DE3343043A1 - Method for the contactless, emittance-independent radiometry of the temperature of an object - Google Patents

Abstract

A method for the contactless, emittance-independent radiometry of the temperature of objects is provided, in which method the respective object assumes two, three or more different temperatures (or is brought to two or more temperatures or comes to the latter itself), and radiation measurements of the radiation emanating from the object are carried out in each case in four or more spectral regions in the infrared and/or visible wavelength region, and these measured values are used to determine exactly, or even in the compensating fashion, the respective object temperatures as well as, likewise, all the remaining unknown variables (spectral emittance of the object, environmental temperature, etc).

Description

Method for contactless, emission-independent

dependent radiation measurement of the temperature of an object The invention relates to a method for non-contact, emission-independent radiation measurement the temperature of an object according to the preamble of claim 1. Here can the radiation measurement of the temperature of natural or artificial objects in the infrared and / or visible spectral range. The great importance of a non-contact, emission level-independent radiation measurement of the temperature of Objects for research and especially for industry is well known.

There is already a method and a device for contactless Proposed radiation measurement of the temperature of a natural or artificial object been.

With this method, the object temperature, the emissivity of the object and the ambient temperature (from the ambient radiation reflected on the object) are determined exclusively by calculation from a series of two (three) or more radiation measurements in limited (specially selected) spectral ranges (P 33 21 874.9). The disadvantage of this method becomes apparent when measurements are carried out, for example, in n spectral ranges, since then n independent equations are available in the following form: where the measured beam density at wavelength Aii is, the a is the beam density calculated according to Planck of an Obj i blackbody of temperature Tobj at wavelength xi, ii is the emissivity of the object at wavelength x, is the radiation density of a black body of temperature TUm g at wavelength Zi, calculated according to Planck, (1- i is the reflectance of the object at wavelength X i, Tobj is the true object temperature and the true ambient temperature.

Amb is the true ambient temperature.

But that means there is a homogeneous assumption Ambient temperature and a homogeneous object temperature n + 2 unknown quantities, namely n unknown spectral emissivity values £. and the unknown temperatures Tobj and T Since there are n + 2 unknowns in n equations, that is System not solvable like this. The disadvantage of such advanced temperature measurement methods it can therefore be seen in the fact that simplifying assumptions must then be made, which in turn lead to the determined temperatures (object and ambient temperature) and emission.

degree values are not exact, and moreover that in general Measurement errors also affect the result or results.

It is therefore the object of the invention to provide a method for contactless emissivity-independent radiation measurement of the temperature of an object in this way to improve that not only without simplifying assumptions the object temperature, spectral emissivity values and the ambient temperature (or ambient temperatures in a thermally inhomogeneous environment) can be determined exactly, but that, in addition, different measurement errors are compensated for. According to the invention, this object is in a method according to the preamble of Claim 1 solved by the features in the characterizing part of claim 1.

Advantageous further developments of the invention are in the subclaims specified.

The method according to the invention is based on the following equations: for i = 3, ..., n where L1M, #i is the measured beam density at the wavelength #i (center wavelength) and the object temperature T1; L2M, #i is the measured ray density at wavelength #i and object temperature T2; ri is the spectral sensitivity of the meter at wavelength 2 i; T. is the transmission of the atmosphere at wavelength Xi; which is the object temperature T1 and T20bj is the object temperature T2.

The following applies here explicitly: where c1 = 3.7418 [W cm2 pm4l; c2 = 1.4388 Em KJ; # = 3.141843 LT1 is the beam density according to Planck for a black body object per temperature T1Obj, the wavelength Epm] and T1Obj is the object temperature T1 [K].

Equation (4) also applies to T2j. Equations (2) and, (3) fully describe the radiance that natural Objects is measured, namely the sum of emitted radiation caused by the Temperature and the spectral emissivity of the object is conditioned, and from reflected Ambient radiation (which is caused by the ambient temperature and the degree of reflection 9 i = of the object is conditional.) Has an object of interest the temperature T10bj and are, for example, only the wavelengths (center wavelengths) i of the one used Known spectral measuring device (and the width of all spectral ranges is identical), then equation (2) contains the unknown factors for n spectral ranges: T10bj, TUmg, ri. . and 6 .. So there are 2n + 2 unknown 1 1 th factors; was doing it provided that the factors r. (the spectral sensitivity of the meter) and I (the transmittance of the atmosphere) only as the product as which they appear, should be determined, and the knowledge of the individual factors is not of interest here.

In Eq. (2) there are only n measured values opposite the 2n + 2 unknowns; an (exact) solution of the system is therefore not possible. Now the object changes its Temperature to the value TZobj, then equation (3) also applies; with that comes on the one hand Another unknown is added, namely T20bj, and on the other hand there are n more Measured values added. Thus there are 2n measured values opposite 2n + 3 unknowns, so that too this system cannot be solved exactly. Now the object changes its temperature the value T30bj, there are 2n + 4 unknowns compared to 3n measured values; i.e. for n = 4 spectral ranges (in which measurements are taken) is the system with 12 measured values and 12 unknowns already exactly solvable (where the expression is exactly under the assumption it is to be understood that the measurements are error-free). Used in n = 5 spectral ranges measured, the equation system with 15 measurements and 14 unknowns is already overdetermined; the solution is therefore iterative (by means of a compensation calculation), the overdetermination compensating for measurement inaccuracies.

The difference between the number of measured values and the number of unknowns 3n - (2n + 4) = n - 4 indicates how large the number of measured values is that are additionally the number of measured values necessary for the solution to compensate for the measurement inaccuracies contributes.

The above statements of course only apply if at the points in time of the measurements ri, #i and TUmg are constant, which is the case with the measurement setup and unchanged environment and if the times between measurements are not long, is ensured, and if, furthermore, 6 for T1Obj, T20bj and T3Obj are each the same Has value, a requirement that is common to most materials in wide temperature ranges and objects is fulfilled. Only in the range of high temperatures (embers) and at the change in aggregate states leads to a clear temperature dependency the emissivity.

The spectral beam density is therefore used to carry out the method of the object at three different object temperatures, e.g. in n = 4 spectral ranges each recorded, and from these 12 measured values the 12 unknown quantities become exact certainly. If n> 4, there are n - 4 measured values obtained by balancing Measurement inaccuracies contribute to the accuracy of the results.

Of course, it is possible to use the spectrometer used in a known manner Type to be calibrated, i.e. its spectral sensitivity values r. (with the help of calibration blasters, i.e. black bodies) and also to select its spectral ranges in such a way that that they t in areas of high atmospheric transmittance. lie so that t. = 1 can be set 1 1 can. (Such areas can be set in a known manner by measurement or model calculation - for example with the help of the "LOWTRAN" - and "HITRAN" models - determine for each measuring distance.) It is the number of unknown quantities reduced to n + 2, so that measurements at two (2) temperatures ratures of the object, which lead to 2n measured values, for n = 2 already 4 unknowns and 4 Measured values are available and thus a solution is possible, and for n> 2 n - 2 measured values cause a compensation.

Of course, other unknown quantities can also be introduced, e.g. different ambient temperatures etc. in a thermally inhomogeneous environment, which with a correspondingly large number n of the spectral ranges and a corresponding Number of different object temperatures determined exactly or even in a compensatory manner can be.

It is also possible to use all the knowledge gained once in the following To use measurement steps; for example, the temperature range is found in which the emissivity is independent of temperature, the once determined spectral Emissivity £ i can be used as known in the following measurements. That That means, as long as the object temperature is in the certain range, every spectral measurement can with only one temperature of the object already compensating for the determination of the object temperature and the ambient temperature are used; this also applies accordingly to the spectral sensitivity ri of the spectrometer and the transmittance Z i der Atmosphere (both of which are of course independent of temperature). Are for example these quantities (t Z i.ri) with n = 4 and determined from 3n = 12 measured values are sufficient in the further steps n = 4 measured values for the compensatory determination of the two unknowns Tobj and T. It is therefore possible for a large number of applications to use the test object only once or only at longer intervals for control purposes at several temperatures, to measure what can also be achieved through artificial heating and what is gained from it Use variables, for example, for monitoring over longer periods of time.

With the method according to the invention it is not only possible to determine the temperature of an object exactly, but can also its spectral emissivity and the temperature of the environment (or the temperatures thermally inhomogeneous environment). A very special benefit is that also from the radiation measurement of the object - without a separate one Calibration - also the influence of the spectral sensitivity of the measuring device and the Atmosphere is determined. So the method is "self-calibrating" and drifting the spectral sensitivity of the measuring device does not falsify the measurement results; so that a calibration and re-calibration of the measuring device is not required, which is a is an invaluable advantage for routinely used measuring instruments.

Another particular advantage of the invention, above described method is that with a correspondingly high number the spectral ranges and / or the object temperatures compensating for the measurement results determined, i.e. measurement inaccuracies are compensated.

The invention will now be described with reference to the attached Drawings explained in more detail. 1 and 2 show graphical representations the transmittance of the atmosphere as a function of the wavelength for path lengths of 1 m or 3 m, those with the "Lowtran 5" model using the "Sommer in medium width "-1 with a spectral resolution of 5cm at a height of 0.5km are calculated with a visibility of 23km; 3 shows a schematic representation an apparatus for carrying out the method according to the invention, and FIG schematically a detailed representation of both for example one Radiation measurement, where the most important radiation parts are indicated.

About the transmittance of the atmosphere in Fig.1 and 2 is for one Wavelength range from 1pm to 15m shown. The method according to the invention is of course not restricted to this wavelength range, but rather from the ultra-violet spectral range continuously to the very long-wave infrared range, thus applicable up to the range of the illi! n; eter waves. The one in Figures 1 and 2 The range shown, including the non-visible spectral range, is however particularly good for carrying out the procedure with the commonly occurring, natural and man-made temperatures of the environment including industrial Processes suitable. Of course, for path lengths from Im to 3m in the visible spectral range the transmittance of the atmosphere is equal to one (# i = 1).

To carry out the method according to the invention, inter alia Energy reasons (radiation energy) Spectral ranges selected in which the transmittance the atmosphere is close to one (t i = 1); but as can be seen from Figures 1 and 2, the entire area shown there is certainly suitable. For longer distances the transmittance of the atmosphere in certain areas (e.g. from 2.6µm to 2.8m or approximately from 5.5m to 7.3µm, etc.) equal to zero (# i = °); one Haeech then no longer makes sense to measure in such areas; the procedure but leads to a result even with such measured values, if in addition to these There are enough other measured values in which radiation from the object to the Meter arrives as long as the number of unknowns is equal to or less than is the number of measured values (which still contain radiation energy).

In the embodiment shown in Figure 3 is of a Object 0 radiation emanating from a telescope T of an interferometer spectrometer IFS (of an interferome ters after Michelson) collected and -over steered a collimator lens KL into the interferometer. In the IFS interferometer is in a known manner by means of a beam splitter ST, a fixed mirror S1 and a movable mirror S2 and a field lens FL including a Detector DO generates an interferogram of the incident radiation.

The interferogram is in the form of an electrical signal in a electrical amplifier V amplified and digitized by an analog-to-digital converter, with the help of a converter clock, which in a known manner with the help of another fixed mirror RS1, another beam splitter RST of a reference interferometer, another detector DL of the reference interferometer and an output amplifier RV from those used in the reference interferometer to measure the position of the mirror S2 Laser light of a laser L (for example a HeNe laser) is obtained.

The digitized measured values (interferogram values) are either directly in a microcomputer through a mathematical Fourier transformation converted into the spectrum of the incident radiation and then converted into stored in a digital memory assigned to the microcomputer, or only on stored in this memory and later transformed. Similar measurements are made after changing the object temperature or the ambient temperature, or similar Calculation of all corresponding spectra, which depend on the spectral Resolving power of the interferometer a number from a few tens to several contain ten thousand or more spectral measured values, all spectral values become and / or from a larger or smaller number of selected values and / or off different groups of selected values the equation system according to the invention formed and loosened or loosened in a compensatory manner. All determined values or individual, such as only the object temperatures, can then with the help of a display device are displayed.

The microcomputer has a command input unit via which all commands pertaining to the procedure can be called up flexibly in a known manner, linked, started, etc.

(e.g. data acquisition from the interferometer spectrometer, Fourier transformation, setting up and solving the system of equations, etc.).

In a modification of the embodiment described, it is also possible use other spectroradiometers (e.g. filter radiometers). Basically any number of spectral ranges can be used under the condition that the system of equations is solvable. The storage, processing and output the measured values and the results can be carried out on various media and computers will. Since, in general, the smallest possible number of measured values is required is a microcomputer for data acquisition and calculation of the results sufficient so that the device for performing the method according to the invention even when using simple, advanced (previously quite complex) interferometer spectrometers Can be designed as a portable device that has wide and economical application possibilities opened.

FIG. 4 shows schematically in a detailed representation, by way of example, a radiation measurement, the most important radiation parts occurring being reproduced. In Fig. 4: the wave number rcm 1 (inverse wavelength), with respect to the environment of the object: L u is the ray density of the environment as a function of 9 'and: Tu the ambient temperature of the emissivity (s) of the environment (which are themselves a function of V) with regard to the object: LK is the radiance of the object, as a function of and: TK is the object temperature, the degree of emission, and also the degree of reflection and the degree of transmission of the object, each of which are functions of V; with respect to the atmosphere: the transmittance At sAt the emissivity P At the reflectance of the atmosphere, which are functions of LAtEM is the density of the radiation emitted by the atmosphere, the function of atmospheric temperature, of U and of S At; LAtSu is the radiation density of the radiation scattered in the atmosphere from objects in the environment (the atmosphere) with respect to the surroundings of the atmosphere (different from that of the object): Eluate is the radiation density of the surroundings of the atmosphere, the function of P and: TuAt the temperature the environment of the atmosphere and EuAt the emissivity of the (objects) in the environment of the atmosphere with respect to the measuring device: LSE the beam density of the measuring device (radiation receiver), which is a function of V and: TE the temperature of the measuring device the emissivity of the inner surfaces of the measuring device ; also: the emissivity the transmittance of the inner components of the measuring device R (Z) the spectral sensitivity of the measuring device as a function of the wave number Z, the sensitivity corresponding to the ri in the previous equations (there as a function of the wavelength t) and UE (C ') that from the received radiation from Detector generated electrical signal from the meter, which is a function of M.

In Fig.4 the parts "object, environment, atmosphere, measuring device" differentiated, and it is indicated which radiation components occur where, or how they are changed; for this purpose, there are small coordinate systems at four locations drawn along the path of the radiation, which contain qualitative spectra that contain indicate how the spectral characteristics of the object radiation from the location of the object (where Planck's law is characteristic, for s K (M) = const.) by the Influences of the environment, atmosphere and measuring device is continuously changed.

The object is determined by its temperature and its spectral emission, Degree of reflection and transmission described; describe the corresponding sizes also the environment, whereby the object and the environment are here for the sake of simplicity of the quantities describing them are viewed as spatially homogeneous (whereby the Transmittance of the object is set to zero). So EK + gK = 1, i.e., if ZK 4 O, it is assumed that the ambient radiation is the object according to #K penetrates from all sides, also from the rear. the Radiation emanating from the object is therefore the sum of the object radiation and the reflected radiation Ambient radiation. On the way through the atmosphere, both parts pass through changes the spectral transmittance of the atmosphere (multiplicatively) and (additively) extended by the radiation emitted by the atmosphere itself and by the Atmosphere scattered ambient radiation (with this environment at least for long Paths through the atmosphere are different from the surroundings of Object). Overlay on the way through the measuring device (from the optics to the detector) (additively) further radiation components of the received radiation, namely the Radiation emitted from the internal components and surfaces of the meter. In addition, the radiation is (multiplicatively) from components such as filters, Lenses, mirror surfaces, etc. of the measuring device, as well as the spectral sensitivity of the detector (if this is not constant in the measuring range). These multiplicative Influences are in the factor R (/) (or ri), the spectral sensitivity of the measuring device summarized, while all radiation components that originate from the measuring device to (natural radiation) Radiance LSE can be summarized.

All the quantities described here are initially unknown; let them but all determine themselves by in accordance with the method according to the invention in sufficiently large number of wavelength ranges and with a sufficient number of different ones Temperatures of the object or the environment, etc. carries out radiation measurements, so that a certain or overdetermined system of equations is obtained. Is one however, as in the present case, mainly in determining the temperature interested in the object, it is of course expedient by appropriate interpretation of the measuring device and the measuring arrangement as many variables as possible (in which one is not interested is) to be made negligible.

For example, the measuring device is used as an interferometer spectrometer only designed with reflective optics and stabilizes the temperature of the entire device, as a good approximation, the combination of the device's own radiation into one applies Beam density LSE given by the temperature T E of the device. The emissivity 6 of the inner surfaces of the E device become the same through extensive use Materials kept uniform. If the measuring task allows it, a detector is used used with a wavelength-independent sensitivity. Become useful the wavelength gen areas of measurement selected so that in them the transmission of the atmosphere can be set to 2-At = 1.

In addition, the (additive) proportion of the radiation components is the Atmosphere LAtSu and LAtEM can be neglected by the path between measuring device and Object is held briefly.

If necessary, appropriate shields (e.g.

through a tube on the measuring device that reaches close to the object) a homogeneous Ambient radiation reached, so that only an ambient temperature is used must become.

When measuring in n wavelength ranges and at m different object temperatures are then unknown: m x TOb the object temperature n x £ i the spectral emissivity of the object 1 x TUmg the ambient temperature 1 x TM the temperature of the measuring device (inside) 1 x r. = const the spectral sensitivity of the measuring device, i.e. n + m + 3unknown Variables are opposed to measured values.

For m = 2 object temperatures and n = 5 wavelength ranges, a self-calibrating measurement is already possible.

Of course, there is generally an increase in the number m of object temperatures more effective than using more wavelength ranges. Provided, that ri + const, i.e. depends on the wavelength, one has n unknown values of ri, So there are 2n + m + 2 unknowns compared to n-m measured values and with m = 3 and n = 5 the system of equations is determined.

For these examples is the emissivity of the interior surfaces of the measuring device has been assumed to be es = const = 1.

The following equations then apply: The different radiation components (in the above explanations) naturally have different meanings in the different wavelength ranges; For example, the natural radiation of the device in the visible can usually be neglected; (The same applies to the emissivity, etc.). The explanations have general validity, but are especially tailored to the infrared radiation range, which is probably the most important for technical implementation.

The method according to the invention also has a further application feasible, which is, however, generally of secondary importance in practice has: Are measurements available at m object temperatures in n spectral ranges each and Apart from these measured values, no other information is available, in particular also not about the n wavelengths (spectral ranges) at which the measurements were carried out (besides the fact that their location should be roughly known, for example in the visible or in the range 3 to 5 pm or in the range 8 to 14 pm), so can all unknown quantities, especially the spectral ranges (wavelengths) of the Measurements can be calculated or calculated to compensate.

Are for example: n spectral ranges of the measurements n values of the spectral emissivity of the object n values r .. ri (product of spectral sensitivity 1 1 of the measuring device and the spectral transmission of the Atmosphere) m object temperatures an ambient temperature and a temperature of the If the measuring device is unknown, there are 3n + m + 2 unknowns opposite again n.m measured values before. Then, for example, for n = 6 and m = 4, the system of equations can be solved; for n = 6 and m = 5 it is already overdetermined (by 5 measured values).

End of description

Claims (14)

Claims (1 9 experienced for contactless, emission level-independent Radiation measurement of the temperature of an object, with which method in n wavelength ranges (Spectral bands) in the visible and / or infrared and at m temperatures of the object one after the other beam densities or strengths are detected, thereby g e k e n n z e i c h n e t that from a series of at least n = 4 beam dense or -strengths from the measurements of at least m = 3 different temperatures of the object (0) an equation system of n.m = 12 unknowns and n.m = 12 measured values is formed will; by the Cl ei chungssysstem the measured values with the help of Planck's law of radiation in each case as the sum of the radiance (intensity) of a radiator with the temperature and the spectral emissivity (E i) of the object and the radiance (intensity) of a radiator (from environmental influences) with the temperature of the environment, which on Object with a spectral reflectance of the object (3 = 1 - (one minus spectral Emissivity) is reflected, shown at the respective n measurement wavelengths (# i) where the sum is still with a product (i from the spectral sensitivity ¢ ri) of the test object and the transmittance (b i) of the atmosphere is multiplied, which product is also for the respective n measurement wavelengths (X i with i = 4, .. ..., n;) can be determined, and when solving the system of equations found m object temperatures' determined as the true m object temperatures will. 2. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that the spectral emissivity found when solving the system of equations of the object (n values of the spectral emissivity at the n wavelengths of a Measuring device tes) as the true spectral emissivity of the object (O) is determined. 3. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that the ambient temperature (ambient temperatures - in a thermally inhomogeneous environment) than the true ambient temperature (ambient temperatures in a thermally inhomogeneous environment) is (are) determined. 4. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that the temperature of the measuring device found when solving the system of equations (Temperatures of the inner surface of the measuring device) than the true temperature (Temperatures of the inner surfaces of the measuring device are determined. 5. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that the product found in the solution (ri Wi) from the spectral sensitivity (ri) of the measuring device and the spectral transmittance (t.) of the atmosphere (n values at the n wavelengths of the measuring device) as the true product (ri ti) of the spectral Sensitivity (ri) of the measuring device and the spectral transmittance (r i) of the Atmosphere is determined. 6. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that all quantities determined from the system of equations, namely m object temperatures, the ambient temperature (ambient temperatures - thermally inhomogeneous environment), the internal temperature of the measuring device, n values of the spectral emissivity of the object and n values of the product ri.Zi from the spectral sensitivity r. of the measuring device and the spectral transmittance Zi of the atmosphere exclusively through solution of the equation system can be determined arithmetically from the measured values. 7. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that with a correspondingly large selection of n spectral ranges and / or m object temperatures the number n.m of the mutually independent measured values is increasingly greater than the Number of unknown quantities that thus an overdetermined system of equations is formed and this system of equations is solved with the help of the equalization calculation, and that measurement inaccuracies are compensated for, whereby the determined Values of the unknown quantities become more precise. 8. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that other than the previously mentioned, unknown, variables to be determined, for example several ambient temperatures in a thermally inhomogeneous environment caused by the atmosphere emitted radiation, or the spectral transmittance of the object, if this Is radiation permeable, or several object temperatures at the same time or one after the other in the case of thermally inhomogeneous objects or the object and / or the environment Geometry factors, generally all factors that affect the radiation emanating from the object, their way to the measuring device and in the measuring device to the final measured value in any one Way to be introduced into the system of equations, according to the given number of unknowns by appropriate choice of n spectral ranges and m object temperatures a system of a corresponding number of n.m measured values is recorded will, and the system of equations thus created is solved or compensated is solved and thereby all unknowns are determined or compensated determined. 9. The method according to claim 1, characterized in that g e k e n n z e i c hn e t, that the object whose temperature is to be determined is based on its function and texture assumes different temperatures, or by any one Kind of heating force assumes different temperatures. 10. The method according to claim 1, characterized in that g e k e n n -z e i c h n e t that the method is applied in a corresponding manner when the object temperature is unchanged, the ambient temperature by itself or forcibly different Values. 11. The method according to claim 1, characterized in that g e k e n n -z e i c h n e t that the method is applied in a corresponding manner, if any Number of arbitrary unknowns takes a number of k different values and at the same time a number 1 of measured values is obtained, with the condition, that 1> k, and that all unknowns are determined or compensated for will. 12. The method according to claim 1, characterized in that g e k e n n -z e i c h n e t that, for repeated measurements, all quantities determined from previous measurements, which are to be regarded as unchangeable (such as the product ri. fi) as known quantities are included in the system of equations, and that from a reduced number of measured values (for example a measurement with only one (m = 1) object temperature) determines or compensates for the remaining unknown variables to be determined. 13. The method according to claim 1, characterized in that g e k e n n -z e i c h n e t that with a correspondingly large number of m (different temperatures of the Object or the Environment, etc.) and from n spectral ranges (Wavelength ranges) of the measuring device only the measured values themselves need to be known, and that all unknown quantities, including the spectral ranges (wavelength ranges) of the measuring device can be calculated or compensated. 14. The method according to any one of claims 1 to 13, characterized g e k e n n z e i c h n e t that an interferometer spectrometer (IFS) is used to measure radiation is used, the number n of spectral ranges (measured values) being very high can be selected, the spectral measured values all have the same spectral width (in [cm-1], i.e. wave numbers), and hence the calculations in wave numbers fcm1 or wavelengths [µm] (i.e. a correction of different spectral widths the measuring ranges are omitted).