GB2326231A

GB2326231A - Method of Calibrating Spectroradiometers

Info

Publication number: GB2326231A
Application number: GB9809660A
Authority: GB
Inventors: Erwin Lindermeir
Original assignee: Deutsches Zentrum fuer Luft und Raumfahrt eV
Current assignee: Deutsches Zentrum fuer Luft und Raumfahrt eV
Priority date: 1997-05-09
Filing date: 1998-05-06
Publication date: 1998-12-16
Anticipated expiration: 2018-05-06
Also published as: DE19719211B4; GB9809660D0; DE19719211A1; FR2763125B1; FR2763125A1; GB2326231B

Abstract

A spectroradiometer is calibrated by measuring the temperature of a blackbody radiator of unknown temperature. The measured and non-calibrated spectrum of the blackbody radiator is described by a radiometric spectrometer model explicitly containing the effect of the atmosphere, the transmissivity of the atmosphere and the apparatus functions, i.e. the spectral sensitivity and the inherent spectral radiation, being formulated in the form of parameterized functions of the wavenumber or the wavelength. A least squares fit is used to determine the parameters for computing the spectral transmissivity of the atmosphere, the parameters of the apparatus functions and the radiation temperature of the blackbody radiator. The method can be used to calibrate IR Fourier spectrometers.

Description

p -.", 1 Method for Calibrating Spectroradiometers The invention relates

to a method for calibrating spectroradiometers,for example Fourier spectrometers.

2326231 One such method of calibrating spectroradiometers, more particularly Fourier spectrometers (also termed Fourier transform spectrometers) and advantageously as designed for analysis in the infrared spectral range, is known from DE 41 28 912 C2. In this known method the spectroradiometer measures the infrared radiation stemming from at least four blackbody radiators dif f ering in temperature (SI I S21 S41 S41,,). From the at least four spectra, groups of at least three differing spectra in each case are formed, i.e. for instance when employing four blackbody radiators and thus the four spectra S11 S2r S3 and S4, the four groups S3., S21 S3; S11 S21 S4; S11 S31 S4; S2r S3 S4. For each group in this known method use is made of a least squares fit to compute the radiation temperatures of the blackbody radiators and the spectral functions described radiometrically by the spectroradiometer (apparatus functions, calibration functions). This calculation presupposes that the measured (non-calibrated) spectra satisfy the following equation, termed the radiometric spectrometer model:

Sh (;i) = R (;1) - L (Th,;i) +G( i); (h = 1,..., H; i = 1,..., I). (1) In this equation the wave numbers are denoted by The apparatus functions consist of the spectral sensitivity R(j) of the spectroradiometer and the inherent spectral radiation G(;,) of the apparatus. The expression L(Th, j) stands for the temperature radiation of the measured blackbody radiator to be calculated by Planck's radiation formula with the radiation temperature Th. The number of spectra measured is designated H and the number of spectral samping points of each spectrum is denoted I.

1 2 It is to be noted in conjunction with the radiometric spectrometer model as formulated by the above equation (1) that unlike the equation stated in DE 41 28 912 C2 the inherent radiation of the apparatus occurs in units as a function of the apparatus concerned, i.e. the equation in this cited patent is merely multiplied out as a result of which the equations evident in the further course of the present patent application are better readable.

In accordance with the method known from DE 41 28 912 C2 a calibration is deemed to be reliable when the results of the individual groups agree within the scope of measuring accuracy of the spectroradiometer.

In the known calibration method as indicated it is a disadvantage in implementing a least squares fit that at least three blackbody radiators need to be present since for calibration a measurement needs to be made with at least three different temperatures; calibrating with only one reference radiator in which the temperature is changed between measurements is usually not possible in actual practice due to the long time involved, it being known namely that the settling time for plane radiators is usually more than 20 minutes. The radiometric spectrometer model as stated in the equation (1) on which the known calibration method, as mentioned, is based fails to also take into account the effect of the atmosphere which is a disadvantage, since the infrared radiation of the reference radiators is attenuated more particularly by the molecules of water and carbon dioxide in the atmosphere for highly specific wavelengths. In the spec t roradiometer model equation (1) the effect of the atmosphere between reference radiator and detector of the spectroradiometer to be calibrated is contained in the spectral sensitivity of the apparatus where it is thus treated as an apparatus property. In addition to this it is a disadvantage that very many unknown parameters occur which need to be determined by a least squares fit. These parameters are the temperatures as well as for each spectral 3 supporting point a value for the spectral sensitivity together with a value for the inherent spectral radiation. Thus, depending on the spectral resolution a few hundred to a few thousand unknowns materialize. Since a least squares fit is based on a nonlinear and thus iterative calculation the algorithm needs to "seek" the solution in a highly dimensional (vector) space, this necessitating many steps in iteration resulting in a relatively long time for computation. In addition to this it is a disadvantage in the known calibration method as cited that the least squares fit required is highly sensitive to noise. One of the reasons for this is the aforementioned large number of parameters needing to be established. To measure spectra with an adequate signal-tonoise ratio many items of information are needed which results in a long measurement time.

The invention is based on the object of providing a method for calibrating spectroradiometers which in avoiding the cited disadvantages defines the calibration functions R(;i), i.e. the spectral sensitivity of the spectroradiometer, and G(i1-,), the inherent spectral radiation of the apparatus as well as the radiation temperatures Th of as few blackbody radiators as possible.

This object is achieved by a method in the field concerned by the features as set forth in the characterizing clause of claim 1.

The method in accordance with the invention is based on at least one measured spectrum of a blackbody radiator.

A preferred example of the invention will now be detailed. Firstly, the effect of the atmosphere is explicitly introduced into the spectrometer model. In addition, only a single blackbody radiator is first considered. Expressed mathematically this is the equation 4 S(;i) = -r( i/'1) R(.i) L (Th, 1j) +G( li); i = 1,... ' 1. (2) where -r(;i) denotes the spectral transmissivity of the atmosphere.

The method exemplifying the following:

the invention then assumes 1. The transmissivity of the atmosphere is described with sufficient accuracy only by its temperature, the concentration of a few gases as well as the length of the optical path between the reference radiator and the detector of the spectroradiometer to be calibrated. Near to the earth's surface it is sufficient, for example, to consider the gases H20 and C02 for the infrared spectral range (for spacings up to a few metres).

2. The two apparatus functions R(;), i.e. the spectral sensitivity of the spectroradiometer, and G(;), the inherent spectral radiation of the apparatus, can be described by simple parameterized functions, polynomials or splines being used for R('j). The parameters are then the polynomial coefficients. For G(;) use can be made for example of Planck's formula with temperature and emissivity as the parameters without it being basically important which function types are used. Suitable function types can be determined by separate tests.

The transmissivity of the atmosphere and the wanted apparatus functions can thus be stated as functions of parameters grouped together into the vectors x:

R(;,XR) G(,XG) where for the parametric vectors x:

(3) (4) (5) l- = R1.... 1 tN, 1:SR R'l, - - -, rN,1 :1G 191, - - 9N, 1 (6) (7) (8) in which N7, NR and NG stand for the number of parameters with which the transmissivity, the spectral sensitivity and the radiation of the apparatus are described.

Computing the transmissivity of the atmosphere can be determined by known technical means, e.g. with the aid of radiation transport programs such as Fascode (line for line computation, very high spectral resolution) or Modtran (low spectral resolution).

The wanted parameters, namely the temperature T and the vectors xr, ?R and Lec are determined in the known way by a nonlinear least squares fit. Analytically, the sum A of the squared differences between the measured and computed results is (9) it merely needing to be assured that the number of parameters N = NT + NR + NG + 1 is smaller than the number of points in the measured spectrum, i. e. N < 1. Achieving this requirement in actual practice is easy, especially in the case of Fourier spectrometers. For the atmosphere transmission it is sufficient to make use of three parameters: the concentrations c(H20) and C(C02) as well as the atmosphere temperature Tatm which, however, may also be measured. For describing the apparatus radiation two parameters will often suffice, namely the radiation temperature and the emissivity of a Planck's formula.

If three polynomials of the third degree are used for the spectral sensitivity (4 coefficients in each case) then an t 6 additional 12 parameters are obtained, the number of parameters thus being approx N = 3 + 12 + 2 + 1 = 18. Basing assumptions on a measurement over a range of approx. 1000 cm-1 and a spectral radiation of approx. 10 cm-1 the result is 1 = 100 measured points so that the condition N << I is satisfied. The aim of making fewer parameters suffice is thus achieved. According to the calibration method known from the aforementioned patent DE 41 28 912 C2 only 18 parameters need to be defined instead of at least 203 parameters (200 values for the apparatus functions and at least 3 radiation temperatures).

Expedient and advantageous aspects of the method exemplifying the invention are evident from the sub-claims.

The complex calculation taken into consideration as a possibility in the aforementioned patent DE 41 28 912 C2 can also be achieved in the calibration method exemplifying the invention. For the imaginary portions of the functions R and G further parameterized functions are used, as a result of which the number of parameters is roughly doubled. At the same time, however, also complex measured values are used, i.e. the number of measured variables is likewise roughly doubled, so that the condition N < I remains satisfied.

The calibration method described hitherto may also be expanded so that the spectra of several blackbody radiators differing in temperature can be used, and although this makes the time needed in measurement for a calibration longer, on the one hand, however, the least squares fit is improved since each spectrum I furnishes additional measured values, but only one unknown, namely the radiation temperature of the blackbody radiator. The sum of the errors squared to be minimized is then given by the following equation (1o):

7 A (T1,..., TH, XG) (10) h-1 {i-1 that the One advantage established is resulting fluctuations in the parameters established caused by unavoidable measurement noise are less when calibrating by the method exemplifying the invention than when applying the calibration method known from DE 41 28 912 C2, this advantage stemming from the fact that fewer parameters need to be determined.

However, additional spectra can also be made use of in other ways to advantage. When a calibration is carried out for each measured spectrum of a blackbody radiator the computed parameters of the apparatus functions need to be equal within the scope of measurement accuracy; this can also be made use of expediently as the criterion for assessing the quality of a calibration.

Suitable function types are to be found only for the apparatus functions, but not for the transmission function, however. The transmission of the atmosphere can be computed with a very good approximation with the aid of radiation transport models, it being basically so that any function systems can be selected for the apparatus functions. Each function can be represented with sufficient accuracy by a sum of llorthoganol base functions" as long as a sufficient number of base functions is employed, this meaning for polynomials, for instance, that the polynomial degree merely needs to be high enough.

In actual practice, however, using too many base functions results in the algorithm of a least squares fit simulating the noise and thus falsifying the result. This is why in achieving useful results additional information is needed, expediently 8 obtained with the aid of preliminary tests. For this purpose calibrations in accordance with DE 41 28 912 C2 can be implemented in the laboratory, for example, whereby variations in the ambient conditions, especially as regards temperature and apparatus settings will produce differing results which are then made use of to find the empirical function types sufficing with as few parameters as possible but which nevertheless provide a good simulation of the apparatus functions. The difficulty in this respect is the disturbing effect of atmosphere transmissivity since the calibration method in accordance with DE 41 28 912 C2 is unable to distinguish between atmospheric transmissivity and spectral sensitivity which is, however, obviated by the spectroradiometer to be calibrated and the reference radiators being operated in such an atmosphere exhibiting no disturbing absorption in the spectral range (in the infrared spectral range, for example, a nitrogen atmosphere) concerned.

9

Claims

1. A method for calibrating spectroradiometers, f or example Fourier spectrometers, for analysis preferably in the infrared spectral range, characterized in that at least one spectrum S(i,,) of a blackbody radiator of unknown temperature is measured, that the measured -and non-calibrated spectrum of the blackbody radiator is described by the equation S Z-( R L (T, i) +G(;i); i = 1,_'I where Z-(i) denotes the spectral transmissivity of the atmosphere between the spectroradiometer and the measurement object, P, the wave number, R(P.) and G(.) functions, i.e.

the apparatus R the spectral sensitivity of the spectroradiometer and G(il-,) the inherent spectral radiation of the apparatus, L (T, j) the temperature radiation of the measured blackbody radiator, computed as per Planck's radiation formula, having the radiation temperature T and I denotes the number of spectral sampling points of each spectrum, that the spectral transmissivity r(.) of the atmosphere and the apparatus functions, i.e. the spectral sensitivity R(i,',) and the inherent spectral radiation G(i) of the spectroradiometer are formulated in the form of parameterized functions of the wave number, or wavelength and that by means of a least squares fit both the parameters for computing the spectral transmissivity T(,) of the atmosphere and the parameters of the apparatus functions R(i,' ,) and G(i) are determined together with the radiation temperature T of the blackbody radiator.

2. The method as set forth in claim 1, characterized in that the spectral transmissivity of the atmosphere is described parameterized by the temperature thereof, by the concentration of the few gases contained therein as well as by the length of the optical path between the blackbody reference radiator and the detector of the spectroradiometer to be calibrated.

3. The method as set forth in claim 2, characterized in that computation of the transmissivity of the atmosphere is implemented with the aid of a radiation transport model.

4. The method as set forth in claim 1, characterized in that the two apparatus functions R(-) and G(,, are described by simple parameterized functions, polynomials or splines with the polynomial coefficients being used as parameters for spectral sensitivity R(.), and Planck's formula with radiation temperature and the emissivity being used as parameter for the inherent spectral radiation G(il,) of spectroradiometer.

the the the the

5. The method as set forth in claim 4, characterized in that suitable parameterized function types are determined with the aid of additional information gleaned from preliminary tests.

6. The method as set forth in claim 5, characterized in that calibrations known as such are implemented beforehand, in which, as in the method in accordance with DE 41 28 912 C2, from the measured spectra of at least four blackbody radiators maintained constant at differing temperatures four different groups of differing spectra are formed from three blackbody radiators in each case, from which, with spectra available for at least four spectral wave numbers, the spectral sensitivity, the inherent spectral radiation of the apparatus and the three radiation temperatures in each case are established from each of the four different groups of differing spectra by a least squares fit and the results of the four groups from three each different spectra compared to each other in a reliability test, that the effect of the atmosphere is thereby eliminated by, for example, the blackbody radiators and the spectroradiometer to be calibrated being operated in a nitrogen atmosphere, that the ambient conditions, more particularly the temperature, and the setting of the spectroradiometer to be calibrated are varied 11 and that the resulting apparatus functions typical to the spec t roradi ometer concerned are then made use of to establish function types empirically which suffice by as few parameters as possible, but which nevertheless permit good simulation of the two apparatus functions R(P,) and G(;,).

7. The method as set forth in any of the preceding claims, characterized in that the measured spectra and thus also the apparatus functions, i.e. the spectral sensitivity R(.) and 10 the inherent spectral radiation G(,) of the apparatus to be calibrated,are viewed as complex variables.

8. The method as set forth in any of the preceding claims, characterized in that several blackbody radiators differing in temperature are used and that all spectra measured are employed in a least squares fit to determine the wanted parameters.

temperature are used, that a

9. The method as set forth in any of the claims 1 to 7, characterized in that several blackbody radiators differing in least squares fit is implemented for each spectrum measured to determine the wanted parameters, and that a calibration can be considered as being reliable when all least squares fits result in values for the parameters of the apparatus functions which are equal within the scope of the measurement accuracy.

10. A method as claimed in claim 1 and substantially as hereinbefore described.