- Email: [email protected]
A method to retrieve blackbody temperature errors in the two points radiometric calibration
Infrared Physics & Technology 52 (2009) 187–192
Contents lists available at ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
A method to retrieve blackbody temperature errors in the two points radiometric calibration Yao Té *, Pascal Jeseck, Isabelle Pépin, Claude Camy-Peyret UPMC Univ. Paris06, UMR7092, LPMAA, F-75005, Paris, France CNRS, IPSL, UMR7092, LPMAA, F-75005, Paris, France
a r t i c l e
i n f o
Article history: Received 4 April 2009 Available online 16 July 2009 PACS: 07.60-j 07.60.Ly 93.85.-q Keywords: Radiometric calibration Infrared Fourier transform spectrometer Temperature errors determination Atmospheric thermal emission Blackbody Radiometry
a b s t r a c t Measurements of the atmospheric thermal emission using an infrared Fourier transform spectrometer need to be radiometrically calibrated. As for several existing instruments (IASI-MetOp, IASI-balloon, NAST-I, AERI, etc.), the two points radiometric calibration is generally performed using two well-characterized blackbodies at two different temperatures (or one blackbody and the cold space), which allow to determine the response and the self-emission of the instrument. To perform an accurate radiometric calibration, the emissivity and the temperature of each blackbody should be known accurately. The blackbody temperatures are chosen to fit the characteristics of the instrument. The measurement of these temperatures is essential. This paper proposes a method to perform an accurate radiometric calibration even when one of the two blackbodies temperatures is not perfectly measured, by numerically retrieving this erroneous temperature. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Fourier transform spectrometers are now widely used for the remote sensing of temperature, water vapour and concentration of trace species in the atmosphere: MIPAS [1], TES [2], IASI [3], MIPAS-B [4], IASI-balloon [5], MIPAS-STR [6], NAST-I [7], AERI-X [8,9], FIRST [10] and REFIR [11]. Current interferometers operating in the thermal infrared region can cover very large spectral intervals at high spectral resolution allowing detailed analyses of many individual spectral signatures of the atmospheric constituents. But the recorded spectra should be very carefully calibrated (spectrally and radiometrically) and powerful processing algorithms are needed for efficient retrievals. The intrinsic characteristics of the instrument (response and self-emission) should also be known and characterized accurately. Indeed in thermal emission, the signal from the instrument is often equivalent to the atmospheric signal. So one needs first to determine the instrument characteristics before the atmospheric contribution can be derived. The two reference targets technique which involves viewing two well-characterized blackbody sources, stabilized at two different tempera* Corresponding author. Address: LPMAA, case 76, 4, Place Jussieu, 75252 Paris Cedex 05 France. Tel.: +33 1 44 27 96 07; fax: +33 1 44 27 70 33. E-mail address: [email protected] (Y. Té). 1350-4495/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2009.07.003
tures (or one blackbody and the cold space), is generally used to determine the instrumental contribution [5,12] and to achieve a proper radiometric calibration. Thermal emission Fourier transform spectro-radiometric instruments (FTIR in the following) operating in a stand alone mode on-board aircraft, balloon or satellite can be hindered by instrumental problems if the temperature of one of the two blackbodies is not correctly measured. During the IASI-MetOp validation campaign with IASI-balloon [5] in winter 2006, the blackbody temperature controller board broke down. A custommade electronic card was realized to read the warm blackbody temperature. Ground tests had provided good results. But during the balloon flight, the temperature of this simplified card had varied in a large range and this generated a drift in the actual temperature reading. In order to save the recorded atmospheric data, we found a new technique to radiometrically calibrate the atmospheric spectra even with an imprecisely known warm blackbody temperature. This method is described and used here to determine a poorly known temperature and then to perform a reliable radiometric calibration. The method is assuming a good knowledge of at least one blackbody temperature. The same method can also serve as a reliability check of the absolute radiometric calibration when the blackbody temperatures are nominally measured.
188
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
2. Determination of the imprecisely known temperature
Scalib scene ¼
Spectra recorded with the IASI-balloon instrument, are used in this paper to demonstrate the efficiency of the proposed method. The IASI-balloon instrument is an infrared Fourier transform spectrometer accommodated on-board a stratospheric gondola allowing to reach an altitude higher than 30 km. From this height, the IASI-balloon interferometer performs the spectral analysis of the upwelling thermal emission with two liquid nitrogen cooled infrared detectors (InSb and MCT) covering a large spectral interval from 3.3 to 15 lm (650–3000 cm1). In order to verify the performances of the radiometric calibration and of the IASI-balloon instrument, a third reference blackbody was realized [13] and completely characterized. It is a cylindrical cavity with a diameter of 200 mm, a length of 360 mm, an aperture of 60 mm diameter and an internal triangular groove of 3 mm pitch. The entire cavity (cylinder part and faces) is surrounded by copper tubes for temperature control and stabilization. This blackbody was specially realized in order to fit the field of view of our spectrometer in an optimized geometry where the instrument is only viewing the uniform rear face of the cavity. The main characteristic of this external reference source is a good temperature stabilization with an uniformity over the blackbody cavity better than ±0.1 K (using PRT probes which are calibrated with respect to a NIST standard with a precision of ±0.03 K) for the temperature range of atmospheric interest from 263 K to 303 K. The emissivity is better than 0.999 ± 0.002 between 600 cm1 and 3000 cm1. This absolute uncertainty is a combination between the statistical error from a ray tracing model (1,000,000 rays generated) and the estimated error on the intrinsic emissivity of the paint (0.96 ± 0.02) used on the blackbody cavity internal surface [13]. This blackbody is used as a reference source for ground calibration tests. 2.1. Radiometric calibration method The input radiance spectrum Strue and the measured spectrum are related linearly in the complex plane due to the optics S and electronics design [5,9], cf. (1). meas
S
meas
~Þ ¼ Gðm ~Þ Strue ðm ~Þ þ Sinst ðm ~Þ ðm
ð1Þ
~ is the wavenumber in cm1, Gðm ~Þ is the In this equation m ~Þ is the complex instrument response (or gain) function and Sinst ðm complex self-emission function of the instrument in radiance unit. The two functions G and Sinst are determined for all the wavenumbers, during the radiometric calibration process, using two blackbodies at different temperatures. In the case of a blackbody view Strue is the product of the emissivity and the Planck function ~Þ given by: BðT; m
~=T Þ 1Þ ~Þ ¼ c1 m~3 =ðexp ðc2 m BðT; m
ð2Þ
where T is the temperature in K, c1 = 1.191042759 1012 W cm2 sr1 and c2 = 1.4387752 cm K. The atmospheric thermal emission Scalib scene (of the atmospheric scene or of an external reference source) is obtained, cf. (3), after the radiometric calibration [5] based on Eq. (1). The superscript ‘‘calib” indicates that the spectrum is radiometrically calibrated without the instrumental contributions (G and Sinst). The subscript points to the source type measured by the instrument. Sources (calibration blackbodies, atmospheric scene, and external reference source) are viewed through a rotating mirror (without any change of the reflexion angle) in different observing directions. In the present case, ‘‘scene” indicates the nadir viewing direction for the atmospheric or the external reference source.
meas meas ecbb Bcbb Smeas ewbb Bwbb Smeas scene Scbb scene Swbb
meas Smeas wbb Scbb
ð3Þ
Here ewbb is the emissivity of the warm blackbody and ecbb the emissivity of the cold blackbody (ewbb = ecbb = 0.995 ± 0.002). Bwbb and Bcbb are the Planck functions, respectively, at the warm blacktrue body temperature T true wbb and at the cold blackbody temperature T cbb . Both blackbody temperatures are measured using platinum resistance thermometers (PRT) with a precision of 0.01 K, provided by ABB Bomem. The PRT probes are located in the rear conical faces of both blackbody cavities viewed by the interferometer through the scene acquisition mirror. The temperature uniformity is better than 0.05 K. The precision on the temperature measurement after the measuring electronics equipment is about 0.03 K. Eq. (3) is applied for each wavenumber and the importance of measuring precisely the two blackbody temperatures is clear since Bwbb and Bcbb true are involving implicitly T true wbb and T cbb . The radiometric accuracy of the IASI-balloon instrument is better than 0.2 K for the spectral regions 700–800 cm1 and 1900–2000 cm1 at 0.1 cm1 spectral resolution. We will discuss the case of a temperature error for the warm blackbody, but the same kind of argument could be applied to the cold blackbody. In the case of a warm blackbody temperature measurement with an error DTwbb, a supplementary term DScalib scene will appear in Eq. (3).
calib calib true true ~ ~ ~ Scalib scene T wbb þ DT wbb ; m ¼ Sscene T wbb ; m þ DSscene ðDT wbb ; mÞ
ð4Þ
An approximate expression for DScalib scene is given in the appendix by Eq. (8). This supplementary term depends on the temperature ~. It introduces also a radiance error DTwbb and the wavenumber m difference DSscene ðm~1 ; m~2 Þ between two wavenumbers m~1 and m~2 , cf. (9) in the appendix. In order to make the discussion easier and more explicit, we can introduce the brightness temperature TB function:
~= lnðc1 m~3 =B þ 1Þ ~Þ ¼ c 2 m T B ðB; m
ð5Þ
where B is the radiance in W/(cm2 sr cm1). For an input spectrum generated by a perfect radiometric calibration blackbody, the corresponding brightness temperature should be constant (within the noise) for all wavenumbers and the difference DT B ðm~1 ; m~2 Þ of two brightness temperatures for two different wavenumbers, should be zero. However, in the case of a temperature error DTwbb on the warm blackbody temperature, the difference DT B ðm~1 ; m~2 Þ obtained from this incorrectly calibrated spectrum, exhibits a non-zero value depending on the temperature error DTwbb and on the two wavenumbers m~1 and m~2 for which the brightness temperature difference has been calculated. In the following section, we will calculate this brightness temperature difference DT B ðm~1 ; m~2 Þ, for a real case based on the spectrum of a reference blackbody source recorded by the IASI-balloon instrument. Using this reference blackbody source provides a perfectly characterized spectrum which allows us to establish the feasibility of the method without introducing any unknown errors or uncertainties. Of course for Earth’s observation (during flight time), the reference blackbody source spectrum will be replaced by an atmospheric view from which a brightness temperature spectrum should be determined by the radiometric calibration procedure. An application of the technique on real atmospheric spectra is provided in Section 2.4. We will use a numerical method and apply our radiometric calibration algorithm for different temperature errors. The method presented in this paper will quantify these temperature errors.
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
2.2. Application on a real radiometrically calibrated spectrum During laboratory measurements performed specifically for the work presented here, the LPMAA (Laboratoire de Physique Moléculaire pour l0 Atmosphère et l0 Astrophysique) reference blackbody source was stabilized at 263.0 ± 0.1 K and used for covering the entrance aperture of the IASI-balloon instrument. In FTIR spectrometry, the noise in the spectrum depends on the alignment of the different optical elements (e.g. field stop, beamsplitter, mirrors, optical filters, detectors) and is increasing (all other parameters being equal) with the spectral resolution [14]. The IASI-balloon instrument was in its nominal mode (no optical misalignment) and in order to minimize the noise effect, it was operated for this purpose at the rather coarse spectral resolution of 3 cm1. At this resolution, the noise from 1000 to 1050 cm1 is lower than 2 108 W/(cm2 sr cm1) and from 2000 to 2050 cm1 lower than 3 109 W/(cm2 sr cm1). A point to verify is the possible non-linearity effect introduced by photoconductive detectors as HgCdTe detectors [15]. In order to check any non-linearity of our HgCdTe detector, the LPMAA reference blackbody source was stabilized at different temperatures: 10 °C, 5 °C, 0 °C, 5 °C, 10 °C, 15 °C and 20 °C. The corresponding radiometrically calibrated radiances calculated from 700 to 1800 cm1 are plotted against the theoretical Planck function radiance (at same temperatures and spectral interval). These spectra do not show any detectable non-linearity [5]. For the HgCdTe detector used in the present work, we have verified that this effect is negligible (within the experimental noise). For photovoltaic detectors as InSb detectors, the non-linearity contribution is also within the spectrum noise.
189
cold blackbody, but using for the warm blackbody temperature, different values Twbb around the true measured value T true wbb . Fig. 1 shows the influence of these small variations around T true wbb . As expected, the smallest value of DT B ðm~1 ; m~2 Þ is obtained when the temperature error is zero with respect to the true measured temperature, cf. Fig. 1. The effect of these variations around T true wbb on the brightness temperature difference, is small: DT B ðm~1 ; m~2 Þ is around 6% of DTwbb. So radiometric noise will limit the precision of the corresponding T true wbb retrieval. 2.2.2. Radiometric calibration using an erroneous temperature In this section, we will simulate a temperature error on the warm blackbody to numerically verify our correction method. If there is a temperature error DTwbb on the warm blackbody temperature and if an erroneous temperature Twbb (T wbb ¼ T true wbb þ DT wbb ) is used to calibrate radiometrically the same spectrum of the LPMAA reference source, a non-zero difference is observed between the two channels. Considering small temperature variations around Twbb, we can observe that a temperature variation of Twbb equal to DTwbb gives the smallest value of DT B ðm~1 ; m~2 Þ, cf. Fig. 2a (in black square for DTwbb = +1 K and in red circle for DTwbb = 1 K) and cf. Fig. 2b (in black square for DTwbb = +10 K and in red circle for DTwbb = 10 K). The temperature error introduced in T true wbb is precisely recovered. We have thus shown that this method allows us to determine the true temperature T true wbb of the warm blackbody if T true cbb is exactly known (or conversely the cold blackbody tempertrue ature T true cbb if T wbb is exactly known) by minimizing the brightness temperature difference between the two channels. 2.3. Theoretical study of a temperature error
Brightness temperature difference ΔTB(ν1,ν2) (K)
2.2.1. Radiometric calibration using the real temperatures First, we calibrate radiometrically the spectrum of the LPMAA reference source using the real temperatures of both internal calibration blackbodies (correctly and precisely measured). The average brightness temperature is calculated between 1000 and 1005 cm1 for the HgCdTe channel (m~1 ¼ 1002:5 cm1 ) and between 2000 and 2005 cm1 for the InSb channel (m~2 ¼ 2002:5 cm1 ). The difference between these two brightness is very small (about 0.02 K). This residual temperatures DT residual B instrument error could come from the temperature measurement inaccuracy, the optical alignment imprecision and/or the non-constant emissivity value over the large spectral range covered. In order to demonstrate the feasibility of the proposed method and to have a better understanding of its application, we calibrate radiometrically the LPMAA reference source spectrum (considered as the ‘‘truth”) with the precisely measured temperature for the
true
Twbb
0.15
true
variable and Tcbb
fixed
0.10
0.05
0.00
-0.05
In order to validate our numerical method, we will compare the results obtained from our radiometric calibration algorithm to the results predicted by an analysis based on a 2nd order of approximation. In the case of a non-zero temperature error (DTwbb – 0) on the real temperature T true wbb of the warm blackbody and when m~1 is different from m~2 , Eq. (9) in the appendix provides a non-zero radiance difference DSscene ðm~1 ; m~2 Þ. Fig. 3a shows the radiance difference DSscene ðm~1 ; m~2 Þ between the two detectors spectral regions (around 1000 cm1 for the HgCdTe channel and around 2000 cm1 for the InSb channel). These results are obtained from the radiometric calibration algorithm for different values of DTwbb (from 10 K to +10 K around T true wbb ), in open black square line, and from the 2nd order of approximation analysis of Eq. (9), in red cross line. There is a good agreement between these two radiance differences DSscene ðm~1 ; m~2 Þ. The agreement is better than 0.05% for a variation of ±10 K (cf. Fig. 3b). For a temperature error DTcbb on the cold blackbody real temperature and when T true wbb is fixed (without any error), the agreement between the radiometric calibration algorithm and the theoretical 2nd order approximation is similar to the case where T true wbb is erroneous. We have proved here, the validity of the 2nd order of approximation analysis as compared with our full numerical algorithm. The approximate method and the full numerical algorithm for the radiometric calibration are in very good agreement (better than 0.05% for a variation of ±10 K). We have also quantified through Eqs. (8) and (10), the effect on the radiance of a temperature error for the calibration blackbodies. 2.4. Application of the numerical method to real balloon flight data
-0.10
-0.15 -2
-1
0
Temperature variation around
1
2
true Twbb (K)
Fig. 1. Brightness temperature difference DT B ðm~1 ; m~2 Þ between the two channels. . We have subtracted the small residual bias DT residual B
In order to assess the feasibility of the method, we have used a perfectly known case (temperature perfectly measured and same emissivity in the studied spectral range) with the LPMAA reference source spectrum (the ‘‘truth”). But in the case of real atmospheric data, difficulties came from the unknown atmospheric spectrum
190
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
(b) 0.20
Twbb = Twbb =
0.15
Brightness temperature difference ΔTB(ν1,ν2) (K)
Brightness temperature difference ΔTB(ν1,ν2) (K)
(a) true Twbb + 1 K true Twbb - 1 K
0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -2
-1
0
1
2.0 true
+ 10 K
true
- 10 K
Twbb = Twbb Twbb = Twbb
1.5
1.0
0.5
0.0
-0.5 -15
2
-10
Temperature variation around Twbb (K)
-5
0
5
10
15
Temperature variation around Twbb (K)
~1 ; m ~2 Þ between the two channels: (a) for DTwbb = ±1 K and (b) for DTwbb = ±10 K (the small DT residual Fig. 2. Brightness temperature difference DT B ðm has been subtracted). B NEDT = 0.08 K around 1000 cm1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(b)
-7
8.0x10
true
-7
6.0x10
true
from the second order approximation (Tcbb fixed)
-7
4.0x10
2
-1
ΔSscene(ν1 , ν2 ) (W/(cm .sr.cm ))
from the radiometric calibration algorithm (Tcbb fixed)
-7
2.0x10
0.0 -7
-2.0x10
-7
-4.0x10
-7
-6.0x10
-10
-5
0
5
10 true
Temperature variation around T wbb
Difference between the radiometric calibration algorithm and the second order approximation (%)
(a)
0.05 true
Twbb
true
variable and T cbb
fixed
0.04
0.03
0.02
0.01
0.00
-10
(K)
-5
0
5
10 true
Temperature variation around T wbb
(K)
~1 ; m ~2 Þ: in black square from the radiometric calibration algorithm and in red circle from the 2nd order Fig. 3. Radiance difference between the two channels DSscene ðm approximation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Wavelength (µm) 20 16
12
8
4
320
Brightness temperature of atmospheric spectra (K)
background temperature and the numerous absorption lines in the calibrated spectrum. Atmospheric spectra were recorded at a 0.1 cm1 resolution during the flight. Degrading the resolution to 3 cm1 provides a good signal to noise ratio to apply the proposed method and reduces the influence of individual absorption lines. We cannot use the 1000 cm1 and 2000 cm1 spectral intervals to determine the channel brightness temperatures due to the influence of the O3 band and of the H2O lines, respectively. The brightness temperatures are calculated from the interval 880 to 920 cm1 for the MCT channel and from 2430 to 2470 cm1 for the InSb, larger spectral regions are used to obtain a better average even if some very weak lines are present. Fig. 4 shows in black the MCT channel spectrum and in red the InSb channel one, with the correct warm blackbody temperature and in green, spectra with a temperature error around 10 K. Overall, the green spectra are higher than the black and red ones. We can notice that strong absorption band levels are unrealistic in the green spectra: the CO2 bands around 650 cm1 and 2350 cm1, the O3 band at 1050 cm1 and the H2O lines after 1600 cm1. After the proper radiometric calibration, the channels present a residual brightness temperature difference DT B ðm~1 ; m~2 Þ of about 0.2 K. This method can be applied even for a spectrometer with only one detector if the detector covers a large spectral interval. Table
300 280 260 240 220 200 180 160 140
MCT channel with correct blackbody temperatures InSb channel with correct blackbody temperatures Spectra with a temperature error around 10 K
120 100 80 600
800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 -1
Wavenumber (cm ) Fig. 4. Brightness temperature of atmospheric radiometrically calibrated spectra obtained with the correct blackbody temperatures (in black and red) and with a blackbody temperature error around 10 K (in green). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
191
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
Table 1 ~1 ; m ~2 Þ for different temperature errors DTwbb and for different wavenumber pairs in the InSb channel. For the pair Brightness temperature difference DT B ðm ~2 ¼ 2000 cm1 ), HgCdTe and InSb channels are used. ~1 ¼ 1000 cm1 ; m (m
DTwbb (K)
4 8 12 16 20
DT(m~1 ; m~2 )(K)
m~1 ¼ 1900 (cm1) m~2 ¼ 1910 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 1930 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 1950 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2000 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2200 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2400 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2000 (cm1)
0.01 0.01 0.02 0.03 0.04
0.02 0.03 0.05 0.07 0.09
0.02 0.05 0.07 0.09 0.12
0.03 0.06 0.09 0.13 0.17
0.08 0.17 0.26 0.36 0.46
0.11 0.23 0.36 0.50 0.64
0.26 0.56 0.89 1.25 1.63
Table 2 ~1 ; m ~2 Þ and brightness temperature difference DT B ðm ~1 ; m ~2 Þ for different emissivity errors Dewbb. Radiance difference DSscene ðm
Dewbb
DSscene ðm~1 ; m~2 Þ (W/cm2 sr cm1) DT B ðm~1 ; m~2 Þ (K)
0.010
+0.010
0.005
+0.005
+4.6 108 +0.16
4.6 108 0.16
+2.3 108 +0.08
2.3 108 0.08
1 shows the influence of the spectral distance between two wavenumbers in the InSb channel, on the brightness temperature difference DT B ðm~1 ; m~2 Þ for different temperature errors DTwbb. We can notice that for a small spectral distance (1900 and 1910 cm1), DT B ðm~1 ; m~2 Þ is very small (about 0.04 K), even for a very large temperature error (DTwbb = 20 K). In order to detect a blackbody temperature error, it is better to use two wavenumbers which are as distant as possible, and of course in the useful spectral range of the given detector. We have already noticed that the uncertainty in the estimation of the temperature error is limited by the radiometrically calibrated spectrum noise which is in our case about 2 108 W/(cm2 sr cm1) around 1000 cm1 and 3 109 W/ (cm2 sr cm1) around 2000 cm1 for an individual acquisition cycle (scene +two blackbody views) of around 50 s. In the case of a summation of two signals (y ¼ x1 þ x2 ), the resulting noise for y will be (Dy)2 = (Dx1)2 + (Dx2)2. In our case, the effective noise is about 2.02 108 W/(cm2 sr cm1). We cannot retrieve a temperature error which introduces a radiance difference smaller than this effective noise. Eq. (9) shows the effect of the temperature error on the radiance difference between two spectral regions (around m~1 and around m~2 ). In our case, the theoretical calculation provides a radiance difference of ±2.05 108 W/(cm2 sr cm1) for a DTwbb = ±0.3 K. So we cannot determine the ‘‘unknown” temperature with a precision better than ±0.3 K using the IASI-balloon instrument. This is an indicative value only because it depends on the actual signal to noise ratio of each specific instrument. 3. Discussion We have assumed here a good knowledge of the emissivity of both blackbodies in order to analyze the possible temperature error determination. However, when the blackbody temperatures are precisely measured, this method could be applied to quantify effective emissivity differences of both blackbodies: differences may exist between the emissivities of the two blackbodies which are sometimes built separately, or a spectral dependence of the emissivity may exist. A simple case assuming a good knowledge of both blackbody temperatures and of the cold blackbody emissivity is used to confirm the potential capabilities of this method for verifying the warm blackbody emissivity. Table 2 shows the radiance difference DSscene ðm~1 ; m~2 Þ and the brightness temperature difference DT B ðm~1 ; m~2 Þ introduced by different errors Dewbb on the emissivity of the warm blackbody. Here m~1 ¼ 1002:5 cm1 and
m~2 ¼ 2002:5 cm1 . A more detailed study of emissivity differences and/or spectral variations could be made, but this was not the purpose of this paper which concentrates on a method to determine the temperature of one blackbody in the framework of the radiometric calibration algorithm or the 2nd order approximation analysis. A method involving three blackbodies whose temperatures are not precisely known, has been proposed to radiometrically calibrate atmospheric spectra [16]. But this method is not easily implemented, because for on-board instruments (satellite, balloon-borne or airborne), at most two calibration blackbodies are employed, due to size and mass constraints.
4. Conclusions This paper has introduced a method to solve the problem of an erroneous temperature for one of the two blackbodies used to calibrate radiometrically atmospheric thermal emission spectra recorded by a FTIR spectrometer. This ‘‘unknown” temperature bias translates into a radiance difference between two spectral regions (or between two detectors) and is theoretically calculated and verified against a real case using a reference blackbody source. The minimization method of the effect on the radiance difference or of the brightness temperature difference allows to determine the poorly known blackbody temperature with a satisfying precision (depending on the instrument noise) assuming a good knowledge of the other blackbody temperature. Using this retrieved temperature, we can perform an accurate radiometric calibration of the atmospheric spectrum. The method could be also applied to check the consistency of the radiometric calibration, to verify the effective emissivity consistency between both blackbodies or to analyze the possible dependence of the emissivity against wavenumber (potentially detecting aging or contamination of the blackbody inner surface) when the corresponding temperatures are known within specifications. Acknowledgements We are very grateful to discussions with H.E. Revercomb and for his advice for improve the manuscript. We thank also J.-Y. Mandin for his useful comments on this work.
192
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
Appendix Results predicted by a 2nd order approximation. We assume here a small temperature error DTwbb on the real temperature T true wbb of the warm blackbody:
T wbb ¼
T true wbb
þ DT wbb
ð6Þ
2 1 true true ~Þ ¼ B T true ~ ~ ~ 1 þ A BðT wbb ; m ; m T ; m D T þ T ; m D T A 1 2 wbb wbb wbb wbb wbb 2
ð7Þ where
m ¼ c2
m~ exp c2 T true wbb 2 m~ T true exp c2 T true 1 wbb
m~
wbb
and
~ A2 T true wbb ; m ¼
2 T true wbb
þ c2
m~ þ1 exp c2 T true wbb true 2 ~ m T wbb exp c2 T true 1
m~
wbb
Applying this approximation to Eq. (3), a supplementary term due to the effect of the temperature error DTwbb, cf. (6), is added.
calib calib true ~ ~ ~ DScalib scene ðDT wbb ; mÞ ¼ Sscene ðT wbb ; mÞ Sscene T wbb ; m 1 2 ~ DT wbb þ A2 ðT true ~ ¼ A1 T true wbb ; m wbb ; mÞDT wbb 2 meas Smeas S cbb ewbb Bwbb scene meas Smeas wbb Scbb
ð8Þ
~ We can notice the influence of DTwbb, T true wbb and m on this new term. When the instrument works perfectly and when there is no temperature error, Eq. (8) leads to a correction equal to zero. But if there is a temperature error (DTwbb – 0), a slight difference is observed. Considering the radiance difference between two wave~2 , the correction term of (8), introduces a new ~1 and m numbers m contribution term, cf. (9). calib ~ ~ DSscene ðm~1 ; m~2 Þ ¼ DScalib scene ðDT wbb ; m2 Þ DSscene ðDT wbb ; m1 Þ
ð10Þ
T true wbb is fixed at the correctly measured value and Tcbb, used in the radiometric calibration algorithm, varies around its true value T true cbb . References
where DTwbb is small compared to T true wbb (expressed in Kelvin). Up to the 2nd order of approximation, Eq. (2) becomes:
~ A1 T true wbb ;
2 1 true true ~ ~ ~ DScalib ð D T ; m Þ ¼ A T ; m D T þ T ; m D T A 1 2 cbb cbb scene cbb cbb cbb 2 meas meas S Swbb ecbb Bcbb scene meas Smeas wbb Scbb
ð9Þ
Eq. (9) leads to a non-zero result when there is a non-zero tem~2 –m ~1 . perature error (DTwbb – 0) and when m In the case of a poorly known temperature T true cbb of the cold blackbody (T true wbb correctly measured), the correction term equivalent to Eq. (8), is given by Eq. (10).
[1] ESA, ENVISAT-MIPAS: An Instrument for Atmospheric Chemistry and Climate Research, ESA SP-1229, European Space Agency, ESTEC, Noordwijk, The Netherlands, 2000. [2] R. Beer, T.A. Glavich, M. Rider, Tropospheric emission spectrometer for the earth observing system’s aura satellite, Appl. Opt. 40 (2001) 2356–2367. [3] B. Tournier, D. Blumstein, F.-R. Cayla, G. Chalon, IASI level 0 and 1 processing algorithms description, in: The 12th International TOVS Study Conference (ITSC-XII), The Cumberland, Lorne, Victoria, Australia, 27 February–5 March 2002. [4] H. Fischer, H. Oelhaf, Remote sensing of vertical profiles of atmospheric constituents with MIPAS limb-emission spectrometers, Appl. Opt. 35 (1996) 2787–2796. [5] Y. Té, P. Jeseck, C. Camy-Peyret, S. Payan, G. Perron, G. Aubertin, Balloonborne calibrated spectroradiometer for atmospheric nadir sounding, Appl. Opt. 41 (2002) 6431–6441. [6] C. Piesch, T. Gulde, C. Sartorius, F. Friedl-Vallon, M. Seefeldner, M. Wölfel, C.E. Blom, H. Fischer, Design of a MIPAS instrument for high-altitude aircraft, in: Second International Airborne Remote Sensing Conference and Exhibition, San Francisco, California, 1996. [7] G. Grieco, G. Masiello, M. Matricardi, C. Serio, D. Summa, V. Cuomo, Demonstration and validation of the sigma-IASI inversion scheme with NAST-I data, Q. J. R. Meteorol. Soc. 133 (S3) (2007) 217–232. [8] R.O. Knuteson, F.A. Best, N.C. Ciganovich, R.G. Dedecker, T.P. Dirkx, S. Ellington, W.F. Feltz, R.K. Garcia, R.A. Herbsleb, H.B. Howell, H.E. Revercomb, W.L. Smith, J.F. Short, Atmospheric emitted radiance interferometer (AERI): part I: instrument design, J. Atmos. Oceanic Technol. 21 (2004) 1763–1776. [9] R.O. Knuteson, F.A. Best, N.C. Ciganovich, R.G. Dedecker, T.P. Dirkx, S. Ellington, W.F. Feltz, R.K. Garcia, R.A. Herbsleb, H.B. Howell, H.E. Revercomb, W.L. Smith, J.F. Short, Atmospheric emitted radiance interferometer (AERI): part II: instrument performance, J. Atmos. Oceanic Technol. 21 (2004) 1777–1789. [10] M.G. Mlynczak, D.G. Johnson, H. Latvakoski, K. Jucks, M. Watson, G. Bingham, D.P. Kratz, W.A. Traub, S.J. Wellard, C.R. Hyde, First light from the far-infrared spectroscopy of the troposphere (FIRST) instrument, Geophys. Res. Lett. 33 (2006) L07704. [11] L. Palchetti, G. Bianchini, F. Castagnoli, B. Carli, C. Serio, F. Esposito, V. Cuomo, R. Rizzi, T. Maestri, Breadboard of a Fourier-transform spectrometer for the radiation explorer in the far infrared atmospheric mission, Appl. Opt. 44 (2005) 2870–2878. [12] H.E. Revercomb, H. Buijs, H.B. Howell, D.D. LaPorte, W.L. Smith, L.A. Sromovsky, Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the high-resolution interferometer sounder, Appl. Opt. 27 (1988) 3210–3218. [13] Y. Té, P. Jeseck, C. Camy-Peyret, S. Payan, S. Briaudeau, M. Fanjeaux, High emissivity blackbody for radiometric calibration near ambient temperature, Metrologia 40 (2003) 24–30. [14] P.R. Griffiths, J.A. de Haseth, Fourier Transform Infrared Spectrometry, WileyInterscience Publication, 2007. [15] P. Jeseck, C. Camy-Peyret, T. Hawat, S. Payan, Detector nonlinearity correction scheme for the LPMA balloon borne Fourier transform spectrometer, Appl. Opt. 37 (1998) 6544–6549. [16] E. Lindermeir, P. Haschberger, V. Tank, H. Dietl, Calibration of a Fourier transform spectrometer using three blackbody sources, Appl. Opt. 31 (1991) 4527–4533.
Contents lists available at ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
A method to retrieve blackbody temperature errors in the two points radiometric calibration Yao Té *, Pascal Jeseck, Isabelle Pépin, Claude Camy-Peyret UPMC Univ. Paris06, UMR7092, LPMAA, F-75005, Paris, France CNRS, IPSL, UMR7092, LPMAA, F-75005, Paris, France
a r t i c l e
i n f o
Article history: Received 4 April 2009 Available online 16 July 2009 PACS: 07.60-j 07.60.Ly 93.85.-q Keywords: Radiometric calibration Infrared Fourier transform spectrometer Temperature errors determination Atmospheric thermal emission Blackbody Radiometry
a b s t r a c t Measurements of the atmospheric thermal emission using an infrared Fourier transform spectrometer need to be radiometrically calibrated. As for several existing instruments (IASI-MetOp, IASI-balloon, NAST-I, AERI, etc.), the two points radiometric calibration is generally performed using two well-characterized blackbodies at two different temperatures (or one blackbody and the cold space), which allow to determine the response and the self-emission of the instrument. To perform an accurate radiometric calibration, the emissivity and the temperature of each blackbody should be known accurately. The blackbody temperatures are chosen to fit the characteristics of the instrument. The measurement of these temperatures is essential. This paper proposes a method to perform an accurate radiometric calibration even when one of the two blackbodies temperatures is not perfectly measured, by numerically retrieving this erroneous temperature. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Fourier transform spectrometers are now widely used for the remote sensing of temperature, water vapour and concentration of trace species in the atmosphere: MIPAS [1], TES [2], IASI [3], MIPAS-B [4], IASI-balloon [5], MIPAS-STR [6], NAST-I [7], AERI-X [8,9], FIRST [10] and REFIR [11]. Current interferometers operating in the thermal infrared region can cover very large spectral intervals at high spectral resolution allowing detailed analyses of many individual spectral signatures of the atmospheric constituents. But the recorded spectra should be very carefully calibrated (spectrally and radiometrically) and powerful processing algorithms are needed for efficient retrievals. The intrinsic characteristics of the instrument (response and self-emission) should also be known and characterized accurately. Indeed in thermal emission, the signal from the instrument is often equivalent to the atmospheric signal. So one needs first to determine the instrument characteristics before the atmospheric contribution can be derived. The two reference targets technique which involves viewing two well-characterized blackbody sources, stabilized at two different tempera* Corresponding author. Address: LPMAA, case 76, 4, Place Jussieu, 75252 Paris Cedex 05 France. Tel.: +33 1 44 27 96 07; fax: +33 1 44 27 70 33. E-mail address: [email protected] (Y. Té). 1350-4495/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2009.07.003
tures (or one blackbody and the cold space), is generally used to determine the instrumental contribution [5,12] and to achieve a proper radiometric calibration. Thermal emission Fourier transform spectro-radiometric instruments (FTIR in the following) operating in a stand alone mode on-board aircraft, balloon or satellite can be hindered by instrumental problems if the temperature of one of the two blackbodies is not correctly measured. During the IASI-MetOp validation campaign with IASI-balloon [5] in winter 2006, the blackbody temperature controller board broke down. A custommade electronic card was realized to read the warm blackbody temperature. Ground tests had provided good results. But during the balloon flight, the temperature of this simplified card had varied in a large range and this generated a drift in the actual temperature reading. In order to save the recorded atmospheric data, we found a new technique to radiometrically calibrate the atmospheric spectra even with an imprecisely known warm blackbody temperature. This method is described and used here to determine a poorly known temperature and then to perform a reliable radiometric calibration. The method is assuming a good knowledge of at least one blackbody temperature. The same method can also serve as a reliability check of the absolute radiometric calibration when the blackbody temperatures are nominally measured.
188
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
2. Determination of the imprecisely known temperature
Scalib scene ¼
Spectra recorded with the IASI-balloon instrument, are used in this paper to demonstrate the efficiency of the proposed method. The IASI-balloon instrument is an infrared Fourier transform spectrometer accommodated on-board a stratospheric gondola allowing to reach an altitude higher than 30 km. From this height, the IASI-balloon interferometer performs the spectral analysis of the upwelling thermal emission with two liquid nitrogen cooled infrared detectors (InSb and MCT) covering a large spectral interval from 3.3 to 15 lm (650–3000 cm1). In order to verify the performances of the radiometric calibration and of the IASI-balloon instrument, a third reference blackbody was realized [13] and completely characterized. It is a cylindrical cavity with a diameter of 200 mm, a length of 360 mm, an aperture of 60 mm diameter and an internal triangular groove of 3 mm pitch. The entire cavity (cylinder part and faces) is surrounded by copper tubes for temperature control and stabilization. This blackbody was specially realized in order to fit the field of view of our spectrometer in an optimized geometry where the instrument is only viewing the uniform rear face of the cavity. The main characteristic of this external reference source is a good temperature stabilization with an uniformity over the blackbody cavity better than ±0.1 K (using PRT probes which are calibrated with respect to a NIST standard with a precision of ±0.03 K) for the temperature range of atmospheric interest from 263 K to 303 K. The emissivity is better than 0.999 ± 0.002 between 600 cm1 and 3000 cm1. This absolute uncertainty is a combination between the statistical error from a ray tracing model (1,000,000 rays generated) and the estimated error on the intrinsic emissivity of the paint (0.96 ± 0.02) used on the blackbody cavity internal surface [13]. This blackbody is used as a reference source for ground calibration tests. 2.1. Radiometric calibration method The input radiance spectrum Strue and the measured spectrum are related linearly in the complex plane due to the optics S and electronics design [5,9], cf. (1). meas
S
meas
~Þ ¼ Gðm ~Þ Strue ðm ~Þ þ Sinst ðm ~Þ ðm
ð1Þ
~ is the wavenumber in cm1, Gðm ~Þ is the In this equation m ~Þ is the complex instrument response (or gain) function and Sinst ðm complex self-emission function of the instrument in radiance unit. The two functions G and Sinst are determined for all the wavenumbers, during the radiometric calibration process, using two blackbodies at different temperatures. In the case of a blackbody view Strue is the product of the emissivity and the Planck function ~Þ given by: BðT; m
~=T Þ 1Þ ~Þ ¼ c1 m~3 =ðexp ðc2 m BðT; m
ð2Þ
where T is the temperature in K, c1 = 1.191042759 1012 W cm2 sr1 and c2 = 1.4387752 cm K. The atmospheric thermal emission Scalib scene (of the atmospheric scene or of an external reference source) is obtained, cf. (3), after the radiometric calibration [5] based on Eq. (1). The superscript ‘‘calib” indicates that the spectrum is radiometrically calibrated without the instrumental contributions (G and Sinst). The subscript points to the source type measured by the instrument. Sources (calibration blackbodies, atmospheric scene, and external reference source) are viewed through a rotating mirror (without any change of the reflexion angle) in different observing directions. In the present case, ‘‘scene” indicates the nadir viewing direction for the atmospheric or the external reference source.
meas meas ecbb Bcbb Smeas ewbb Bwbb Smeas scene Scbb scene Swbb
meas Smeas wbb Scbb
ð3Þ
Here ewbb is the emissivity of the warm blackbody and ecbb the emissivity of the cold blackbody (ewbb = ecbb = 0.995 ± 0.002). Bwbb and Bcbb are the Planck functions, respectively, at the warm blacktrue body temperature T true wbb and at the cold blackbody temperature T cbb . Both blackbody temperatures are measured using platinum resistance thermometers (PRT) with a precision of 0.01 K, provided by ABB Bomem. The PRT probes are located in the rear conical faces of both blackbody cavities viewed by the interferometer through the scene acquisition mirror. The temperature uniformity is better than 0.05 K. The precision on the temperature measurement after the measuring electronics equipment is about 0.03 K. Eq. (3) is applied for each wavenumber and the importance of measuring precisely the two blackbody temperatures is clear since Bwbb and Bcbb true are involving implicitly T true wbb and T cbb . The radiometric accuracy of the IASI-balloon instrument is better than 0.2 K for the spectral regions 700–800 cm1 and 1900–2000 cm1 at 0.1 cm1 spectral resolution. We will discuss the case of a temperature error for the warm blackbody, but the same kind of argument could be applied to the cold blackbody. In the case of a warm blackbody temperature measurement with an error DTwbb, a supplementary term DScalib scene will appear in Eq. (3).
calib calib true true ~ ~ ~ Scalib scene T wbb þ DT wbb ; m ¼ Sscene T wbb ; m þ DSscene ðDT wbb ; mÞ
ð4Þ
An approximate expression for DScalib scene is given in the appendix by Eq. (8). This supplementary term depends on the temperature ~. It introduces also a radiance error DTwbb and the wavenumber m difference DSscene ðm~1 ; m~2 Þ between two wavenumbers m~1 and m~2 , cf. (9) in the appendix. In order to make the discussion easier and more explicit, we can introduce the brightness temperature TB function:
~= lnðc1 m~3 =B þ 1Þ ~Þ ¼ c 2 m T B ðB; m
ð5Þ
where B is the radiance in W/(cm2 sr cm1). For an input spectrum generated by a perfect radiometric calibration blackbody, the corresponding brightness temperature should be constant (within the noise) for all wavenumbers and the difference DT B ðm~1 ; m~2 Þ of two brightness temperatures for two different wavenumbers, should be zero. However, in the case of a temperature error DTwbb on the warm blackbody temperature, the difference DT B ðm~1 ; m~2 Þ obtained from this incorrectly calibrated spectrum, exhibits a non-zero value depending on the temperature error DTwbb and on the two wavenumbers m~1 and m~2 for which the brightness temperature difference has been calculated. In the following section, we will calculate this brightness temperature difference DT B ðm~1 ; m~2 Þ, for a real case based on the spectrum of a reference blackbody source recorded by the IASI-balloon instrument. Using this reference blackbody source provides a perfectly characterized spectrum which allows us to establish the feasibility of the method without introducing any unknown errors or uncertainties. Of course for Earth’s observation (during flight time), the reference blackbody source spectrum will be replaced by an atmospheric view from which a brightness temperature spectrum should be determined by the radiometric calibration procedure. An application of the technique on real atmospheric spectra is provided in Section 2.4. We will use a numerical method and apply our radiometric calibration algorithm for different temperature errors. The method presented in this paper will quantify these temperature errors.
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
2.2. Application on a real radiometrically calibrated spectrum During laboratory measurements performed specifically for the work presented here, the LPMAA (Laboratoire de Physique Moléculaire pour l0 Atmosphère et l0 Astrophysique) reference blackbody source was stabilized at 263.0 ± 0.1 K and used for covering the entrance aperture of the IASI-balloon instrument. In FTIR spectrometry, the noise in the spectrum depends on the alignment of the different optical elements (e.g. field stop, beamsplitter, mirrors, optical filters, detectors) and is increasing (all other parameters being equal) with the spectral resolution [14]. The IASI-balloon instrument was in its nominal mode (no optical misalignment) and in order to minimize the noise effect, it was operated for this purpose at the rather coarse spectral resolution of 3 cm1. At this resolution, the noise from 1000 to 1050 cm1 is lower than 2 108 W/(cm2 sr cm1) and from 2000 to 2050 cm1 lower than 3 109 W/(cm2 sr cm1). A point to verify is the possible non-linearity effect introduced by photoconductive detectors as HgCdTe detectors [15]. In order to check any non-linearity of our HgCdTe detector, the LPMAA reference blackbody source was stabilized at different temperatures: 10 °C, 5 °C, 0 °C, 5 °C, 10 °C, 15 °C and 20 °C. The corresponding radiometrically calibrated radiances calculated from 700 to 1800 cm1 are plotted against the theoretical Planck function radiance (at same temperatures and spectral interval). These spectra do not show any detectable non-linearity [5]. For the HgCdTe detector used in the present work, we have verified that this effect is negligible (within the experimental noise). For photovoltaic detectors as InSb detectors, the non-linearity contribution is also within the spectrum noise.
189
cold blackbody, but using for the warm blackbody temperature, different values Twbb around the true measured value T true wbb . Fig. 1 shows the influence of these small variations around T true wbb . As expected, the smallest value of DT B ðm~1 ; m~2 Þ is obtained when the temperature error is zero with respect to the true measured temperature, cf. Fig. 1. The effect of these variations around T true wbb on the brightness temperature difference, is small: DT B ðm~1 ; m~2 Þ is around 6% of DTwbb. So radiometric noise will limit the precision of the corresponding T true wbb retrieval. 2.2.2. Radiometric calibration using an erroneous temperature In this section, we will simulate a temperature error on the warm blackbody to numerically verify our correction method. If there is a temperature error DTwbb on the warm blackbody temperature and if an erroneous temperature Twbb (T wbb ¼ T true wbb þ DT wbb ) is used to calibrate radiometrically the same spectrum of the LPMAA reference source, a non-zero difference is observed between the two channels. Considering small temperature variations around Twbb, we can observe that a temperature variation of Twbb equal to DTwbb gives the smallest value of DT B ðm~1 ; m~2 Þ, cf. Fig. 2a (in black square for DTwbb = +1 K and in red circle for DTwbb = 1 K) and cf. Fig. 2b (in black square for DTwbb = +10 K and in red circle for DTwbb = 10 K). The temperature error introduced in T true wbb is precisely recovered. We have thus shown that this method allows us to determine the true temperature T true wbb of the warm blackbody if T true cbb is exactly known (or conversely the cold blackbody tempertrue ature T true cbb if T wbb is exactly known) by minimizing the brightness temperature difference between the two channels. 2.3. Theoretical study of a temperature error
Brightness temperature difference ΔTB(ν1,ν2) (K)
2.2.1. Radiometric calibration using the real temperatures First, we calibrate radiometrically the spectrum of the LPMAA reference source using the real temperatures of both internal calibration blackbodies (correctly and precisely measured). The average brightness temperature is calculated between 1000 and 1005 cm1 for the HgCdTe channel (m~1 ¼ 1002:5 cm1 ) and between 2000 and 2005 cm1 for the InSb channel (m~2 ¼ 2002:5 cm1 ). The difference between these two brightness is very small (about 0.02 K). This residual temperatures DT residual B instrument error could come from the temperature measurement inaccuracy, the optical alignment imprecision and/or the non-constant emissivity value over the large spectral range covered. In order to demonstrate the feasibility of the proposed method and to have a better understanding of its application, we calibrate radiometrically the LPMAA reference source spectrum (considered as the ‘‘truth”) with the precisely measured temperature for the
true
Twbb
0.15
true
variable and Tcbb
fixed
0.10
0.05
0.00
-0.05
In order to validate our numerical method, we will compare the results obtained from our radiometric calibration algorithm to the results predicted by an analysis based on a 2nd order of approximation. In the case of a non-zero temperature error (DTwbb – 0) on the real temperature T true wbb of the warm blackbody and when m~1 is different from m~2 , Eq. (9) in the appendix provides a non-zero radiance difference DSscene ðm~1 ; m~2 Þ. Fig. 3a shows the radiance difference DSscene ðm~1 ; m~2 Þ between the two detectors spectral regions (around 1000 cm1 for the HgCdTe channel and around 2000 cm1 for the InSb channel). These results are obtained from the radiometric calibration algorithm for different values of DTwbb (from 10 K to +10 K around T true wbb ), in open black square line, and from the 2nd order of approximation analysis of Eq. (9), in red cross line. There is a good agreement between these two radiance differences DSscene ðm~1 ; m~2 Þ. The agreement is better than 0.05% for a variation of ±10 K (cf. Fig. 3b). For a temperature error DTcbb on the cold blackbody real temperature and when T true wbb is fixed (without any error), the agreement between the radiometric calibration algorithm and the theoretical 2nd order approximation is similar to the case where T true wbb is erroneous. We have proved here, the validity of the 2nd order of approximation analysis as compared with our full numerical algorithm. The approximate method and the full numerical algorithm for the radiometric calibration are in very good agreement (better than 0.05% for a variation of ±10 K). We have also quantified through Eqs. (8) and (10), the effect on the radiance of a temperature error for the calibration blackbodies. 2.4. Application of the numerical method to real balloon flight data
-0.10
-0.15 -2
-1
0
Temperature variation around
1
2
true Twbb (K)
Fig. 1. Brightness temperature difference DT B ðm~1 ; m~2 Þ between the two channels. . We have subtracted the small residual bias DT residual B
In order to assess the feasibility of the method, we have used a perfectly known case (temperature perfectly measured and same emissivity in the studied spectral range) with the LPMAA reference source spectrum (the ‘‘truth”). But in the case of real atmospheric data, difficulties came from the unknown atmospheric spectrum
190
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
(b) 0.20
Twbb = Twbb =
0.15
Brightness temperature difference ΔTB(ν1,ν2) (K)
Brightness temperature difference ΔTB(ν1,ν2) (K)
(a) true Twbb + 1 K true Twbb - 1 K
0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -2
-1
0
1
2.0 true
+ 10 K
true
- 10 K
Twbb = Twbb Twbb = Twbb
1.5
1.0
0.5
0.0
-0.5 -15
2
-10
Temperature variation around Twbb (K)
-5
0
5
10
15
Temperature variation around Twbb (K)
~1 ; m ~2 Þ between the two channels: (a) for DTwbb = ±1 K and (b) for DTwbb = ±10 K (the small DT residual Fig. 2. Brightness temperature difference DT B ðm has been subtracted). B NEDT = 0.08 K around 1000 cm1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(b)
-7
8.0x10
true
-7
6.0x10
true
from the second order approximation (Tcbb fixed)
-7
4.0x10
2
-1
ΔSscene(ν1 , ν2 ) (W/(cm .sr.cm ))
from the radiometric calibration algorithm (Tcbb fixed)
-7
2.0x10
0.0 -7
-2.0x10
-7
-4.0x10
-7
-6.0x10
-10
-5
0
5
10 true
Temperature variation around T wbb
Difference between the radiometric calibration algorithm and the second order approximation (%)
(a)
0.05 true
Twbb
true
variable and T cbb
fixed
0.04
0.03
0.02
0.01
0.00
-10
(K)
-5
0
5
10 true
Temperature variation around T wbb
(K)
~1 ; m ~2 Þ: in black square from the radiometric calibration algorithm and in red circle from the 2nd order Fig. 3. Radiance difference between the two channels DSscene ðm approximation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Wavelength (µm) 20 16
12
8
4
320
Brightness temperature of atmospheric spectra (K)
background temperature and the numerous absorption lines in the calibrated spectrum. Atmospheric spectra were recorded at a 0.1 cm1 resolution during the flight. Degrading the resolution to 3 cm1 provides a good signal to noise ratio to apply the proposed method and reduces the influence of individual absorption lines. We cannot use the 1000 cm1 and 2000 cm1 spectral intervals to determine the channel brightness temperatures due to the influence of the O3 band and of the H2O lines, respectively. The brightness temperatures are calculated from the interval 880 to 920 cm1 for the MCT channel and from 2430 to 2470 cm1 for the InSb, larger spectral regions are used to obtain a better average even if some very weak lines are present. Fig. 4 shows in black the MCT channel spectrum and in red the InSb channel one, with the correct warm blackbody temperature and in green, spectra with a temperature error around 10 K. Overall, the green spectra are higher than the black and red ones. We can notice that strong absorption band levels are unrealistic in the green spectra: the CO2 bands around 650 cm1 and 2350 cm1, the O3 band at 1050 cm1 and the H2O lines after 1600 cm1. After the proper radiometric calibration, the channels present a residual brightness temperature difference DT B ðm~1 ; m~2 Þ of about 0.2 K. This method can be applied even for a spectrometer with only one detector if the detector covers a large spectral interval. Table
300 280 260 240 220 200 180 160 140
MCT channel with correct blackbody temperatures InSb channel with correct blackbody temperatures Spectra with a temperature error around 10 K
120 100 80 600
800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 -1
Wavenumber (cm ) Fig. 4. Brightness temperature of atmospheric radiometrically calibrated spectra obtained with the correct blackbody temperatures (in black and red) and with a blackbody temperature error around 10 K (in green). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
191
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
Table 1 ~1 ; m ~2 Þ for different temperature errors DTwbb and for different wavenumber pairs in the InSb channel. For the pair Brightness temperature difference DT B ðm ~2 ¼ 2000 cm1 ), HgCdTe and InSb channels are used. ~1 ¼ 1000 cm1 ; m (m
DTwbb (K)
4 8 12 16 20
DT(m~1 ; m~2 )(K)
m~1 ¼ 1900 (cm1) m~2 ¼ 1910 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 1930 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 1950 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2000 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2200 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2400 (cm1)
m~1 ¼ 1900 (cm1) m~2 ¼ 2000 (cm1)
0.01 0.01 0.02 0.03 0.04
0.02 0.03 0.05 0.07 0.09
0.02 0.05 0.07 0.09 0.12
0.03 0.06 0.09 0.13 0.17
0.08 0.17 0.26 0.36 0.46
0.11 0.23 0.36 0.50 0.64
0.26 0.56 0.89 1.25 1.63
Table 2 ~1 ; m ~2 Þ and brightness temperature difference DT B ðm ~1 ; m ~2 Þ for different emissivity errors Dewbb. Radiance difference DSscene ðm
Dewbb
DSscene ðm~1 ; m~2 Þ (W/cm2 sr cm1) DT B ðm~1 ; m~2 Þ (K)
0.010
+0.010
0.005
+0.005
+4.6 108 +0.16
4.6 108 0.16
+2.3 108 +0.08
2.3 108 0.08
1 shows the influence of the spectral distance between two wavenumbers in the InSb channel, on the brightness temperature difference DT B ðm~1 ; m~2 Þ for different temperature errors DTwbb. We can notice that for a small spectral distance (1900 and 1910 cm1), DT B ðm~1 ; m~2 Þ is very small (about 0.04 K), even for a very large temperature error (DTwbb = 20 K). In order to detect a blackbody temperature error, it is better to use two wavenumbers which are as distant as possible, and of course in the useful spectral range of the given detector. We have already noticed that the uncertainty in the estimation of the temperature error is limited by the radiometrically calibrated spectrum noise which is in our case about 2 108 W/(cm2 sr cm1) around 1000 cm1 and 3 109 W/ (cm2 sr cm1) around 2000 cm1 for an individual acquisition cycle (scene +two blackbody views) of around 50 s. In the case of a summation of two signals (y ¼ x1 þ x2 ), the resulting noise for y will be (Dy)2 = (Dx1)2 + (Dx2)2. In our case, the effective noise is about 2.02 108 W/(cm2 sr cm1). We cannot retrieve a temperature error which introduces a radiance difference smaller than this effective noise. Eq. (9) shows the effect of the temperature error on the radiance difference between two spectral regions (around m~1 and around m~2 ). In our case, the theoretical calculation provides a radiance difference of ±2.05 108 W/(cm2 sr cm1) for a DTwbb = ±0.3 K. So we cannot determine the ‘‘unknown” temperature with a precision better than ±0.3 K using the IASI-balloon instrument. This is an indicative value only because it depends on the actual signal to noise ratio of each specific instrument. 3. Discussion We have assumed here a good knowledge of the emissivity of both blackbodies in order to analyze the possible temperature error determination. However, when the blackbody temperatures are precisely measured, this method could be applied to quantify effective emissivity differences of both blackbodies: differences may exist between the emissivities of the two blackbodies which are sometimes built separately, or a spectral dependence of the emissivity may exist. A simple case assuming a good knowledge of both blackbody temperatures and of the cold blackbody emissivity is used to confirm the potential capabilities of this method for verifying the warm blackbody emissivity. Table 2 shows the radiance difference DSscene ðm~1 ; m~2 Þ and the brightness temperature difference DT B ðm~1 ; m~2 Þ introduced by different errors Dewbb on the emissivity of the warm blackbody. Here m~1 ¼ 1002:5 cm1 and
m~2 ¼ 2002:5 cm1 . A more detailed study of emissivity differences and/or spectral variations could be made, but this was not the purpose of this paper which concentrates on a method to determine the temperature of one blackbody in the framework of the radiometric calibration algorithm or the 2nd order approximation analysis. A method involving three blackbodies whose temperatures are not precisely known, has been proposed to radiometrically calibrate atmospheric spectra [16]. But this method is not easily implemented, because for on-board instruments (satellite, balloon-borne or airborne), at most two calibration blackbodies are employed, due to size and mass constraints.
4. Conclusions This paper has introduced a method to solve the problem of an erroneous temperature for one of the two blackbodies used to calibrate radiometrically atmospheric thermal emission spectra recorded by a FTIR spectrometer. This ‘‘unknown” temperature bias translates into a radiance difference between two spectral regions (or between two detectors) and is theoretically calculated and verified against a real case using a reference blackbody source. The minimization method of the effect on the radiance difference or of the brightness temperature difference allows to determine the poorly known blackbody temperature with a satisfying precision (depending on the instrument noise) assuming a good knowledge of the other blackbody temperature. Using this retrieved temperature, we can perform an accurate radiometric calibration of the atmospheric spectrum. The method could be also applied to check the consistency of the radiometric calibration, to verify the effective emissivity consistency between both blackbodies or to analyze the possible dependence of the emissivity against wavenumber (potentially detecting aging or contamination of the blackbody inner surface) when the corresponding temperatures are known within specifications. Acknowledgements We are very grateful to discussions with H.E. Revercomb and for his advice for improve the manuscript. We thank also J.-Y. Mandin for his useful comments on this work.
192
Y. Té et al. / Infrared Physics & Technology 52 (2009) 187–192
Appendix Results predicted by a 2nd order approximation. We assume here a small temperature error DTwbb on the real temperature T true wbb of the warm blackbody:
T wbb ¼
T true wbb
þ DT wbb
ð6Þ
2 1 true true ~Þ ¼ B T true ~ ~ ~ 1 þ A BðT wbb ; m ; m T ; m D T þ T ; m D T A 1 2 wbb wbb wbb wbb wbb 2
ð7Þ where
m ¼ c2
m~ exp c2 T true wbb 2 m~ T true exp c2 T true 1 wbb
m~
wbb
and
~ A2 T true wbb ; m ¼
2 T true wbb
þ c2
m~ þ1 exp c2 T true wbb true 2 ~ m T wbb exp c2 T true 1
m~
wbb
Applying this approximation to Eq. (3), a supplementary term due to the effect of the temperature error DTwbb, cf. (6), is added.
calib calib true ~ ~ ~ DScalib scene ðDT wbb ; mÞ ¼ Sscene ðT wbb ; mÞ Sscene T wbb ; m 1 2 ~ DT wbb þ A2 ðT true ~ ¼ A1 T true wbb ; m wbb ; mÞDT wbb 2 meas Smeas S cbb ewbb Bwbb scene meas Smeas wbb Scbb
ð8Þ
~ We can notice the influence of DTwbb, T true wbb and m on this new term. When the instrument works perfectly and when there is no temperature error, Eq. (8) leads to a correction equal to zero. But if there is a temperature error (DTwbb – 0), a slight difference is observed. Considering the radiance difference between two wave~2 , the correction term of (8), introduces a new ~1 and m numbers m contribution term, cf. (9). calib ~ ~ DSscene ðm~1 ; m~2 Þ ¼ DScalib scene ðDT wbb ; m2 Þ DSscene ðDT wbb ; m1 Þ
ð10Þ
T true wbb is fixed at the correctly measured value and Tcbb, used in the radiometric calibration algorithm, varies around its true value T true cbb . References
where DTwbb is small compared to T true wbb (expressed in Kelvin). Up to the 2nd order of approximation, Eq. (2) becomes:
~ A1 T true wbb ;
2 1 true true ~ ~ ~ DScalib ð D T ; m Þ ¼ A T ; m D T þ T ; m D T A 1 2 cbb cbb scene cbb cbb cbb 2 meas meas S Swbb ecbb Bcbb scene meas Smeas wbb Scbb
ð9Þ
Eq. (9) leads to a non-zero result when there is a non-zero tem~2 –m ~1 . perature error (DTwbb – 0) and when m In the case of a poorly known temperature T true cbb of the cold blackbody (T true wbb correctly measured), the correction term equivalent to Eq. (8), is given by Eq. (10).
[1] ESA, ENVISAT-MIPAS: An Instrument for Atmospheric Chemistry and Climate Research, ESA SP-1229, European Space Agency, ESTEC, Noordwijk, The Netherlands, 2000. [2] R. Beer, T.A. Glavich, M. Rider, Tropospheric emission spectrometer for the earth observing system’s aura satellite, Appl. Opt. 40 (2001) 2356–2367. [3] B. Tournier, D. Blumstein, F.-R. Cayla, G. Chalon, IASI level 0 and 1 processing algorithms description, in: The 12th International TOVS Study Conference (ITSC-XII), The Cumberland, Lorne, Victoria, Australia, 27 February–5 March 2002. [4] H. Fischer, H. Oelhaf, Remote sensing of vertical profiles of atmospheric constituents with MIPAS limb-emission spectrometers, Appl. Opt. 35 (1996) 2787–2796. [5] Y. Té, P. Jeseck, C. Camy-Peyret, S. Payan, G. Perron, G. Aubertin, Balloonborne calibrated spectroradiometer for atmospheric nadir sounding, Appl. Opt. 41 (2002) 6431–6441. [6] C. Piesch, T. Gulde, C. Sartorius, F. Friedl-Vallon, M. Seefeldner, M. Wölfel, C.E. Blom, H. Fischer, Design of a MIPAS instrument for high-altitude aircraft, in: Second International Airborne Remote Sensing Conference and Exhibition, San Francisco, California, 1996. [7] G. Grieco, G. Masiello, M. Matricardi, C. Serio, D. Summa, V. Cuomo, Demonstration and validation of the sigma-IASI inversion scheme with NAST-I data, Q. J. R. Meteorol. Soc. 133 (S3) (2007) 217–232. [8] R.O. Knuteson, F.A. Best, N.C. Ciganovich, R.G. Dedecker, T.P. Dirkx, S. Ellington, W.F. Feltz, R.K. Garcia, R.A. Herbsleb, H.B. Howell, H.E. Revercomb, W.L. Smith, J.F. Short, Atmospheric emitted radiance interferometer (AERI): part I: instrument design, J. Atmos. Oceanic Technol. 21 (2004) 1763–1776. [9] R.O. Knuteson, F.A. Best, N.C. Ciganovich, R.G. Dedecker, T.P. Dirkx, S. Ellington, W.F. Feltz, R.K. Garcia, R.A. Herbsleb, H.B. Howell, H.E. Revercomb, W.L. Smith, J.F. Short, Atmospheric emitted radiance interferometer (AERI): part II: instrument performance, J. Atmos. Oceanic Technol. 21 (2004) 1777–1789. [10] M.G. Mlynczak, D.G. Johnson, H. Latvakoski, K. Jucks, M. Watson, G. Bingham, D.P. Kratz, W.A. Traub, S.J. Wellard, C.R. Hyde, First light from the far-infrared spectroscopy of the troposphere (FIRST) instrument, Geophys. Res. Lett. 33 (2006) L07704. [11] L. Palchetti, G. Bianchini, F. Castagnoli, B. Carli, C. Serio, F. Esposito, V. Cuomo, R. Rizzi, T. Maestri, Breadboard of a Fourier-transform spectrometer for the radiation explorer in the far infrared atmospheric mission, Appl. Opt. 44 (2005) 2870–2878. [12] H.E. Revercomb, H. Buijs, H.B. Howell, D.D. LaPorte, W.L. Smith, L.A. Sromovsky, Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the high-resolution interferometer sounder, Appl. Opt. 27 (1988) 3210–3218. [13] Y. Té, P. Jeseck, C. Camy-Peyret, S. Payan, S. Briaudeau, M. Fanjeaux, High emissivity blackbody for radiometric calibration near ambient temperature, Metrologia 40 (2003) 24–30. [14] P.R. Griffiths, J.A. de Haseth, Fourier Transform Infrared Spectrometry, WileyInterscience Publication, 2007. [15] P. Jeseck, C. Camy-Peyret, T. Hawat, S. Payan, Detector nonlinearity correction scheme for the LPMA balloon borne Fourier transform spectrometer, Appl. Opt. 37 (1998) 6544–6549. [16] E. Lindermeir, P. Haschberger, V. Tank, H. Dietl, Calibration of a Fourier transform spectrometer using three blackbody sources, Appl. Opt. 31 (1991) 4527–4533.