CROSS REFERENCE TO RELATED APPLICATIONS

This Application is a 35 U.S.C. § 371 National Phase Entry of International Patent Application No. PCT/NL2019/050267 filed May 3, 2019, which designates the U.S. and claims benefit of foreign priority under 35 U.S.C. § 119(b) of NL Application Number 2020863 filed May 3, 2018, the contents of which are incorporated herein in their entireties by reference.

TECHNICAL FIELD

Embodiments described herein generally relate to determining presence of a gas. More particularly, although not exclusively, embodiments relate to obtaining polarisation-dependent radiation intensity measurements from which the presence of a gas may be determined. Some embodiments relate to remotely determining presence of a gas. Some embodiments relate to determining the concentration of the gas.

BACKGROUND

Remote sensing of gases in the Earth's atmosphere is essential for air pollution monitoring, source detection and gas leak detection. Many optical gas sensing instruments are based on spectroscopic measurements in which trace gases such as NO2or CH4, can be detected through their specific spectral features. In order to achieve a two-dimensional image of the presence of trace gas it is common for a spectrometer to use a scanning mechanism in which the field of view can be scanned in both a spatial and a spectral domain. A scanning mechanism may require substantial time for the 2D image to be built up. Other mechanisms for obtaining a 2D image of trace gas concentration include hyperspectral imaging and compressive sensing techniques. Such methods may implement a dispersive or wavelength-selective element to obtain an inherent spectral resolution sufficient to discern the spectral features of the gas.

Multi Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) instruments can be used to determine concentrations of gases in the atmosphere by utilising scattered sunlight from multiple viewing directions. The scattered sunlight may be detected using spectrographs which may collect light through an optical fibre and scan the sky to record complete spectral features in all directions. Instruments which use optical fibre may have several viewing directions at the same time. In scanning systems, the entire system (including optical fibres) may be pointed towards the target area to prevent transmission differences from causing erroneous readings.

A further example of gas detection involves using a multiple optical path intensity based interferometer method such as a using a Michelson Interferometer or a Fourier Transform Spectrometer, where an incoming beam of radiation is split into two physically separate independent arms before being recombined. A yet further example involves the use of a Mach-Zender interferometer which utilises different optical paths and has two outputs which are out of phase with each other by 180°. Due to the complex optical system associated with such interferometers, they are prone to become misaligned and are particularly sensitive to vibrations. The multiple optical paths in such interferometers may mean that small misalignments or movements may lead to erroneous measurements. Vibrations and temperature changes can affect different optical paths differently. As a result, such interferometric techniques may be considered unsuitable in many environments, such as for an example in a drone, satellite or any moving vehicle, when a large amount of stabilisation may be required. Furthermore, such interferometers with multiple physically separate optical paths are highly sensitive to temperature and vibration changes, or require regular scanning of the interferometer path length, resulting in temperature and vibration stabilisation being required. The stabilisation requirements and sensitive alignments lead to a bulky set-up. There is thus a need for a compact and robust imaging apparatus for detecting gases.

SUMMARY

A first aspect of the disclosure provides an apparatus for determining presence of a gas. The apparatus typically comprises one or more retarders to spectrally modulate, typically within a selected frequency range, polarisation of received (typically electromagnetic) radiation in accordance with a plurality of polarised spectral modulation profiles which are offset in phase from each other. The apparatus typically comprises one or more radiation detectors to detect radiation output from the one or more retarders filtered for a respective polarisation state by one or more polarisers, the one or more detectors selectively (and typically separately—e.g. on the same detector at a different time or on different detectors at the same time or at different times) detecting polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the apparatus comprises one or more polarisers.

It may be that the apparatus comprises radiation detectors to detect radiation output from the one or more retarders filtered for respective polarisation states by the one or more polarisers, the detectors selectively and separately detecting on different detectors at the same time polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

Thus, it may be that the radiation detectors comprise at least first and second radiation detectors to selectively, separately and simultaneously detect polarised radiation filtered for respective polarisation states, the polarised radiation detected by each of the at least first and second radiation detectors conforming to a different one of the said polarised spectral modulation profiles, to thereby provide respective polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the apparatus further comprises a filter to selectively transmit received radiation having a frequency within the selected frequency range. Typically the gas has a plurality of spectral features offset in frequency from each other within the selected frequency range. For example, an absorption or emission spectrum of the gas may have a plurality of absorption or emission lines offset in frequency from each other within the selected frequency range.

A second aspect of the disclosure provides a method for determining presence of a gas. The method typically comprises: one or more retarders spectrally modulating, typically within a selected frequency range, polarisation of received (typically electromagnetic) radiation in accordance with a plurality of polarised spectral modulation profiles which are offset in phase from each other. The method typically further comprises selectively detecting radiation output from the one or more retarders filtered for a respective polarisation state by one or more polarisers and conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements. The method typically further comprises determining the presence of the gas based on the at least first and second polarisation dependent radiation intensity measurements.

It may be that the method comprises radiation detectors detecting radiation output from the one or more retarders filtered for respective polarisation states by one or more polarisers, the radiation detectors selectively and separately detecting on different detectors at the same time polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements, and determining the presence of the gas based on the at least first and second polarisation dependent radiation intensity measurements.

It may be that the method further comprises selectively transmitting received radiation having a frequency within the selected frequency range. Typically the gas has a plurality of spectral features offset in frequency from each other within the selected frequency range. For example, an absorption or emission spectrum of the gas may have a plurality of absorption or emission lines offset in frequency from each other within the selected frequency range.

By providing one or more retarders to spectrally modulate polarisation of received radiation in accordance with a plurality of polarised spectral modulation profiles which are offset in phase from each other, and selectively (and typically separately) detecting polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles, a compact arrangement can be provided which enables polarisation-dependent radiation intensity measurements to be performed from which the presence of the gas can be determined. Such an apparatus can also be provided with a tolerable sensitivity to ambient temperature changes without having to stabilise the temperature of the apparatus itself. By providing apparatus with tolerable sensitivity to ambient temperature changes, any calibration required for the apparatus is more robust and does not need to be repeated for every change in ambient temperature. The apparatus is also more tolerant to vibration. As the polarisation of received radiation is spectrally modulated in accordance with the polarised spectral modulation profiles by the one or more retarders, two polarised components of the same beam of the received radiation travel along essentially the same trajectory with a path length difference. Intensity modulation of the beam of received radiation (typically in accordance with a said polarised spectral modulation profile) may then be obtained by a polariser filtering the radiation output by the one or more retarders for a respective polarisation state. Accordingly, an interferometer with multiple optical paths is not required in order to provide the radiation with the said plurality of polarised spectral modulation profiles, which helps the apparatus to have more tolerable temperature and vibration sensitivity. By contrast, splitting the beam into two arms and recombining using a classical interferometric method such as a Michelson interferometer, or using a Mach-Zender interferometer having more than one optical path, provides a larger scope for errors due to properties of the multiple optical paths varying differently with temperature and vibrations.

Typically the radiation output from the one or more retarders comprises radiation having polarisation spectrally modulated in accordance with the said plurality of polarised spectral modulation profiles in a common beam of radiation. Typically the radiation filtered for a respective polarisation state and conforming to the first said polarised spectral modulation profile is filtered from a beam of radiation comprising radiation having polarisation spectrally modulated in accordance with the at least first and second said polarised spectral modulation profiles (and typically similarly for the radiation filtered for a respective polarisation state and conforming to the second polarised spectral modulation profile). By providing radiation having polarisation spectrally modulated in accordance with the said plurality of polarised spectral modulation profiles in a common beam of radiation, the radiation modulated in accordance with each of the polarised spectral modulation profiles follows substantially the same optical path from the one or more retarders to the detectors. This helps to keep the apparatus compact and avoids the need for multiple discrete optical paths, thereby helping to improve the tolerance of the apparatus to temperature changes and vibration.

By the radiation detectors selectively and separately detecting on different detectors at the same time polarised radiation conforming to each of the at least first and second of the said polarised spectral modulation profiles, the number of moving parts of the apparatus can be reduced, making the apparatus more robust and reliable. In addition, more sensitive and accurate gas detection can be achieved at least because the at least first and second polarisation dependent radiation intensity measurements are made under the same temperature, vibration, optical alignment and gas concentration conditions.

It may be that the one or more retarders is to spectrally modulate polarisation of received radiation in accordance with the plurality of polarised spectral modulation profiles by causing frequency dependent interference between orthogonal polarisation components of received radiation.

It will be understood that, when it is mentioned that radiation may be detected which conforms to at least first and second of the said polarised spectral modulation profiles on different detectors at the same time, the different detectors may be different in the sense that they are discrete from each other, but they may otherwise be substantially the same type of detector. The different detectors may be different pixels on the same array of radiation detectors, such as a two-dimensional array of radiation detectors.

It may be that the polarised spectral modulation profiles are linearly polarised spectral modulation profiles. It may be that the one or more radiation detectors detect radiation output from the one or more retarders filtered for a respective linear polarisation state. It may be that the one or more detectors selectively (and typically separately, for example on different detectors at the same time) detect linearly polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the one or more polarisers comprise one or more polarising beam splitters which each provide at separate outputs polarised radiation at different predefined (e.g. orthogonal) linear polarisations, for example to respective detectors. It may be that the one or more polarisers comprise a plurality of linear polarising filters which each have a single output to provide radiation having a single predefined linear polarisation, for example to a respective detector.

Typically, when polarisation of radiation is spectrally modulated by the one or more retarders in accordance with each of a plurality of polarised spectral modulation profiles, the polarisation of radiation is spectrally modulated such that, when the spectrally modulated radiation is filtered at a polarisation angle corresponding to a respective said polarised spectral modulation profile, the intensity of the filtered radiation varies (typically substantially periodically) with frequency of radiation in accordance with that profile. Typically each of the polarised spectral modulation profiles, and thus the intensity of the radiation filtered at a polarisation angle corresponding to that polarised spectral modulation profile, comprises alternating maxima and minima which are substantially periodic with frequency of radiation, typically within the selected frequency range. Typically the maxima and minima of the first said polarised spectral modulation profile are offset in phase from the maxima and minima of the second said polarised spectral modulation profile. It may be that the maxima and minima are interference maxima and minima caused by frequency dependent interference between orthogonal polarisation components caused by the one or more retarders.

Typically the said polarised spectral modulation profiles have alternating maxima and minima which are substantially periodic with frequency of radiation, typically within the selected frequency range, the frequency spacing between successive maxima being substantially equal to the frequency spacing between peaks of a pair of spectral features of the gas within the selected frequency range. It may be that the first polarised spectral modulation profile has successive minima the frequency spacing between which is substantially equal to the frequency spacing between peaks of a pair of spectral features of the gas within the selected frequency range. It may be that the respective minima of the first polarised spectral modulation profile substantially do not overlap with the peaks of the respective spectral features of the gas in the selected frequency range.

It may be that the spectral features are absorption lines or emission lines of the gas.

It may be that a plurality of spectral features of the gas within the selected frequency range are at least quasi-periodic or periodic. It may be that the maxima and minima of the polarised spectral modulation profiles are provided with a frequency spacing which is substantially equal to the frequency spacing between peaks of spectral features of the said plurality of spectral features within the selected frequency range. It may be that the first polarised spectral modulation profile has successive maxima the frequency spacing between which is substantially equal to the frequency spacing between peaks of a pair of spectral features of the gas within the selected frequency range. It may be that a plurality of the respective maxima of the first polarised spectral modulation profile substantially overlap with the respective spectral features (preferably the peaks of the spectral features) of the gas within the selected frequency range corresponding to the said (e.g. absorption) peaks. The closer the period between maxima (and the period between minima) of the polarised spectral modulation profiles to the period between peaks of spectral features of the gas, the more sensitive the resulting fractional linear polarisation to the presence of the gas.

It may be that the first polarised spectral modulation profile is substantially 180° out of phase with the second polarised spectral modulation profile. It may be that the second polarised spectral modulation profile has successive maxima the frequency spacing between which is substantially equal to the frequency spacing between peaks of a pair of spectral features of the gas within the selected frequency range. It may be that the respective maxima of the second polarised spectral modulation profile substantially do not overlap with the respective peaks of the spectral features of the gas within the selected frequency range.

It may be that the one or more retarders comprise one or more retarder elements and a quarter wave plate. It may be that the one or more retarders comprise one or more retarder elements to provide received radiation with components which are linearly polarised at linear polarisation angles of 0° and 90° and components which are right and left hand circularly polarised. It may be that the one or more retarders comprise a quarter wave plate. It may be that the quarter wave plate is to convert the components of the radiation output by the retarder elements having linear polarisation angles of 0° and 90° and right and left hand circularly polarisation to linearly polarised components at linear polarisation angles of 0°, 45°, 90° and 135°. It may be that the one or more retarder elements and quarter waveplate (where provided) together provide the received radiation with components which are linearly polarised at linear polarisation angles of 0°, 45°, 90° and 135°. These linear polarisation angles may relate to modulation phases of 0°, 90°, 180° and 270°.

It may be that the plurality of polarised spectral modulation profiles comprises at least three polarised spectral modulation profiles offset in phase from each other.

It may be that the plurality of polarised spectral modulation profiles comprises at least four polarised spectral modulation profiles offset in phase from each other.

It may be that the one or more detectors selectively (and typically separately, for example on different detectors at the same time) detect (or it may be that the method comprises selectively detecting, for example on different detectors at the same time) polarised radiation conforming to each of at least first, second and third of the said polarised spectral modulation profiles to thereby provide at least respective first, second and third polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the radiation detectors comprise at least first, second and third radiation detectors to selectively, separately and simultaneously detect polarised radiation filtered for respective polarisation states, the polarised radiation detected by each of the at least first, second and third radiation detectors conforming to a different one of the said polarised spectral modulation profiles, to thereby provide respective polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

The fractional linear polarisation of the detected radiation, and thus the presence of the gas, can be determined from the respective at least first, second and third polarisation-dependent radiation intensity measurements to thereby determine presence (and typically absorption or emission strength or concentration) of the gas without any of the first, second and third of the said polarised spectral modulation profiles having to be aligned with the absorption lines of the gas. This helps to further reduce the temperature sensitivity of the apparatus as temperature dependent spectral shifts of the polarised spectral modulation profiles can be more easily tolerated.

It will be understood that the more distributed the relative phases of the first, second and third of the said polarised spectral modulation profiles throughout a 360° cycle, the more efficiently the fractional linear polarisation can be determined based on the at least first, second and third polarisation-dependent radiation intensity measurements. Accordingly, preferably respective ones of the first, second and third polarisation-dependent spectral modulation profiles which are adjacent to each other in phase are offset in phase from each other by substantially 120°. Preferably, the fractional linear polarisation determined by the controller is at least 5% of the average (e.g. mean) relative absorption depth of the spectral features of the gas within the selected frequency range.

It may be that each of the at least first, second and third polarised spectral modulation profiles have a plurality of maxima in the selected frequency range which do not align (or overlap) with peaks of spectral features of the gas in the selected frequency range.

It may be that the one or more detectors selectively (and typically separately, for example on different detectors at the same time) detect (or it may be that the method comprises one or more detectors selectively detecting, for example on different detectors at the same time) polarised radiation conforming to each of at least first, second, third and fourth of the said polarised spectral modulation profiles to thereby provide at least respective first, second, third and fourth polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the radiation detectors comprise at least first, second, third and fourth radiation detectors to selectively, separately and simultaneously detect polarised radiation filtered for respective polarisation states, the polarised radiation detected by each of the at least first, second, third and fourth radiation detectors conforming to a different one of the said polarised spectral modulation profiles, to thereby provide respective polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that respective ones of the first, second, third and fourth polarisation-dependent spectral modulation profiles which are adjacent to each other in phase are offset in phase from each other by substantially 90°.

It may be that each of the at least first, second, third and fourth polarised spectral modulation profiles have a plurality of maxima in the selected frequency range which do not align (or overlap) with peaks of spectral features of the gas in the selected frequency range.

It may be that the one or more detectors selectively (and typically separately) detect (or it may be that the method comprises one or more detectors selectively detecting) polarised radiation conforming to each of at n said polarised spectral modulation profiles to thereby provide at least respective n polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that respective ones of the n polarisation-dependent spectral modulation profiles which are adjacent to each other in phase are offset in phase from each other by substantially 360/n°.

It may be that n is, for example, an integer greater than or equal to two, greater than equal to three, greater than equal to four or greater than equal to eight.

It may be that the respective maxima of the polarised spectral modulation profiles to which the radiation selectively detected by the one or more detectors conform substantially do not overlap with the respective peaks of the spectral features of the gas in the selected frequency range.

It may be that the one or more retarders are to spectrally modulate the linear polarisation state of the received radiation to provide the received radiation with a plurality of polarised spectral modulation profiles which are offset in phase from each other. It may be that each of the said plurality of polarised spectral modulation profiles is associated with a different linear polarisation angle (typically such that when the spectrally modulated radiation is filtered at the linear polarisation angle associated with a respective said polarised spectral modulation profile, the intensity of the filtered radiation varies (typically substantially periodically) with the frequency of radiation in accordance with that profile).

It may be that radiation incident on the one or more retarders at different angles of incidence is modulated by the one or more retarders (typically one or more birefringent elements) in accordance with respective different polarised spectral modulation profiles which are offset in phase from each other (or it may be that the method comprises the one or more retarders modulating radiation incident on the one or more retarders at different angles of incidence in accordance with respective different polarised spectral modulation profiles which are offset in phase from each other), the said different polarised spectral modulation profiles being associated with the same (typically linear) polarisation angle.

It may be that the one or more retarders are to spectrally modulate the linear polarisation state of the received radiation in accordance with different polarised spectral modulation profiles for different angles of incidence of the radiation on the one or more retarders.

It may be that the one or more retarders are to apply a combination of modulations, such as spectral modulations, to the received radiation, such as to the polarisation of the received radiation, in different modulation domains. For example it may be that the one or more retarders are to apply any combination of the following modulations to received radiation: to spectrally modulate the linear polarisation state of the received radiation to provide the received radiation with a plurality of polarised spectral modulation profiles which are offset in phase from each other, each of which is associated with a different linear polarisation angle; to spectrally modulate the linear polarisation state of the received radiation in accordance with different polarised spectral modulation profiles for different angles of incidence of the radiation on the one or more retarders (e.g. for radiation of the same linear polarisation angle); to modulate the polarisation state of radiation output by the one or more retarders (e.g. periodically) over time.

It may be that the apparatus is to apply a plurality of polarisation modulations to the received radiation, the plurality of polarisation modulations comprising the one or more retarders spectrally modulating the linear polarisation state of the received radiation to provide the received radiation with a plurality of polarised spectral modulation profiles which are offset in phase from each other, each of which is associated with a different linear polarisation angle, and any one or more of: the one or more retarders spectrally modulating the linear polarisation state of the received radiation in accordance with different polarised spectral modulation profiles for different angles of incidence of the radiation on the one or more retarders (e.g. for radiation of the same linear polarisation angle); the apparatus modulating the polarisation state of radiation output by the one or more retarders differently (e.g. periodically) over time; the apparatus spatially modulating the received radiation by a plurality of groups of radiation detectors detecting radiation output from the one or more retarders, each of the groups of detectors comprising radiation detectors to detect radiation output from the one or more retarders filtered for respective polarisation states by one or more polarisers, the radiation detectors selectively and separately detecting on different detectors at the same time polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined, the respective groups of radiation detectors being offset from each other, for example in a common focal plane. It may be that the respective groups of radiation detectors are offset from each other in a periodic tessellated arrangement, the periodicity of the tessellated arrangement being in respect of the linear polarisation angles of radiation which the detectors of the groups are configured to detect.

It may be that the spectral polarisation modulation provided by the one or more retarders provides the received radiation with the polarised spectral modulation profiles which allow the presence of gas to be determined, while the additional angular, temporal and/or spatial modulation(s) helps to improve the accuracy with which radiation conforming to those profiles can be measured.

It may be that the radiation detectors and the one or more polarisers are provided by a pixelated polarisation camera. It may be that the pixelated polarisation camera is to perform the said spatial modulation.

Although gas detection can be performed by way of modulation in a single modulation domain (for example the spectral modulation applied by the one or more retarders to provide the radiation with polarised spectral modulation profiles offset in phase with each other, the different polarised spectral modulation profiles being associated with different linear polarisation angles), by adding modulations in different modulation domains to the radiation, systematic errors, for example in a fractional linear polarisation measurement or in the polarisation-dependent intensity measurements from which the presence of the gas is determined can be reduced or removed. This enables more accurate, and more sensitive, polarisation measurements and thus gas detection.

It may be that the detected radiation conforming to at least one of the said at least first and second polarised spectral modulation profiles is radiation filtered for a first linear polarisation angle and wherein the detected radiation conforming to at least one of the said at least first and second polarised spectral modulation profiles is radiation filtered for a second linear polarisation angle different from the first linear polarisation angle.

It may be that the second linear polarisation angle is offset from the first linear polarisation angle by substantially 90° (e.g. between 80° and 100°, or between 85° and 95° or between 88° and 92° or between 89° and 91°). This provides a substantially 180° phase difference between the polarised spectral modulation profiles associated with the first and second linear polarisation angles, thereby enabling the maxima of one of the polarised spectral modulation profiles to be aligned with peaks of the spectral features of the gas while the maxima of the other polarised spectral modulation profile are aligned with portions of the spectrum of the gas off the said peaks.

It may be that detected radiation conforming to at least one of the at least first and second polarised spectral modulation profiles is radiation polarised at a first linear polarisation angle which was incident on a first of the said one or more retarders at a first angle of incidence, and wherein the detected radiation conforming to at least one of the at least first and second polarised spectral modulation profiles is radiation polarised at the said first linear polarisation angle which was incident on the said first of the said one or more retarders at a second angle of incidence different from the first angle of incidence.

It may be that the apparatus comprises one or more radiation detectors to selectively detect radiation output from the one or more retarders filtered for a respective polarisation state by one or more polarisers, the one or more detectors selectively detecting polarised radiation conforming to each of a plurality of the said polarised spectral modulation profiles to thereby provide a respective plurality of polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined. Typically the plurality of polarised spectral modulation profiles are offset in phase from each other. It may be that the said plurality of polarised spectral modulation profiles comprise a plurality of polarised spectral modulation profiles associated with each of a plurality of different polarisations (typically a plurality of linear polarisations), the said plurality of polarised spectral modulation profiles associated with each of the plurality of different polarisations being associated with radiation incident on the one or more retarders at different angles of incidence.

It may be that the one or more retarders comprise a temporal polarisation modulator (e.g. rotating half waveplate or switching liquid crystal) to (typically cyclically) vary the (typically linear) polarisation state (or it may be that the method comprises a temporal polarisation modulator (typically cyclically) varying the (typically linear) polarisation state) of the radiation output from the one or more retarders with respect to time. It may be that the temporal polarisation modulator sequentially allows linearly polarised radiation at different angles of linear polarisation to pass through the combination of the temporal polarisation modulator and the one or more (typically fixed angle linear) polarisers onto the said one or more radiation detectors. Thus, the one or more radiation detectors detecting radiation filtered for a particular polarisation state can detect radiation in accordance with different said polarised spectral modulation profiles over time. It may be that the temporal modulation modulator is provided in addition to one or more retarders that perform spectral modulation of the received radiation, the spectral modulation providing the received radiation with a plurality of polarised spectral modulation profiles offset in phase with each other, each of the said polarised spectral modulation profiles being associated with a different linear polarisation angle.

It may be that the one or more radiation detectors comprise a plurality of radiation detectors.

It may be that the plurality of radiation detectors include at least one respective radiation detector for (or it may be that the method comprises a plurality of radiation detectors including at least one respective radiation detector) detecting radiation conforming to each of the respective at least first and second polarised spectral modulation profiles. It may be that the said plurality of radiation detectors are provided in a tessellated arrangement.

It may be that the apparatus comprises a plurality of (typically fixed angle) linear polarisers, each to receive (or it may be that the method comprises a plurality of (typically fixed angle) linear polarisers each receiving) radiation having spectrally modulated polarisation from the one or more retarders and output (or outputting) linearly polarised radiation (e.g. at a respective linear polarisation angle) to a respective radiation detector of the said plurality of radiation detectors, typically to provide respective polarisation dependent intensity measurements from which presence of the gas can be determined. It may be that the plurality of linear polarisers comprise linear polarisers of different linear polarisation angles.

It may be that the linear polarisers of the said plurality are provided on a common focal plane.

It may be that the linear polarisers of the said plurality are offset from each other, for example in the common focal plane.

It may be that the plurality of linear polarisers are provided in a tessellated arrangement.

It may be that the one or more polarisers are provided over corresponding detectors.

It may be that the linear polarisers of the plurality of linear polarisers are provided over the corresponding detectors.

It may be that the said plurality of radiation detectors are provided on a common focal plane.

It may be that the radiation detectors of the said plurality are offset from each other, for example in the common focal plane.

It may be that the one or more radiation detectors comprise one or more radiation detectors each to sequentially detect (or it may be that the method comprise one or more radiation detectors each sequentially detecting) radiation filtered for respective different angles of linear polarisation. It may be that the radiation detector is to detect (or it may be that he method comprises the radiation detector detecting) radiation filtered for a first angle of linear polarisation to thereby obtain the first polarisation dependent intensity measurement, and to subsequently detect (or subsequently detecting) radiation filtered for a second angle of linear polarisation different from the first angle to thereby obtain the second polarisation dependent intensity measurement.

It may be that the apparatus comprises an adjustable (e.g. rotating) linear polariser (i.e. adjustable to thereby adjust the linear polarisation angle of the linear polariser), or a combination of a temporal polarisation modulator and a fixed angle linear polariser together, to receive (or it may be that the method comprises an adjustable (e.g. rotating) linear polariser receiving) radiation having spectrally modulated polarisation from the one or more retarders to sequentially allow (or sequentially allowing) linearly polarised radiation at different angles of linear polarisation to pass through the adjustable linear polariser, or through the said combination of the temporal polarisation modulator and fixed angle linear polariser, onto the said one or more radiation detectors. Thus, the one or more radiation detectors can detect radiation in accordance with different said polarised spectral modulation profiles over time.

It may be that the one or more retarders are arranged in an athermal combination. For example, it may be that the one or more retarders comprise a plurality of retarder (e.g. birefringent) elements at least two of which have different retardances (e.g. birefringences), the said plurality of retarder (e.g. birefringent) elements being combined such that temperature dependent variations in retardance (e.g. birefringence) of the said plurality of retarder (e.g. birefringent) elements at least substantially cancel out. It may be that the said at least two retarder (e.g. birefringent) elements have retardances which have different relative temperature-dependences (as determined by the coefficient of thermal expansion and the thermo-optic coefficients for neand no). It may be that the at least two retarder elements comprise at least two birefringent elements each comprising fast and slow axes, and it may be that the fast axis of a first said birefringent element is aligned with the slow axis of a second birefringent element. It may be that the birefringence of the first said birefringent element is different from the birefringence of the second birefringent element. It may be that the change with temperature of the path length difference between the fast and slow axes of the first said birefringent element is substantially equal to the change with temperature of the path length difference between the fast and slow axes of the second said birefringent element.

By arranging the one or more retarders in an athermal combination, it can be ensured that the alignment between the maxima of the first polarised spectral modulation profile and the peaks of spectral features of the gas (and the alignment between the maxima of the second polarised spectral modulation profile with portions of the spectrum of the gas off the said peaks) remains stable with changes in temperature of the apparatus. This helps to enable the presence of gas to be determined from two polarisation-dependent intensity measurements. When more than two polarisation-dependent intensity measurements are provided, such alignment is not necessary. However, the athermal combination can still help to improve the accuracy of measurements, for example by reducing or eliminating measurement errors caused by temperature fluctuations causing corresponding fluctuations in retardances of the one or more retarders.

It may be that the filter comprises a bandpass filter. It may be that the filter comprises an interference filter.

It may be that the filter comprises one or more birefringent filters. It may be that the filter comprises one or more retarder (e.g. birefringent) elements and one or more polarisers. It may be that the filter comprises one or more retarders in an athermal combination. For example, as above, it may be that the one or more retarders of the filter comprise a plurality of retarder (e.g. birefringent) elements at least two of which have different retardances (e.g. birefringences), the said plurality of retarder (e.g. birefringent) elements being combined such that temperature dependent variations in retardance (e.g. birefringence) of the said plurality of retarder (e.g. birefringent) elements at least substantially cancel out.

It may be that the filter comprises a bandpass (e.g. interference) filter and one or more birefringent filters. It may be that a transmission response of the one or more birefringent filters has transmission minima at the lower and upper cut-off frequencies of the bandpass filter. It may be that the one or more birefringent filters shape the combined transmission profile of the bandpass filter and the one or more birefringent filters between the said transmission minima.

It may be that the one or more retarders comprise one or more birefringent elements, wherein the one or more birefringent filters comprise one or more birefringent elements, and wherein the overall temperature dependence of the retardance of the birefringent elements of the one or more retarders is substantially matched to the overall temperature dependence of the retardance of the birefringent elements of the one or more birefringent filters. It may be that the temperature dependence of the one or more retarders and/or the temperature dependence of the one or more birefringent elements of the one or more birefringent filter(s) match the temperature dependence of the bandpass (e.g. interference) filter.

It may be that the radiation received by the apparatus is (e.g. linearly) polarised, or it may be that the radiation received by the apparatus is unpolarised or it may be that the radiation received by the apparatus is partially polarised. It may be that the apparatus further comprises a linear polariser to receive radiation and output linearly polarised radiation to the one or more retarders.

It may be that the apparatus further comprises a controller configured to determine presence of the gas based on the at least first and second polarisation-dependent intensity measurements. For example, it may be that the controller is configured to compare the first polarisation-dependent intensity measurement to the second polarisation-dependent intensity measurement to thereby determine the presence of the gas. It may be that the controller is configured to determine a gas detection measurement based on the at least first and second polarisation-dependent intensity measurements.

It will be understood that the controller typically comprises a hardware processor. Typically the controller comprises data acquisition circuitry in data communication with processing circuitry, or a hardware computer processor executing computer program code (which is typically provided in a computer memory in data communication with the hardware processor) causing the hardware computer processor, to receive and process the polarisation-dependent intensity measurements in accordance with the functionality of the controller as set out herein.

It may be that the controller is to determine (or it may be that the method comprises determining) fractional linear polarisation data relating to the fractional linear polarisation of the radiation output by the one or more retarders, typically based on the polarisation-dependent intensity measurements. For example, it may be that the controller is to determine (or it may be that the method comprises determining) fractional polarisation data relating to a fractional linear polarisation of the radiation output by the one or more retarders based on the polarisation-dependent intensity measurements by: determining Qmeas, Umeasand Imeasbased on the polarisation-dependent intensity measurements; determining Qmeas/Imeasand Umeas/Imeasfrom the determined Qmeas, Umeasand Imeas; applying a transformation to the [Qmeas, Umeas] co-ordinate system to provide a transformed co-ordinate system [Qmeas, Umeas] whereby Qmeas′/Imeas>0 and Umeaameas=0; and determining the fractional linear polarisation data based on Qmeas′/Imeas.where: Qmeasis the measured polarisation at 0°/90° of a Stokes vector derived from the polarisation-dependent radiation intensity measurements.Umeasis the measured polarisation at 45°/135° of a Stokes vector derived from the polarisation-dependent radiation intensity measurements.Imeasis the measured intensity of a Stokes vector derived from the polarisation-dependent radiation intensity measurements.

It may be that applying the transformation comprises taking into account a zero target gas concentration reference. It may be that the zero target gas concentration reference relates to a measure of the fractional linear polarisation of the radiation output by the one or more retarders for a zero target gas concentration in the target gas measurement volume. It may be that the zero target gas concentration reference is a temperature dependent zero target gas concentration reference. For example, the zero target gas concentration reference may be dependent on the temperature of the apparatus when the polarisation-dependent intensity measurements were made. It may be that the method comprises measuring the temperature of the apparatus (e.g. or the temperature of the one or more retarders), selecting a zero target gas concentration reference in dependence on the measured temperature, and determining the fractional linear polarisation data taking into account the selected zero target gas concentration reference.

Thus, it may be that the fractional linear polarisation data comprises a measure of the fractional linear polarisation of the radiation output by the one or more retarders. It may be that the measure of the fractional linear polarisation of the radiation output by the one or more retarders is with respect to a zero target gas concentration reference which may be dependent on the temperature of the apparatus (in particular, the temperature of the one or more retarders) when the polarisation dependent radiation intensity measurements were made.

It may be that the apparatus is designed to provide a negligible Umeas(e.g. by not providing polarised radiation at linear polarisation angles of 45° and 135°). In this case, it may be that the fractional linear polarisation can be determined from Qmeas/Imeas.

It may be that the controller is configured to determine the presence of the gas based on the fractional linear polarisation data.

It may be that the controller is configured to determine (or it may be that the method comprises determining) an absorption or emission strength or concentration (e.g. a column integrated concentration in an atmospheric volume) of the gas based on the said fractional linear polarisation data. It may be that the controller is configured to determine (or it may be that the method comprises determining) an absorption or emission strength or concentration of the gas (e.g. a column integrated concentration in an atmospheric volume) based on the determined fractional linear polarisation data, typically with reference to one or more calibration references.

It may be that the fractional linear polarisation data determined by the controller (or by the method) is indicative of a fractional linear polarisation of at least 5% of the average relative depth of the spectral features of the gas within the selected frequency range.

It may be that the apparatus further comprises an objective lens for (or it may be that the method comprises an objective lens) receiving received radiation and directing it towards the filter.

It may be that the objective lens is a telecentric lens. In this case, radiation received and output by the telecentric objective lens is typically incident on the one or more retarders at an angle of incidence independent of its angle of incidence on the telecentric objective lens.

It may be that the objective lens is a non-telecentric lens. In this case, radiation received and output by the non-telecentric objective lens is typically incident on the one or more retarders at an angle of incidence which is dependent on its angle of incidence on the non-telecentric objective lens.

It may be that the apparatus comprises a plurality of groups of radiation detectors, each of the said groups comprising one or more radiation detectors to detect (or it may be that the method comprises detectors of each of a plurality of groups of radiation detectors detecting) radiation output from the one or more retarders filtered for a respective polarisation state by one or more polarisers, the one or more detectors selectively (and typically separately) detecting polarised radiation conforming to each of (e.g. the) at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the apparatus comprises a plurality of groups of radiation detectors, each of the said groups comprising radiation detectors to detect radiation output from the one or more retarders filtered for respective polarisation states by one or more polarisers, the radiation detectors of each of the groups selectively and separately detecting on different detectors at the same time polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined.

It may be that the plurality of groups of radiation detectors are configured to selectively and separately detect radiation filtered for the said respective polarisation states at the same time as each other.

It may be that the radiation detectors of the said plurality of groups of radiation detectors are provided on a common focal plane.

It may be that the said plurality of groups of radiation detectors are offset from each other, for example in the common focal plane.

It may be that the apparatus is configured to spatially modulate the polarisation of the received radiation by the said plurality of groups of radiation detectors detecting polarised radiation output from the one or more retarders, the respective groups of radiation detectors being offset from each other, for example in a common focal plane.

It may be that the radiation detectors of the said plurality of groups of radiation detectors are provided in a tessellated arrangement.

It may be that the plurality of groups of radiation detectors are provided in a periodic tessellated arrangement, the periodicity of the tessellated arrangement being in respect of the linear polarisation angles of radiation which the detectors of the groups are configured to detect. This allows the polarisation of the detected radiation to be spatially modulated across the tessellated arrangement.

It may be that the said radiation detectors within each of the said groups are tessellated in a respective 2×2 or a 2×3 arrangement or a 2×4 arrangement. It may be that the 2×2, 2×3 or 2×4 arrangements are repeating patterns in respect of the linear polarisation states of the radiation to be detected by the detectors of the respective arrangements.

It may be that the radiation detectors within each of the said groups are adjacent to each other.

It may be that the radiation detectors of a group of the said plurality of groups are configured to detect radiation output from the one or more retarders filtered for the same respective linear polarisation states as respective radiation detectors of one or more or each of the other groups of the plurality of groups.

It may be that, within each of the groups of radiation detectors, the radiation detectors are each to detect radiation filtered for a different linear polarisation state from the other detectors in the respective group.

It may be that the apparatus comprises, for each of the groups of radiation detectors, a corresponding group of polarisers for filtering for the respective polarisation states the radiation output by the one or more retarders, the corresponding group of polarisers comprising one or more polarisers.

It may be that each of the said groups of radiation detectors are provided with a plurality of (typically fixed angle) linear polarisers, each to receive (or it may be that the method comprises each of the said groups of radiation detectors having a plurality of (typically fixed angle) linear polarisers each receiving) radiation having spectrally modulated polarisation from the one or more retarders and output (or outputting) linearly polarised radiation (e.g. at a respective linear polarisation angle) to a respective radiation detector of the said plurality of radiation detectors of the said group, typically to provide respective polarisation dependent intensity measurements from which presence of the gas can be determined. It may be that the plurality of linear polarisers for each group comprise linear polarisers of different linear polarisation angles.

It may be that the groups of polarisers are provided in a tessellated arrangement.

It may be that the groups of polarisers are provided in a periodic tessellated arrangement, the periodicity being in respect of the linear polarisation angles of the polarisers of the said groups. This helps to enable the spatial modulation of the polarisation of the detected radiation across the tessellated arrangement.

It may be that the groups of polarisers are provided on a common focal plane.

It may be that the groups of polarisers are offset from each other, for example in the common focal plane.

It may be that the said groups of radiation detectors are provided adjacent to each other in a (typically two dimensional) radiation detector array.

It may be that the apparatus comprises a controller to determine (or it may be that the method comprises determining), for each of the said groups, the presence of a gas (preferably the absorption or emission strength of the gas). It may be that the controller is configured to determine (or it may be that the method comprises determining), in dependence on the said determinations, an (typically two-dimensional) image selectively indicating presence of gas (preferably relative absorption or emission strengths of the gas) at a plurality of locations across the image. It may be that the controller is configured to determine gas detection measurements based on the respective at least first and second polarisation-dependent intensity measurements for each of the respective groups, for example by determining a measure of fractional linear polarisation based thereon.

It may be that the controller is configured to reduce or remove systematic errors (e.g. in the fractional linear polarisation measurement or in the polarisation dependent radiation intensity measurements from which the presence of gas may be determined) depending on a combination of polarisation modulations applied to the received radiation in different domains. It may be that the controller is configured to reduce or remove systematic errors depending on a plurality of polarisation modulations applied to the received radiation by the apparatus, the plurality of polarisation modulations comprising the one or more retarders spectrally modulating the linear polarisation state of the received radiation to provide the received radiation with a plurality of polarised spectral modulation profiles which are offset in phase from each other, each of which is associated with a different linear polarisation angle, and any one or more of: the one or more retarders spectrally modulating the linear polarisation state of the received radiation in accordance with different polarised spectral modulation profiles for different angles of incidence of the radiation on the one or more retarders (e.g. for radiation of the same linear polarisation angle); the apparatus modulating the polarisation state of radiation output by the one or more retarders differently over time; the apparatus spatially modulating the received radiation by the said plurality of groups of radiation detectors detecting radiation output from the one or more retarders, each of the groups of detectors comprising radiation detectors selectively and separately detecting on different detectors at the same time polarised radiation conforming to each of at least first and second of the said polarised spectral modulation profiles to thereby provide at least respective first and second polarisation-dependent radiation intensity measurements from which the presence of the gas can be determined, the respective groups of radiation detectors being offset from each other, for example in a common focal plane. It may be that the respective groups of radiation detectors are offset from each other in a periodic tessellated arrangement, the periodicity of the tessellated arrangement being in respect of the linear polarisation angles of radiation which the detectors of the groups are configured to detect.

Thus, it may be that the one or more retarders are to spectrally modulate the linear polarisation state of the received radiation to provide the received radiation with a plurality of polarised spectral modulation profiles which are offset in phase from each other, each of which is associated with a different linear polarisation angle, and that the apparatus is to additionally modulate the polarisation of the received radiation in one or more other domains, such as the angular, temporal and/or spatial domains. In this case, the polarised spectral modulation profiles to which the radiation detected by the detectors conform may be provided by the said spectral modulation, while the additional modulation helps to improve the accuracy with which radiation conforming to those profiles can be measured. In this case, it may be that the controller is configured to reduce or remove systematic errors depending on the said additional modulation.

As mentioned above, it may be that the groups of radiation detectors, the corresponding groups of polarisers, or each of the groups of radiation detectors and the corresponding groups of polarisers are arranged in a respective periodic tessellation arrangement, the periodicity being in respect of the linear polarisation angles of radiation which the detectors of the groups are configured to detect or the linear polarisation angles of the polarisers of the said groups. This periodicity constitutes a polarisation modulation in the spatial domain. This may be complementary to, for example, the polarisation modulation provided by the one or more retarders spectrally modulating the linear polarisation state of the received radiation to provide the received radiation with a plurality of polarised spectral modulation profiles which are offset in phase from each other, each of which is associated with a different linear polarisation angle. In this case, the polarisation modulation provided by the one or more retarders may provide the received radiation with the polarisation spectral modulation profiles which allow the presence of gas to be determined, while the additional spatial modulation helps to improve the accuracy with which radiation conforming to those profiles can be measured. This polarisation modulation in the spatial domain may provide additional information which can be used to mitigate systematic errors, for example in the fractional linear polarisation measurement or in the polarisation dependent intensity measurements from which the presence of gas may be determined.

It may be that the controller is to determine (or it may be that the method comprise determining), for each of a plurality of radiation detectors (e.g. for each radiation detector of one or more or each of the said groups), whether gas is present in dependence on polarisation-dependent radiation intensity measurements (i.e. radiation intensity measurements of polarised radiation) by that radiation detector and by one or more radiation detectors proximal to that radiation detector. The said one or more radiation detectors proximal to the said radiation detector may comprise one or more radiation detectors of a said group comprising the said radiation detector. The said one or more radiation detectors proximal to the said radiation detector may comprise one or more radiation detectors of a said group which does not comprise the said radiation detector.

It may be that the controller is configured to use a polarisation-dependent radiation intensity measurement from one of the radiation detectors in the determination of the presence of the gas for a plurality of (e.g. two or more, three or more or four or more) positions in the focal plane. It may be that the controller is configured to use a polarisation-dependent radiation intensity measurement from each of a plurality of detectors in the determination of the presence of the gas for a respective plurality of positions in the focal plane. In this way, the spatial resolution of the image may be increased (for example compared to determining whether the gas is present once per group of detectors). For example, a determination as to whether gas is present may be determined in this way for each detector (e.g. for each detector of each group). In addition, systematic errors which may otherwise appear in the fractional linear polarisation measurement or in polarisation dependent intensity measurements, for example due to aliasing and/or due to dead pixels, can be reduced or removed (for example as compared to determining whether the gas is present once per group of detectors). For example it may be that the controller is configured to determine whether gas is present in respect of a first position on a focal plane depending on polarisation-dependent radiation intensity measurements (i.e. radiation intensity measurements of polarised radiation) by at least a first one of the radiation detectors and a second one of the radiation detectors, and to determine whether gas is present in respect of a second position on the focal plane depending on polarisation-dependent radiation intensity measurements by at least the first one of the radiation detectors and a third one of the radiation detectors different from the second one of the radiation detectors. It may be that the controller is configured to determine whether gas is present in respect of a first position on a focal plane depending on polarisation-dependent radiation intensity measurements (i.e. radiation intensity measurements of polarised radiation) by at least a first one of the radiation detectors, a second one of the radiation detectors and a third one of the radiation detectors, and to determine whether gas is present in respect of a second position on the focal plane depending on polarisation-dependent radiation intensity measurements by at least the first one of the radiation detectors, the second one of the radiation detectors and a fourth one of the radiation detectors different from the third one.

Thus, by spatially modulating the polarisation of the received radiation by the plurality of groups of radiation detectors detecting radiation output from the one or more retarders, the respective groups of radiation detectors being offset from each other in a periodic tessellated arrangement, the periodicity of the tessellated arrangement being in respect of the linear polarisation angles of radiation which the detectors of the groups are configured to detect, information from respective proximal (e.g. surrounding) pixels can be used to determine the fractional linear polarisation, and thus the presence of the gas, in respect of the location of each of the detectors (e.g. in respect of the location of each pixel in the array). It may be typically assumed that the gas concentration varies smoothly, and thus that the fractional linear polarisation varies smoothly (e.g. at a frequency greater than the individual pixel level, or at a frequency greater than the spatial modulation frequency) across the radiation detectors of the plurality of groups (e.g. over the focal plane of the detector array). As such, a systematic issue with an individual pixel can be mitigated by the spatial modulation. In the Fourier domain, this can be thought of as considering information at a predefined spatial modulation carrier frequency (i.e. the frequency with which the polarisation is spatially modulated across the detectors) and removing or discarding information at frequencies which differ (or which differ significantly) from the predetermined spatial modulation frequency (which may be information from individual pixels producing systematic errors).

It may be that the polarisation-dependent radiation intensity measurements detected by the first and second, or first, second and third, or first, second and fourth ones of the radiation detectors, are determined by detecting polarised radiation conforming to different ones of the polarised spectral modulation profiles.

It may be that the apparatus (e.g. the controller) is configured to output the said two-dimensional image to a user interface such as a display.

It may be that the said plurality of groups of radiation detectors comprises a first group arranged to receive (or receiving) radiation incident on the objective lens at a first angle of incidence and a second group arranged to receive (or receiving) radiation incident on the objective lens at a second angle of incidence different from the first angle of incidence. It may be that the first and second angles of incidence are offset from each other by at least 45°.

It may be that each of one or more of the said groups, or each of the said groups, comprise a first detector to detect (or detecting) radiation filtered for a first linear polarisation angle and conforming to the said first polarised spectral modulation profile and a second detector to detect (or detecting) radiation filtered for a second linear polarisation angle and conforming to the said second polarised spectral modulation profile. It may be that each of one or more of the said groups, or each of the said groups, comprise a third detector to detect (or detecting) radiation filtered for a third linear polarisation angle and conforming to a third said polarised spectral modulation profile. It may be that each of one or more of the said groups, or each of the said groups, comprise a fourth detector to detect (or detecting) radiation filtered for a fourth linear polarisation angle and conforming to a fourth said polarised spectral modulation profile.

It may be that the apparatus comprises a controller to derive (or it may be that the method comprises deriving) a concentration of the gas in the atmosphere from the polarisation-dependent intensity measurements by the first and second groups of radiation detectors.

It may be that the received radiation comprises or consists of radiation emitted by the sun (and typically scattered by the Earth's atmosphere).

It may be that the received radiation received by the one or more retarders has passed through a gas measurement volume within which the gas is to be detected.

A third aspect of the disclosure provides a method of determining presence of a gas, the method comprising: obtaining (e.g. retrieving from a memory or receiving from one or more radiation detectors) at least first and second polarisation dependent radiation intensity measurements; and determining presence of a gas based on the at least first and second polarisation dependent intensity measurements. It may be that determining presence of the gas based on the at least first and second polarisation dependent radiation intensity measurements comprises determining fractional linear polarisation data based on the at least first and second polarisation dependent intensity measurements. It may be that determining presence of the gas based on the at least first and second polarisation dependent radiation intensity measurements comprises comparing the first and second polarisation dependent radiation intensity measurements.

It may be that the method comprises obtaining (e.g. retrieving from a memory or receiving from one or more radiation detectors) at least first, second and third polarisation dependent radiation intensity measurements; and determining presence of a gas based on the at least first, second and third polarisation dependent intensity measurements. It may be that the method comprises determining presence of the gas based on the at least first, second and third polarisation dependent intensity measurements by determining fractional polarisation data based on the at least first, second and third polarisation dependent intensity measurements.

It may be that the fractional linear polarisation data is indicative of a fractional linear polarisation of a beam of radiation from which the at least first and second (and, where provided, third, and, where provided, fourth etc.) polarisation dependent intensity measurements are made. It may be that the fractional linear polarisation data comprises a measure of the fractional linear polarisation of the said beam of radiation, for example with respect to a zero target gas concentration reference which may be selected depending on a measured temperature. It may be that the method comprises obtaining a measured temperature, selecting a zero target gas concentration reference dependent on the measured temperature, and determining the fractional linear polarisation data in dependence on the selected zero target gas concentration reference.

It may be that the method comprises determining an absorption or emission strength or a concentration of the gas by comparing the said fractional linear polarisation data to a calibration curve. It may be that the calibration curve relates a measure of fractional linear polarisation to a concentration of the gas. It may be that the gas is a target gas.

A fourth aspect of the disclosure provides data processing apparatus comprising processing circuitry to perform the method according to the third aspect of the disclosure.

A fifth aspect of the disclosure provides machine readable instructions executable by a hardware computer processor to perform the method of the third aspect of the disclosure.

A sixth aspect of the disclosure provides a non-transitory computer readable medium comprising machine readable instructions executable by a hardware computer processor to perform the method of the third aspect of the disclosure.

It will be understood that optional and preferred features of each aspect of the present disclosure are also optional or preferred features of each other aspect of the present disclosure where appropriate. For example, it may be that apparatus features correspond to method features.

