro-optic phase modulator arranged to add a plurality of sidebands to the laser beam responsive to an RF modulation signal; optics arranged to transmit the laser beam including the plurality of sidebands through a sample; a photodetector arranged to receive the laser beam from the optics following transmission through the sample, and to generate a corresponding electrical photodetector output; a DC / RF splitter arranged to split the photodetector output into a DC component and an RF modulated component; an IQ demodulator arranged to demodulate the RF modulated component to form demodulated quadrature components; and a calculation element arranged to calculate a phase parameter which is related to optical phase of the laser beam following transmission of the laser beam through the sample using the DC and demodulated quadrature components.

18. The laser dispersion spectrometer of claim 17 wherein the calculation element is arranged to calculate the phase parameter using a ratio of: a first weighted sum of a measurements of the DC and a first of the demodulated quadrature components; and asecond weighted sum of measurements of the DC and a second of the demodulated quadrature components.

19. The laser dispersion spectrometer of claim 17 or 18 wherein the plurality of sidebands comprise at least four, and optionally at least six or at least eight sidebands.

20. The laser dispersion spectrometer of any of claims 17 to 19 further comprising a data conditioning element arranged to apply data conditioning to the demodulated quadrature components, wherein the data conditioning optionally comprises one or more of: fitting a curve to each demodulated quadrature component and subtracting the respective fitted curve from the corresponding demodulated quadrature component to effect a baseline correction to each demodulated quadrature component; and carrying out one or more polar coordinate system rotation operations on the demodulated quadrature components.21 . The laser dispersion spectrometer of any of claims 17 to 20 further comprising a laser driver arranged to frequency scan the laser beam across a spectral feature of a component species of the sample, wherein the calculation element is arranged to calculate the phase parameter, as a function of the scanned laser beam frequency.

22. The laser dispersion spectrometer of claim 17 further comprising an analyser arranged to determine a concentration of the component species of the sample using the phase parameter calculated as a function of the scanned laser beam frequency.

23. The laser dispersion spectrometer of claim 22 wherein the analyser is arranged to determine a concentration of the component species using a parameterised forward model of the laser dispersion spectrometer to derive synthetic values of the phase parameter, and an optimization process to adjust one or more parameters of the forward model so as to fit the synthetic values of the phase parameter to the calculated values of the phase parameter.

24. A method of calculating a phase parameter which is related to optical phase of a laser beam comprising a plurality of sidebands, following transmission of the laser beam through a sample, the method comprising:receiving a DC component, and demodulated quadrature components of an RF component, of an output signal from a photodetector detecting the laser beam; and calculating the phase parameter from the received DC and demodulated quadrature components, optionally using a ratio of: a first weighted sum of the measured DC and a first of the measured demodulated quadrature components, and a second weighted sum of the measured DC and the second of the measured demodulated quadrature components, and optionally as an arctangent of that ratio.

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