GB2433316A

GB2433316A - A method for determining profiles of the concentration, pressure and temperature of gases in combustion processes and their exhaust gas flows and plumes

Info

Publication number: GB2433316A
Application number: GB0624388A
Authority: GB
Inventors: Erwin Lindermeier; Volker Tank
Original assignee: Deutsches Zentrum fuer Luft und Raumfahrt eV
Current assignee: Deutsches Zentrum fuer Luft und Raumfahrt eV
Priority date: 2005-12-14
Filing date: 2006-12-06
Publication date: 2007-06-20
Anticipated expiration: 2026-12-06
Also published as: GB0624388D0; GB2433316B; DE102005060245B3

Abstract

For a determination of profiles of the concentration, the pressure and the temperature of gases in combustion processes and their exhaust gas flows and plumes, in a least squares fit calculation, the absorption coefficients a necessary for the calculation of model spectra are considered as a function of pressure p and temperature T for each wave number. These functions are approximated by means of interpolating, two-dimensional, cubic spline functions a (p,T) and, in a p,T plane, a desired pressure and temperature range, is divided into rectangular partial ranges that are axially parallel without overlapping each other. For each partial rectangle a two-dimensional cubic polynomial is true as an interpolating function (eq. 1), the first derivatives thereof with respect to pressure or temperature and the mixed derivatives with respect to pressure and temperature are equal at the corners. Measured spectra, such as radiance and transmission spectra, the volumes of combustion gases and other gases, are compared to the calculated spectra.

Description

A METHOD FOR DETERMINING PROFILES OF THE CONCENTRATION. THE PRESSURE

AND THE TEMPERATURE OF GASES IN IHTCRNAI COMBUSTION 4' -

PROCESSES AND THEIR EXHAUST GAS FLOWS AND PLUMES

The invention refers to a method for determining profiles of the concentration, the pressure and the temperature of gases in iDtomat combustion processes and their exhaust gas flows and plumes. 614" io Combustion processes of various forms and frequencies occur on earth. Man burns fossil fuels for purposes of heating and generating current and combusts them as fuel in motor vehicles, ships and planes. All over the world, large amounts of combustible biomass (forests, savannas, etc.) are burnt either in a controlled or an uncontrolled manner (heating, forest fires, steppe tires, peat fIres).

Combustion products are released into the atmosphere in large amounts.

Some combustion products, such as carbon dioxide, nitric oxides, methane, soot etc., are harmful to the environment and/or to health, and have an influence on the development and change of the world's climate. Various efforts are made to quantify the gases and particles emitted by all the combustion processes on earth and to study their effects, as well as to develop methods for their reduction.

Among other efforts, internal combustion engines and combustion plants are optimized to save fuel through a higher efficiency and to change the composition of undesired combustion products and to reduce the amount thereof. Meanwhile, legal pollution control provisions and exhaust gas regulations set limit values for allowable amounts of pollutants that are allowed to be released from such systems both in the industrial and the domestic domain.

For monitoring, combustion products in exhaust gases have to/must be measured. Measurements can be performed in certain intervals, for example for exhaust gases of vehicles, domestic combustion installations, or continuously, as for example in power plants, or also sporadically for research purposes. These measurements include a variety of measuring tasks of different complexity. The exhaust gases are hot, Inhomogeneous in their composition and temperature distribution, often hard to access and/or extending over large areas, such as in forest fires or steppe fires. A great number of gases is always present; in most cases, several of these are to be detected.

The combustion processes can be controlled or regulated using the measured exhaust gas parameters, i.e. the actual exhaust gas compositions and the combustion efficiency have to be continuously compared to the desired parameters and the process flows have to be corrected, if need be. Among other things, this requires an exact and, above all, quick measuring technique.

In well controlled combustion processes, such as in thermal power stations, airplane turbines on a test stand, etc., measuring methods taking samples or using in situ sensors have prevailed. Temperatures are measured in situ, exhaust gas samples are supplied to conventional analyzing devices such as NDIR (Non Dispersive Infrared) Instruments, for example. Generally, a specific analyzer is required for each gas species. For this reason and because of the necessary withdrawal and processing of gas, these methods can not be implemented everywhere, for example, they can not be implemented in flight, and/or suffer from the drawback that they do not capture the entire exhaust gas, but to supply only measured values of the conditions at the sampling site or the location of the sensor.

In the domain of science, exhaust gas analyses of uncontrolled fires are performed using contactless methods, namely remote measuring methods.

Here, spectrometnc radiation measurements are performed in wide spectral ranges in the visible and/or the infrared spectral range. Parameters of the combustion gases are detemiined from the spectra. It is particularly advantageous that, different from the conventional analyzers, a plurality of gases and, simultaneously, also temperature and pressure are detected. The measurements can be made from a plane or a satellite thus allowing to cover large events of fire.

Particularly useful are methods in the infrared, since, in this range, the relevant gases have distinctive spectral absorption properties, on the one hand, but also showing measurable spectral emissions at higher temperatures, on the other hand. For the separation of the spectral signatures of the different gases, a measurement with a high spectral resolution is required, which is why large amounts of data are accumulated and have to be processed.

Preferably, Fourier transformation spectrometers are employed that supply the spectra as a function of the wave number a. This method, especially in its tomographic embodiment, allow for the determination of profiles of the concentration, pressure and temperature of exhaust gases, and thus yield accurate measurement results which is a great advantage because of the above mentioned inhomogeneity of the exhaust gases. Their implementation in the examination of exhaust gases of controlled combustions, such as in airplane turbines, large combustion installations and the like, is very desirable, which is why developments are made for these fields of application.

A current drawback still existing is that the gas parameters are obtained by so-called retrieval methods such as the least square fit, which are iterative, and that these methods mostly require a high number of iteration steps.

Moreover, each iteration step requires the calculation of a spectrum and its derivatives with respect to the gas parameters. These spectra are obtained using intricate, calculation-intensive radiation models. As a result, the If * a evaluation of the measuring spectra presently take. very long computing times even with high computing powers.

For the data evaluation of spectroscopic measurements, the profiles of concentration, pressure and temperature are determined using the non-linear least square fit. Here, the measured spectra, such as the radiance and transmission spectra, the volumes of combustion gases and other gases, are compared to calculated spectra. The latter are functions of the profiles of concentration, pressure and temperature. In a least square fit, the profiles are varied iteratively until the calculated spectra match as well as possible with the measured spectra. This is done based on iteration algorithms that improve the match of measurement and calculation step by step.

The calculation of a transmission spectrum and a radiance spectrum for the line of sight of the spectrometer is divided into three steps: 1. First, profiles of concentration, pressure and temperature are discretized along the line of sight. In most cases, this Is done in a temperature-equidistant manner, i.e. a sample is taken every time the temperature changes by a defined amount (T) (typical values are 10, ..., 20 K).

2. Thereafter, spectra of the absorption coefficients are determined for the pressure and temperature values thus obtained. This is achieved by using so-called tine-to-line programs and molecule data bases which, for each spectral line of a species (CO. C02, NO etc.), contain the data necessary for the corn putation.

3. Transmission and radiance spectra are determined by solving an integral equation (Schwarzschild's equation) based on the absorption coefficients.

Here, the second step (2.) is the most intricate. The spectra of the absorption coefficients depend on the pressure, the temperature and the species. 1*

Therefore, each spectral line of every species has to be calculated individually for each combination of pressure and temperature obtained in the first step.

Thus, several thousands spectra lines have to be determined for each transmission or radiance spectrum.

The computational effort is even increased further by quickly converging least square fit algorithms requiring in each iteration step the derivatives of the calculated spectra with respect to the parameters to be determined, i.e. the sampling values obtained in the first step. Even if one assumes the application of the most simple (and most inaccurate) method for approximating the derivatives, a further spectrum must be calculated for each parameter.

Depending on the speed of convergence of the least square fit algorithm and the number of the lines of sight used, it may happen that a high number, often more than 100 radiance and transmission spectra and thus several 100,000 spectral lines, has to be computed. Therefore, determining profiles of concentration, pressure and temperature from measured spectra requires a vast amount of computing time -often several ten hours.

It is therefore considered a drawback that, due to the long computing times, an application of spectrometric methods as technical measuring methods is impossible, their use rather being limited to purely scientific applications. Yet, even in scientific studies the long computing times are a great disadvantage, since they increase the expenditure of time. In the domain of development, where, for example, the effects of process modifications are to be determined by measurements, the long computing times are opposed to a reasonable use of these measuring methods.

For a reduction of computing times, it is possible to limit the evaluation to only one gas species and to perform the calculations only for this, for example. The drawback of this method is that the measured spectrum represents the sum of the spectral contributions of all species, which also overlap, which is why the evaluation starts from simplified conditions, resulting in erroneous measurement results.

It is also possible to limit the number of spectral lines of each species used in the evaluation, for example to a few spectral lines. This also saves computation time, however, the result is less exact as when wide spectral ranges with a much larger content of information are used.

DE 198 21 936 Al describes a method for the quantitative analysis of gas volumes, wherein emission or absorption spectrometers are used to determine geometrically defined and reproducibly adjustable observation planes. In a first series of measurements, a number m of spectral measurements are taken, the optical axis of a spectrometer being shifted in parallel by a first distance from one measurement to the next, respectively. In a second series of measurements, n measurements are taken, the optical axis of a spectrometer being shifted in parallel by a second distance from one measurement to the next, respectively. The (m + n) measurements form two orthogonal sets of sight lines forming a grid of (m+n) intersection volumes.

Using the (m+n) measurements, each measurement yields the spectral transmission 1(v) or the spectral radiance (1(v), respectively, which is integrated over the entire gas volume in the bundle of rays of the field of view of the spectrometer.

US 5 308 982 A describes a method for determining the concentration of an analyte in a sample, wherein a spectrum of a selected analyte is generated, a spectrum of an unknown sample is generated, first and second derivatives of the sample spectrum are calculated, a matrix model is derived that includes the analyte spectrum and the derivatives, and the matrix model is applied to the sample spectrum such that a parameter Is obtained that represents the concentration of the selected analyte in the unknown sample. I)

It is thus an object of the invention to provide a method with which, from measured broad-band spectra of high spectral resolution, a simultaneous determination of gas parameters of a number of a plurality of species of a gas volume can be performed with high accuracy and at a high evaluation speed, while at the same time including a high number of spectral elements (spectral lines).

In the method according to the preamble of claim 1, this object is achieved with the features mentioned in the characterizing part thereof. Advantageous embodiments form the subject matter of the claims directly or indirectly referring to claim 1.

When the method of the present invention is applied, measurement results are available very shortly after a measurement. Therefore, the present method is useful in technical and industrial applications for process monitoring and control, as well as for development tasks.

In the accompanying drawings, the figures show: Fig. 1 a partial rectangle In the pressure/temperature (pT) plane, the absorption coefficient and its derivatives in the corners determine the polynomial coefficients; Fig. 2 test points, at which relative deviations between exact and interpolated absorption coefficients are calculated; and Fig. 3 a division of the rectangle according to the algorithm for automatically obtaining a certain Interpolation accuracy.

For a faster evaluation of measured spectra and for the determination of profiles of concentration, pressure and temperature, the present invention provides for a simplification, and thus a quickening, of the computation-4* intensive and time-consuming repeated determination of the absorption coefficients in particular. According to the present invention, this is achieved with an interpolation method allowing for a very quick determination of absorption coefficients. Here, the absorption coefficient of a certain species is a function of the pressure p, the temperature T, and the wave number a.

Instead of calculating the absorption coefficient separately for each value of the three parameters, an interpolation method for the variables pressure and temperature is provided, an interpolating function c&(p,T) for the pressure and the temperature being determined for each wave number a.

In the present invention, a two-dimensional cubic spline function is used preferably. For the purposes of a geometric illustration, the function c&(p,T) will be represented in a Cartesian coordinate system. In the plane (pT), the spline function shall be valid in the range from Pstart to Pend and T5to Id, which range will be referred to as a domain. This rectangular domain is divided into smaller partial rectangles that do not overlap, but cover the entire domain.

For each of these partial rectangles, = (ao(or) + a1(o)T+ a2(cr)T2 +a3(u)T3) + (b0(cr) +bj(o)T+b2(o)T2+b3(o)T3)p+ (1) (co(o) + c1(o) T + c2(c)T2 1-c(u) T3)p2 + (d0(o) + d1(ti)T + d2(cr)T2 d3(cr) T)p3 is used as the interpolating function, where a1, b1, c1 and d1 are polynomial coefficients that depend on the wave number a. In the following, the dependence of the interpolation function on the wave number will be omitted for the simplification of the notation. ft I

For a determination of the polynomial coefficients, according to eq. (1), 16 polynomial coefficients have to be determined for each rectangle which requires 16 conditions (equations). These conditions result from the requirement of continuity and continuous differentiability of the spline function at the corners of the rectangles (see eq. 2). The values occurring in eq. (2) are illustrated in Fig. 1. =

8a1 Oa (p,T1) = 07) (P (2)

___ -

aT "i' âC(PT) = T' (i=0...3).

Eq. (2) represents a system of linear equations. In a vector/matrix notation, an almost completely occupied coefficient matrix is obtained. The condition of the system of equations is poor, because the columns of the matrix vary considerably in size. The computational effort can be reduced and the condition can be considerably improved by carrying out the following transformation (scaling).

p-pb T-T0 (3) =1_7)0; Tt=TT This requires a scaling of the derivatives: &I8p = Oo TaO (4) (T1-82a 82a ___ = (p -po)(T1 -f0) Thereby, the 16x16 system is simplified to four simple equations that merely have to be evaluated, and six independent 2x2 systems of the same coefficient matrix. The equations are mentioned below, with the following abbreviations being used: ôo 8 Oa 80 (5) = a(pt.i, T4): -= -(pt,, Ti.,); -= 7,), etc. ôa a1 = (6) b0 = b1 = 8p8T00 001 -000 - 1 1 = ôa 8o (7) 8T00 apt01 8Pt00 8PtâTI($) [a b21_ [23 63j (8) 82a 82o oa8Pttoo ft 8a O2cir [1 i] OT 8T OPt8TtLO1 23jd1 = (9) 82cI 82o 8p18T &tI 1 a10 --(10) [1 i} c0] 23 d0 = aaj OaI. Oat)

2 (_Q0O + aio -a11 - 01 -0a - 00_ 0l + T 82a1 [1 i C3] (11) 2 3j b3j = (8a 8a 8a)-2. + 00 8Pt 01 10 8Pt i 8201 82I 8Pt8T1 1 + Opt OTL 10 8P 8T I Oa 3 1 a0 -a10 ----8p 8Pt0 Oar Oar -2 + -2 cu1 10 &2ar _ +8 87. +28 87.

1 1 C2 -(12) 23 d2 -Oar Oar Oar 3I8Pt8*PQlO1)tjo 0Ps11 -82a _____ +2 -ooi00 ai01 -2 82a -82 aa'r 11 Thus, the absorption coefficient a(p.T) for a wave number is calculated by 1. determining the rectangle win which the point (p,T) is located, 2. carrying out the transformation (p,T) - (pr, T1) according to eq. (2), and 3. evaluating eq. (1) using the polynomial coefficients calculated before with the eqs. (6) to (12).

En order to have to perform the search for a rectangle and the transformation only once, it is preferably provided upon defining the partial rectangles that the same division of the domain is valid for all wave numbers.

According to the invention, a data base (a memory) is provided in which the pressure and temperature values at the corners, as well as the respective polynomial coefficients (for each wave number) are stored for each partial rectangle. Neglecting the values of pressure and temperature, given N wave numbers and 16 polynomial coefficients, this results in 16 N values to be stored per partial rectangle. For a spectrum of 50,000 values (spectral range: 1,000 cm1, resolution: 0.02 cm', typical for p 1,000 hPa), for example, 800,000 values have to be stored.

Since -as explained above -the calculation of the polynomial coefficients can be carried out very quickly, the memory requirements is reduced, according to the invention, by storing the absorption coefficients and their derivatives at the corners of the partial rectangles instead of the polynomial coefficients. The memory requirements can thus be reduced to slightly more than a quarter, because one corner belongs to a plurality of partial rectangles. "Slightly more", because the corners of the rectangles at the edge of the domain only belong to one or two partial rectangles.

A further reduction of the amount of data can be achieved, according to the invention, when the data base has to cover a large pressure and/or temperature range. In these instances, the necessary spectral resolution of the absorption coefficients is very high, since the spectral widths of the spectral lines vary strongly, especially with the pressure. If the calculation implies only one spectral resolution, the highest resolution, i.e. the smallest distance between sampling points, has to be used so as to correctly include also the narrowest lines.

However, the invention provides that the absorption coefficients and their derivatives are stored in the data base only with the respective necessary spectral resolution. Prior to their use in the above formulas for a specific rectangle, the distance of the spectral sampling points of the required spectra are approximated implementing a preferably cubic polynomial interpolation.

Here, the resulting sampling point distance is the smallest distance in the specters stored in the rectangle observed.

The above described reduction of data for large pressure and/or temperature ranges initially means an increased computation effort and an increased expenditure of time for the calculation of the absorption coefficients, which is

I

caused by the additional spectral interpolation. However, when calculating transmission and radiance spectra, for which a low spectral resolution (large sampling point distance) suffices, this is easily compensated by the fact that the Schwarzschild equation (an integral equation) has to be solved only for a few wave numbers. When a high spectral resolution is required, the additional effort cannot be obviated.

In another embodiment, the data base is divided into a plurality of sections (corresponding to pressure and/or temperature ranges). For each data base section a specific resolution is used which is fixed for this section. This allows for an optimization with respect to the number of the necessary spectral interpolations and the spectral resolution used.

The quality of the interpolation is determined by the congruence of the interpolating and the exact functions between the corners of the partial rectangles. This interpolation accuracy depends on the number of partial rectangles and their arrangement. In order to keep the effort of defining the partial rectangles low, an automatic method for obtaining a predetermined interpolation accuracy is used.

To this end, first, a definition of the term of interpolation accuracy within a partial rectangle is established. Since the interpolation function is a 31( order polynomial along the pressure or temperature axis, respectively, the largest deviation from the exact value of the absorption coefficient (i.e. the value determined by line-to-line calculation) is near 25%, 50% or 75% of the edge length of the rectangle. Therefore, the test points illustrated in Fig. 2 are defined. Their coordinates are permutations of the following pressure and temperature values: po; p + 0.25 (pi-po); p0+0.5 (pi-po); po+0.75 (pi-po); Pi Io; T0 + 0.25 (T1-To); T0 + 0.5 (T1-T0); T0 + 0.75 (T,-To); T1 wherein the corners of the rectangle are not used, since, in this case, the deviations are equal to zero by definition (Cf. eq. (2)).

For these pairs of temperature and pressure, the relative deviations between the exact absorption coefficient and the absorption coefficient calculated by interpolation are determined for each wave number. The maximum of these relative deviations is defined as the interpolation accuracy.

The basis of the automatic method for defining the partial rectangles is the requIrement that the interpolation accuracy has to be higher than a predetermined threshold f1: __________ (13) maxi i<f ((a) / wherein the index I covers all spectra at all test points.

This requirement is met with a recursive algorithm having the following sequence of steps: 1. The first rectangle covers the entire domain.

2. The maximum deviations are determined for the test points on the edges of the rectangle.

a. If the deviations at the test points on the edges parallel to the temperature axis are smaller than f, and the deviations at the points on the other edges are larger than fm,, the rectangle is divided in half along the pressure axis (cf. Fig. 3; continue at 4.), 4. 1 b. if the deviations at the test points on the edges parallel to the pressure axis are smaller than f1, and the deviations at the points on the other edges are larger than fret, the rectangle is divided in half along the temperature axis (Cf. Fig. 3; continue at 4.), c. if the deviations at test points on an edge parallel to the temperature axis and an edge parallel to the pressure axis are larger than f1, the rectangle is divided into four partial rectangles of equal size (cf. Fig. 3; continue at 4.), d. otherwise (i.e. the relative deviations at all test points on the edges are smaller than f,), step 3 is executed.

3. The maximum deviations are determined for the test points inside the rectangle.

a. If one of these deviations is larger than frei, the rectangle is divided into four partial rectangles of the same size (as in 2c; continue at 4.), b. otherwise, the rectangle is not further divided.

4. If the rectangle has been divided, the accuracy check (items 2 and possibly 3, above) are carried out for the newly generated rectangles.

This method is performed recursively until all rectangles meet the required accuracy.

In practical use, this method has two advantages: Step 2 allows to subdivide the domain in partial rectangles as large in size as possible. Thereby, the search for a rectangle is quickened, if the data base is used for interpolation. 4-1

The intricate calculation of the exact absorption coefficients of the spectra that are required in step 3 has to be carried out only, if step 3 is actually carried out.

Instead of the Interpolation function in eq. (1), polynomials of lower order may also be used. Thus, fewer polynomial coefficients are available, i.e. the conditions in eq. (2) have to be reduced to this number of coefficients as well; this results in a faster calculation of the polynomial values. With a smaller number of polynomial coefficients, the conditions of eq. (2) also have to be reduced. Here, for example, the requirement for equality of the mixed derivatives can be dropped. (these are difficult to calculate numerically). Then, 12 conditions are still available for 12 polynomial coefficients. The pressure dependence in eq. (1) wIll then be represented by a polynomial of the 2 order (i.e. d1 = 0).

The polynomial orders may be further reduced, if the requirement that one or all first derivatives be equal is abandoned. The maximum simplification is achieved at four (4) polynomial coefficients (linear interpolation in pressure and temperature). Thus, only the equality of the function values at the corners of the partial rectangles can be required.

The advantage of these simplifications Is that fewer or no derivatives are required in calculating the polynomial coefficients. However, this advantage is obtained at the cost of a lower interpolation accuracy (if the position of the partial rectangles is maintained) or a higher number of partial rectangles and thus a larger amount of data necessary to store the spline function. Therefore, this simplification is recommendable only fort small domains.

According to the invention, the method can be implemented In two ways to improve the accuracy of the measured values to be detected. 4. 1

1. For example, upon the evaluation of the measurements (forward calculation and retrieval), gas species are included in the determination of the absorption coefficients, which have contributed to the measured spectrum, yet whose parameters are not of immediate interest. The contribution of carbon monoxide Co may be included, for example, even if the interest is directed only towards carbon dioxide CO2. Due to the present method, the additional computing time is considerably shorter than with conventional methods.

2. Broad spectral ranges and many spectral lines of the gases to be examined are included, without the computing time increasing thereby in the typical manner previously known. This also enhances the accuracy of the measured values, since the additional lines include information about the parameters searched for and the least squares fit averages (compensates) measurement inaccuracies.

Claims

Claims 1. A method for determining profiles of the concentration, the

pressure and the temperature of gases in ernü1 combustion processes and their exhaust s gas flows and plumes, characterized in that in a least squares fit calculation, the absorption coefficients a necessary for the calculation of model spectra are considered as a function of pressure p and temperature T for each wave number, I0 these functions are approximated by means of interpolating, two-dimensional, cubic spline functions a(p,T), each function a(p,T) therefore being represented in a Cartesian coordinate system, and is in a p,T plane, a desired pressure and temperature range, referred to as a domain, is divided into rectangular partial ranges, the rectangular partial ranges being axially parallel, covering the entire domain without overlapping each other, and for each partial rectangle a two-dimensional cubic polynomial is true as an interpolating function, i.e. according to eq. 1: c1(p,T,o) = (ao(a) a1(o-)T + a2(o)T2 +a3(cr)T3) + (bo(cr)+bi(a)T +b(c)T2 b3(c)T3)p+ (co(a)+ci(a)T+c2(a)T2+cr)T3)p2+ (do(u)+d1(cr)T+d2(cr)T2 +d3(u)T3)p3 where a,, b,, c, and d, are polynomial coefficients and a is the wave number, and the first derivatives thereof with respect to pressure or temperature, the mixed derivatives with respect to pressure and temperature and also the function a are continuous at the corners, namely 0UL(P,,T,) = Qu,t 0 (pj,T,) = -(p,,7), op op (p,T,) = ___ = ,(p17) (i=0...3).

2. The method of claim 1, characterized in that polynomials of a lower order are used in eq. (1) instead of the cubic polynomials.

3. The method of claim 1 or 2, charactenzed in that the partial rectangles are defined automatically using a recursive algorithm until a predetermined interpolation accuracy Is approximately obtained.

4. The method of one of claims 1 to 3, characterized in that instead of the polynomial coefficients of the spline functions the spectra and their first and mixed derivatives with respect to pressure and temperature are stored and the polynomial coefficients are calculated therefrom.

5. The method of one of claims 1 to 3, characterized in that, for a large domain, the wave number resolution is optimized by dividing the domain into a plurality of partial domains and by generating and storing the data of the interpolating spline functions for the respective partial domains with an adjusted wave number resolution.

6. The method of claim 5, characterized in that, if absorption coefficients from different partial domains are used in the least squares fit, the different wave number resolutions are approximated to the best occurring wave number resolution by one-dimensional, preferably cubic polynomial interpolation.

7. The method of claim 1, characterized in that the evaluation also includes gas species whose spectral lines interfere with the signatures of the species to be determined, but whose concentrations are not relevant.

8. The method of claims 1 and 2, characterized in that the evaluation includes wide spectral ranges of the measurement with as many spectral elements as possible regarding the species of interest.