Method for estimating the intensity of a wave emitted by an emitting source

Abstract

A method for analyzing a gaseous sample, by comparing an incident light wave and a transmitted light wave, the method comprising: i) illuminating the sample with a light source emitting the incident light wave propagating up to the sample; ii) detecting a light wave transmitted by the sample; iii) detecting a reference light wave emitted by the light source and representing a light wave reaching a reference photodetector without interacting with the sample; iv) repeating i) to iii) at different measurement instants; v) estimating, at each measurement instant, an intensity of the reference light wave; vi) taking into account the estimated intensity of the reference light wave and the detected intensity of the transmitted light wave to perform a comparison, at each measurement instant; and vii) analyzing the gaseous sample as a function of the comparison.

Claims

1. A method for analyzing a gas sample, by comparison between a light wave incident on the sample and a light wave transmitted by the sample, the method comprising: i) illuminating the sample, with a light source, the light source emitting an incident light wave that propagates to the sample; ii) detecting, with a measurement photodetector, a transmitted light wave transmitted by the sample, the transmitted light wave resulting from an attenuation of the incident light wave by the sample; iii) detecting a reference light wave with a reference photodetector, the reference light wave being emitted by the light source, the reference light wave being representative of a light wave reaching the reference photodetector without interaction with the sample; iv) reiterating i) to iii) at various measurement times; v) from each reference light wave detected in each step iii), at each measurement time, estimating an intensity of the reference light wave at the measurement times, by implementing: b) estimating an intensity of the reference light wave at a measurement time based on an initial intensity or an estimation of the intensity of the reference light wave at a prior measurement time; c) measuring an intensity of the reference light wave detected at the measurement time; d) updating the estimation of the intensity of the reference light wave at the measurement time, depending on the intensity measured in c) and the intensity estimated in b); and e) reiterating b) to d), on the basis of the estimation of the intensity of the reference light wave obtained in d), while incrementing the measurement time; vi) taking into account the intensity of the reference light wave estimated, at each measurement time, including the estimated intensity resulting from v), and an intensity of the transmitted light wave detected in ii) and performing a comparison, at each measurement time, based on the reference light wave and on the transmitted light wave transmitted by the sample; and vii) analyzing the gas sample depending on the comparison performed in vi).

2. The method of claim 1, wherein v) further comprises: a) determining an initial intensity of the reference light wave.

3. The method of claim 2, wherein a) further comprises detecting, with the reference photodetector, the reference light wave during an initialization period.

4. The method of claim 3, wherein a) comprises: ai) detecting the reference light wave at a plurality of preliminary times, during the initialization period, and measuring an intensity of the reference light wave detected at each preliminary time; and aii) determining the initial intensity from a mean or a median of the intensities measured in ai).

5. The method of claim 1, wherein b) further comprises estimating a state vector, at each measurement time, the state vector comprising an estimation of the intensity of the reference light wave detected at the measurement time.

6. The method of claim 5, wherein the state vector also comprises a term representing an estimation of a drift in the intensity of the reference light wave between two successive measurement times.

7. The method of claim 5, wherein b) comprises estimating the state vector at each measurement time, by applying a prediction matrix to the state vector determined at a time preceding the measurement time.

8. The method of claim 5, wherein d) comprises: di) performing a comparison between the measurement of the reference intensity carried out in c) preceding d), and the estimation resulting from b) preceding d); and dii) updating the state vector depending on the comparison resulting from di).

9. The method of claim 5, wherein b) to d) are implemented using a recursive estimator of a Kalman-filter type.

10. The method of claim 1, wherein the incident light wave being attenuated by the sample, the method further comprises, in vi), calculating a ratio of the estimated intensity of the reference light wave and the intensity of the transmitted light wave, the ratio corresponding to the attenuation of the incident light wave by the sample.

11. The method of claim 1, wherein the sample comprises a gaseous species that attenuates the incident light wave, the method further comprising, in vii), estimating an amount of the gaseous species in the sample, at each measurement time, from the attenuation determined in vi) at the measurement time.

12. A device for analyzing a gas sample, the device comprising a light source configured to emit an incident light wave that propagates toward the sample; a measurement photodetector, configured to detect a light wave transmitted by the sample, at various measurement times, the transmitted light wave resulting from an interaction of the incident light wave with the sample; a reference photodetector, configured to detect a reference light wave emitted by the light source, at various measurement times, the reference light wave being representative of a light wave reaching the reference photodetector without interaction with the sample; a first processor, configured to estimate an intensity of the reference light wave at the various measurement times, from the reference light wave detected by the reference photodetector at each measurement time, the first processor being configured to implement v) of the method of claim 1; and a second processor configured to compare, at each measurement time, the reference light wave and the light wave transmitted by the sample, at the measurement time, from the intensity of the reference light wave estimated by the first processor at each measurement time, and from an intensity of the transmitted light wave detected by the measurement photodetector, the second processor being programmed to implement vi) of the method of claim 1.

13. The device of claim 12, wherein the first processor and the second processor are one and the same.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A shows a device allowing the disclosure to be implemented. FIG. 1B illustrates the temporal form of a light pulse produced by the light source of the device. FIG. 1C shows a variation in the light intensity of a plurality of successive pulses of the light source.

(2) FIG. 2A illustrates the main steps of one embodiment of the disclosure. FIG. 2B shows the substeps of one step of FIG. 2A.

(3) FIG. 3A shows the result of an experimental trial, comparing, at various successive times, the measurement of an intensity of a reference light wave and its estimation by the method of the disclosure.

(4) FIG. 3B illustrates an estimation of the drift in the reference light intensity during the experimental trial.

(5) FIG. 3C shows another result of an experimental trial, comparing, at various successive times, the measurement of an intensity of a reference light wave and its estimation by the method of the disclosure. This result was obtained using a measurement acquisition frequency lower than the frequency that allowed the data shown in FIG. 3A to be obtained.

(6) FIG. 4 illustrates the main steps of a method for estimating a light attenuation, with a view to estimating an amount of gaseous species in a sample.

DETAILED DESCRIPTION

(7) FIG. 1A is an example of a device 1 for analyzing gas. This device comprises an enclosure 10 defining an internal space inside of which the following are found: a light source 11, able to emit a light wave, called the incident light wave 12, so as to illuminate a gas G lying in the internal space, the gas forming a sample 13; and a photodetector, called the measurement photodetector 20, able to detect a light wave 14 transmitted by the sample 13, under the effect of illumination of the latter by the incident light wave 12.

(8) The gas G may be a gas mixture comprising a plurality of gaseous species G.sub.1 . . . G.sub.S . . . G.sub.S, S being a positive integer quantifying the number of different gaseous species present in the gas G.

(9) The light source 11 is able to emit the incident light wave 12, in an illumination spectral band , the latter possibly extending between the near ultraviolet and the mid infrared, i.e., between 200 nm and 10 m, and most often between 1 m and 10 m. The light source 11 may notably be a pulsed source, the incident light wave 12 being a pulse of duration generally comprised between 100 ms and 1 s, such as shown in FIG. 1B. The light source may notably be a suspended filament heated to a temperature comprised between 400 C. and 800 C.

(10) In the example in question, the photodetector is a thermopile, able to deliver a signal dependent on the intensity of the light wave to which the photodetector is exposed. It may also be a question of a photodiode or another type of photodetector.

(11) The device may comprise a bandpass filter 18, the spectral band of which corresponds to a spectral band of a gaseous species G.sub.S for which it is desired to determine an amount C.sub.s,k in the gas mixture, at a measurement time k. The intensity I.sub.k of the light wave 14 detected by the measurement photodetector 20, at the measurement time k depends on the amount C.sub.s,k, according to the Beer-Lambert equation:

(12) $\begin{array}{cc}{\mathrm{att}}_k=\frac{I_k}{I_{0,k}}=e^{-\left(C_{s,k}\right)l}& \left(1\right)\end{array}$
where: (C.sub.s,k) is an attenuation coefficient, dependent on the sought-after amount C.sub.s,k; l is the thickness of gas passed through by the incident light wave 12; and I.sub.0,k is the intensity of the incident light wave 12 at the measurement time k.

(13) The comparison between I.sub.k and I.sub.0,k, which takes the form of a ratio

(14) $\frac{I_k}{I_{0,k}},$
corresponds to an attenuation att.sub.k of the incident light wave 12 by the sample 13 at the measurement time k.

(15) During each pulse of the light source 11, it is thus possible to determine (C.sub.s,k), this allowing C.sub.s,k to be estimated, given that the relationship between C.sub.s,k and (C.sub.s,k) is known.

(16) Equation (1) assumes the intensity I.sub.0,k of the incident light wave 12 is known at the measurement time k. To this end, the device comprises a reference photodetector 20.sub.ref, arranged such that it detects a light wave, called the reference light wave 12.sub.ref, representative of the incident light wave 12. The reference light wave reaches the reference photodetector without interacting with the sample 13, or without significantly interacting with the latter. The intensity of the reference light wave 12.sub.ref, detected by the reference photodetector 20.sub.ref, at the measurement time k, is referred to as the reference intensity I.sub.ref,k.

(17) In this example, the reference photodetector 20.sub.ref is placed beside the measurement photodetector 20. It is associated with an optical filter, called the reference optical filter 18.sub.ref. The reference optical filter 18.sub.ref defines a passband corresponding to a range of wavelengths not absorbed by the sample. The reference passband is, for example, centered on the wavelength 3.91 nm. The various configurations described with reference to the prior art may also be employed, in particular, the variants in which: the reference photodetector 20.sub.ref is placed in an enclosure isolated from the gas to be analyzed; and the reference photodetector 20.sub.ref and the measurement photodetector 20 are merged into one, a filter-adjusting means allowing the photodetector to be alternatively associated with the bandpass filter 18 and with the reference optical filter 18.sub.ref. It may, for example, be a question of a filter wheel.

(18) In the prior-art devices, the measurement of I.sub.ref,k allows equation (1) to be used with I.sub.0,k replaced by I.sub.ref,k, this allowing (C.sub.s,k) to be determined, then .sub.s,k to be estimated.

(19) The device comprises a first processor 30, for example a microprocessor or a microcontroller. The latter is configured to receive a signal representative of an intensity I.sub.ref,k of the reference light wave 12.sub.ref, measured by the reference photodetector 20.sub.ref at each measurement time k, and to implement a method in order to estimate the intensity of the reference light wave, such as described below, with reference to FIGS. 2A and 2B. The first processor 30 is connected to a memory 32 containing instructions allowing certain steps of this method to be implemented.

(20) The device also comprises a second processor 30 configured to receive a signal representative of an intensity I.sub.k of the light wave 14 transmitted by the sample 13, this intensity being measured by the measurement photodetector 20. The second processor is programmed to determine, at each measurement time, a quantity representative of the attenuation att.sub.k of the incident light wave 12 by the sample 13. The first processor 30 and the second processor 30 may be one and the same.

(21) It is known that the emissivity of black-body and grey-body light sources varies over time, and may notably undergo a decrease. Use of a reference photodetector such as described above is therefore necessary to take into account this temporal variation. FIG. 1C shows a temporal variation in the intensity I.sub.ref,k of each light pulse, detected by a reference photodetector, at various times k, between a time k=0 and a time k=K, with K=2.6 10.sup.7. The index k is a temporal index, and designates a pulse emitted at a measurement time k. The time interval separating two successive measurement times k and k+1 is, in this example, 1 s. This curve was obtained by measuring, with a reference photodetector, the variation in the intensity emitted by a light source in a time period of 2.610.sup.7 seconds, i.e., 7220 hours, i.e., about 300 days. This measurement was carried out using the Heimann Sensor thermopile of reference HCM Cx2 Fx that played the role of reference photodetector 20.sub.ref.

(22) Each pulse of the light source has a temporal form similar to that shown in FIG. 1B. Thus, during a pulse, the intensity of the pulse is variable and has a shape close to that of a top hat. The intensity of each pulse may be obtained by considering the maximum value or the mean value of such a pulse. In the present case, the intensity I.sub.ref,k corresponds to the mean value of the intensity of each pulse. The measurements shown in FIG. 1C were carried out using a pulse frequency of 1 Hz, the duration of each pulse being equal to 300 ms. It may be seen that the reference intensity gradually decreases, from an initial value I.sub.ref,k=0 of about 101 mV to a final value I.sub.ref,k=K of about 72 mV. Substantial fluctuations in the measured reference intensity may also be observed. These fluctuations are essentially due to detection noise in the photodetector, in this case the thermopile. The intensities of the pulses are here expressed in units of voltage, corresponding to the voltage across the terminals of the thermopile.

(23) Taking into account the reference intensity in equation (1), i.e., considering I.sub.0,k=I.sub.ref,k, the estimation .sub.s,k of the amount of the sought-after gaseous species is affected by the fluctuations in the measurement of the reference intensity I.sub.ref,k. In other words, the fluctuations affecting the determination of the reference intensity I.sub.ref,k propagate to the estimation .sub.s,k, this possibly leading to an uncertainty affecting the estimation of the amount of the sought-after gaseous species.

(24) The disclosure aims to attenuate the fluctuations affecting the determination of the reference intensity I.sub.ref,k, and to take into account the gradual decrease in this intensity over time. To do this, it is based not on a measurement of the reference intensity I.sub.ref,k, but rather on an estimation .sub.ref,k of the latter, based on an observation and on an iterative predictive model. The estimation .sub.ref,k may notably be obtained, at each time k, by implementing a recursive estimator. Such an estimator may, for example, be a Kalman filter, the main steps of which are illustrated in FIG. 2A and described below.

(25) Step 100: initialization measurements. In this step, the light source 11 is activated and the intensity called the preliminary intensity, I.sub.ref,p, of one or more pulses is measured using the reference photodetector 20.sub.ref. The index p designates the rank of the initialization iterations: it is comprised between 1 and P, P being a positive integer higher than or equal to 1. P is, for example, equal to 30.

(26) Step 110: determining initialization values. In this step, an initialization measurement (step 100) is reiterated provided that p<P. When the iteration end condition is met (p=P), an initial reference light intensity I.sub.ref,k=0 is determined from the various measured preliminary intensities I.sub.ref,p. This determination may be carried out using a mean, according to the expression:

(27) $\begin{array}{cc}{I}_{\mathrm{ref},k=0}=\underset{p}{\mathrm{mean}}\left(I_{\mathrm{ref},p}\right),& \left(2\right)\end{array}$
where mean is the mean operator.

(28) An initial variance is also determined

(29) $\begin{array}{cc}{\mathrm{var}}_{\mathrm{ref},k=0}=\underset{p}{\mathrm{var}}\left(I_{\mathrm{ref},p}\right),& \left(3\right)\end{array}$
where var is the variance operator.

(30) In this step, an initial state vector,

(31) $x_{k=0}=\left(\begin{array}{c}{I}_{\mathrm{ref},k=0}\\ 0\end{array}\right),$
is also determined.

(32) Alternatively, the initial intensity I.sub.ref,k=0 may be established arbitrarily or assigned a value determined during tests following manufacture of the source.

(33) Step 120: taking into account a first measurement time (k=1) and starting the iterative method. Following the initialization phase, which encompasses steps 100 and 110, the iteration temporal index k, representing the iteration rank of the recursive method, it is initialised and given the value k=1.

(34) At each time k, the reference light wave 12.sub.ref may be represented by a state vector

(35) $x_k=\left(\begin{array}{c}{I}_{\mathrm{ref},k}\\ d_k\end{array}\right),$
where: I.sub.ref,k is the reference light intensity at the time k; and d.sub.k is a drift in the reference light intensity at the time k. The drift d.sub.k corresponds to a comparison of the reference light intensity between two successive times k and k1.

(36) During the establishment of the initial state vector {circumflex over (x)}.sub.k=0, the first term I.sub.ref,k=0 of the vector corresponds to the initial intensity whereas the second term of the vector corresponds to an arbitrary value of the drift, this value, for example, being 0.

(37) Two successive state vectors x.sub.k1, x.sub.k are related by the following state-evolution equations:
I.sub.ref,k=I.sub.ref,k+d.sub.k+w.sub.k.sup.1(4)
d.sub.k=d.sub.k1+w.sub.k.sup.2(5)
where w.sub.k.sup.1 and w.sub.k.sup.2 are noise terms described by normal distributions of zero mean and of variances equal to var(w.sub.k.sup.1) and var(w.sub.k.sup.2), respectively.

(38) Each iteration aims to estimate a state vector {circumflex over (x)}.sub.k={circumflex over (x)}.sub.k|k, representative of the reference light intensity at the time k, such that

(39) ${\hat{x}}_k=\left(\begin{array}{c}{\hat{I}}_{\mathrm{ref},k}\\ {\hat{d}}_k\end{array}\right).$
The symbol {circumflex over ()} designates an estimated quantity.

(40) Step 130: estimating. From an estimation of the reference intensity I.sub.ref,k1 resulting from a preceding iteration k1, estimating a reference intensity at the time k. In the first iteration (k=1), the estimation is based on the initial reference intensity I.sub.ref,k=0 obtained in step 110. The estimation is obtained using the following estimation equation:
{circumflex over (x)}.sub.k|k1=A.Math.{circumflex over (x)}.sub.k1|k1(6).
A is a prediction matrix, relating the state vector {circumflex over (x)}.sub.k1|k1 resulting from the preceding iteration to the estimation of the state vector at the time k. In this example, the prediction matrix A is such that:

(41) $A=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$

(42) This step also comprises estimating an error covariance matrix {circumflex over (P)}.sub.k|k1 using the expression:
{circumflex over (P)}.sub.k|k1=A.Math.P.sub.k1.Math.A.sup.T+Q(7) {circumflex over (P)}.sub.k being a covariance matrix of the error estimated at the time k; T being the transpose operator; A being the prediction matrix described in conjunction with equation (6); and Q being a noise covariance matrix of the process.

(43) The noise covariance matrix Q of the process is such that:

(44) $Q=\left[\begin{array}{cc}\mathrm{var}\left(w_k^1\right)& 0\\ 0& \mathrm{var}\left(w_k^2\right)\end{array}\right]$
with var(w.sub.k.sup.1)=var(w.sub.k.sup.2)=110.sup.5.

(45) Step 140: Updating.

(46) The updating step comprises the following substeps, which are described with reference to FIG. 2B: Substep 141: observing. A measurement is taken of the reference intensity I.sub.ref,k at the time k, from which measurement a quantity z.sub.k, called the observation quantity is determined, this quantity being such that:
z.sub.k=I.sub.ref,k+v.sub.k(8),
where v.sub.k is a noise term, described by a normal distribution of zero mean and variance equal to var.sub.ref,k=0, as defined with reference to equation (3). Substep 142: determining an innovation y.sub.k using the following expression:
y.sub.k=z.sub.kC.Math.{circumflex over (x)}.sub.k|k1(9)
with C=[1 0].Math.{circumflex over (x)}.sub.k|k1 results from step 130. Substep 143: determining a covariance S.sub.k of the innovation with:
S.sub.k=C.Math.{circumflex over (P)}.sub.k|k1.Math.C.sup.T+R(10),
R being equal to the variance determined in the initialization phase using equation (3). Substep 144: calculating the gain K.sub.k:
K.sub.k={circumflex over (P)}.sub.k|k1.Math.C.sup.T.Math.S.sub.k.sup.1(11) Substep 145: updating the state vector:
{circumflex over (x)}.sub.k={circumflex over (x)}.sub.k|k={circumflex over (x)}.sub.k|k1+K.sub.k.Math.y.sub.k(12) Substep 146: updating the error covariance matrix:
{circumflex over (P)}.sub.k=(IK.sub.k.Math.C).Math.{circumflex over (P)}.sub.k|k1(13).
I is an identity matrix of (2, 2) size.

(47) Step 150: reiterating: The iteration temporal index k is incremented and the iterative process starts again from step 130, on the basis of the estimations {circumflex over (x)}.sub.k|k and {circumflex over (P)}.sub.k obtained in substeps 145 and 146, respectively.

(48) Each estimation {circumflex over (x)}.sub.k|k of the state vector makes it possible to obtain an estimation .sub.ref,k of the intensity of the reference light wave and an estimation {circumflex over (d)}.sub.k of the drift at each measurement time k. FIGS. 3A and 3B show the estimations .sub.ref,k and {circumflex over (d)}.sub.k obtained based on the variation in the intensity of the reference light wave 12.sub.ref shown in FIG. 1C, respectively. It may be seen that the estimations .sub.ref,k are clearly less affected by the noise measured by taking a measurement of I.sub.ref,k. Specifically, the curve showing the temporal variation in the estimation .sub.ref,k is clearly less subject to temporal fluctuations than the measurements I.sub.ref,k. This is due to the fact that the Kalman filter takes into account the variance of the noise of the reference photodetector, the variance notably being learnt during the initialization period, using the preliminary measurements. The method thus allows the intensity of the reference light wave to be estimated while limiting, or even completely removing, the fluctuations caused by the reference photodetector 20.sub.ref. This estimation allows the temporal variation in the reference intensity, due to the decrease in the emissivity of the light source 11, to be taken into account. This makes it possible to obtain an estimation of the amount .sub.s,k of gaseous species that is less subject to the fluctuations of the reference photodetector 20.sub.ref, while taking into account the variation in the emissivity of the light source 11.

(49) FIG. 3C shows the results of another simulation, in which the acquisition frequency was sub-sampled by a factor of 1000 with respect to the simulation shown in FIG. 3A. The temporal variation in the measurements I.sub.ref,k is again subject to substantial fluctuations, whereas the temporal variation in the estimation .sub.ref,k is clearly less noisy.

(50) With reference to FIG. 4, the main steps of a method for estimating the attenuation of an incident light wave produced by a light source will now be described, with reference to the application illustrated in FIG. 1A. In a first step 200 of initialization, initialization data are obtained. This step encompasses the initialization phase described above (steps 100 and 110). Following this initialization phase, the method comprises the following steps:

(51) Step 210: activating the light source 11 at a time k and measuring the intensity I.sub.k of the light wave 14 transmitted by the gas present in the sample, using the measurement photodetector 20. Simultaneously, the reference light wave 12.sub.ref is measured using the reference photodetector 20.sub.ref, this allowing a measurement of the reference intensity I.sub.ref,k to be obtained.

(52) Step 220: based on the reference light wave I.sub.ref,k measured at the time k, an iteration of the recursive estimating method described with reference to steps 130 to 150 is implemented. This notably allows an estimation .sub.ref,k of the reference intensity at the time k to be obtained. This estimation is calculated by the first processor 30, which is, for example, a microcontroller.

(53) Step 230: comparing the reference intensity .sub.ref,k estimated in step 220 with the intensity I.sub.k measured in step 210 in order to obtain an attenuation att.sub.k of the incident light wave 12 by the sample. This comparison may be carried out by the second processor 30, which is, for example, a microprocessor connected to the first processor 30.

(54) The method may comprise a step 240 of determining an amount .sub.s,k of a gaseous species G.sub.s based on the attenuation att.sub.k obtained at the end of step 230, as described above with reference to equation (1).

(55) Steps 210 to 230, or even 240, may be reiterated at various measurement times k.

(56) The disclosure is not limited to the estimation of a light intensity emitted by a light source, and may be applied to other types of wave-emitting sources. It may, for example, be a question of a source of ionizing electromagnetic radiation, for example, an x-ray source, or a source of an acoustic wave, a piezoelectric transducer, for example. The targeted applications thus encompass nondestructive-testing and medical-imaging applications. The disclosure is notably applicable when it is desired to achieve an estimation of a reference intensity emitted by an emitting source, this reference intensity corresponding to a wave emitted by the emitting source and that propagates toward a sample to be examined. The advantage is that fluctuations due to the detection, by a sensor, of the reference wave are avoided. It is then possible to compare an intensity of a wave having interacted with the sample, by reflection, transmission, scattering, or refraction, with the reference wave estimated by implementing the disclosure. The comparison allows the sample to be analyzed, and, for example, of an amount of scattering elements to be determined.

(57) When the emitting source is a light wave, the advantage of the disclosure is to allow an estimation that is not affected by noise of the intensity of a light wave incident on the examined sample. The examined sample may interact with the incident light wave by absorbing it partially, as described in the detailed example, or even by scattering it or diffracting it. The comparison between the intensity of the reference wave and the intensity of the scattered, absorbed or refracted wave, allows a property of the object to be estimated, and, in particular, a content of a particular species or a refractive index.