Design and Optimization of the Calibration Procedure for aMiniaturized Fourier Transform Spectrometer

BORTOLINO SAGGIN* and DIEGO SCACCABAROZZIPolitecnico di Milano, Department of Mechanics, Campus of Lecco, Via M. d’Oggiono 18/a, 23900, Lecco, Italy

This paper presents a Fourier transform infrared (FT-IR) spectrometer

calibration procedure based on an unusual source made from a spectrally

selective surface. An alternative solution to the usual calibrators has been

developed to cope with the tight mass budget of an instrument devoted to

Mars surface exploration. The designed system has proved effective, in

terms of achievable radiometric accuracy, despite the drawbacks due to

the significant reflectivity of the sources. The proposed procedure is a

standard ‘‘two-source’’ approach in which both cold and hot sources are

thermally controlled surfaces, similar to an optical solar reflector,

associated to a filament lamp. Such a system allows the required signal

to be achieved in the 2–25 lm instrument wavelength range. Source

optimization was performed using, as a cost function, the computed

radiometric uncertainty, while the required absolute accuracy of the

instrument was imposed as the optimization constraint.

Index Headings: Fourier transform infrared spectrometers; FT-IR

spectrometry; Calibration; Uncertainty; Radiometric accuracy; Mars

exploration; Instrumentation.

INTRODUCTION

Calibration is a key function for any Fourier transformspectrometer (FTS) and in particular for space-borne ones,which are intended to face harsh and often not controllableenvironments and endure ‘‘dramatic events’’ (such as launchand landing accelerations) or high radiation levels. These issuescan affect instrument performance, impairing the calibrationperformed on the ground, so in-flight calibration is mandatory.Calibration is a well-known procedure and is always critical, asconfirmed by the continuous production of papers on this topicaddressing issues arising in various instruments.1–6

The Mars Infrared MApper (MIMA) is a miniaturizedFourier transform infrared (FT-IR) spectrometer developed forESA mission Exomars Pasteur.7 Despite its advanced devel-opment stage, it was removed last year from the payload afterthe mission redesign, which was carried out under the need tosubstantially reduce mass and costs. MIMA’s geological andatmospheric studies were considered secondary to the mainexobiological goals of the mission. Nevertheless, this very lowresource-demanding spectrometer is a candidate for thepayload of future planetary missions. The instrument spectralrange (2–25 lm) is covered by two channels (short wavelength,SW, and long wavelength, LW) derived from a compositedetector with a PbSe element situated next to a pyroelectricelement.7,8 The detectors share the same optical system,leading to two separate but almost contiguous fields of view.MIMA had to be mounted on a rover pointing platform with 2degrees of freedom (DOF) to scan the Mars surface; due to this

critical location, its overall mass was restrained to 1 kg. Thisrequirement can be understood if one considers the 2.5 kg massof the Mini-TES experiment (miniature thermal emissionspectrometer), a FTS similar to the MIMA’s LW channel thatwas mounted onboard the rovers of the NASA-MER mission(Mars Exploration Rover mission). Along with the limitationsfor mass, the instrument size was limited to a volume of 140mm 3 140 mm 3 120 mm and the allowed power consumptionhad a ceiling of 7 W.9

Under these constraints, MIMA calibration had to beconceived in terms of non-conventional, compact, lightweightsolutions. A forced choice was the integration of theinstrument’s calibrators on the existing cover mechanismbecause the overall mass allocated for the calibration system,10 grams, excluded the possibility of adding a dedicatedmechanism. The main problem was to implement a source thatcould provide the radiance needed for the calibration of bothchannels over the full spectral range, i.e., 2–25 lm. Moreover,the second requirement was that the sources needed tocompletely fill the field of view (FOV) of both channels; thisrequires a disk of about 40 mm diameter with an aperture anglelarger than 68 in one direction and 38 in the other at the opticalentrance of the instrument. Lambertian behavior was preferredfor the emitter. As a driving condition, the absolute radiometricaccuracy of the MIMA was required to be better than 10%.Calibration was scheduled at the beginning of each measure-ment session as a baseline. However, based on prior experiencewith the Planetary Fourier Spectrometer (PFS) instrument, itwas expected that after the initial sessions, once the calibrationparameters had proved to be stable, the calibration frequencycould be reduced to only a periodic check of instrument health.

This paper is organized as follows: the calibration model isfirst described, then the causes of uncertainty are analyzed andthe optimization of the calibration procedure is presented; thedesign of the calibration sources and the predicted radiometricaccuracy complete the paper.

CALIBRATION MODEL

A real interferogram can be written as a function of theoptical path difference (OPD) x between the interferometerarms:10

IðxÞ ¼ 1

2AXZ rmax

rmin

gðrÞDRðrÞ½OðrÞ þ REðrÞ�

3½1þ mðr; xÞei2prx� dr ð1Þ

The product AX is the instrument throughput, DR(r) stands fordetector responsivity, O(r) and RE(r) are the observed sourceand instrument radiances, g(r) is the optical efficiency, andm(r, x) is the interferometer modulation factor. The integral ofEq. 1 is computed within rmin�rmax, i.e., the instrument’sspectral range. The mean value of the interferogram is usually

Received 20 December 2010; accepted 2 March 2011.

* Author to whom correspondence should be sent. E-mail: bortolino.saggin@polimi.it.

DOI: 10.1366/10-06215

Volume 65, Number 6, 2011 APPLIED SPECTROSCOPY 6270003-7028/11/6506-0627$2.00/0

� 2011 Society for Applied Spectroscopy

filtered out using an electrical high pass filter. By Fouriertransforming Eq. 1 within the xmin�xmax OPD range, themeasured spectrum M(r) is evaluated:

MðrÞ ¼Z xmax

xmin

1

2AXZ rmax

rmin

gðrÞDRðrÞ½OðrÞ þ REðrÞ�

3 mðr; xÞei2prxdre�i2prx dx

¼ SðrÞ½OðrÞ þ REðrÞ� ð2Þ

In Eq. 2 all the terms related to instrument characteristics havebeen grouped under the instrument responsivity S(r) in orderto isolate the radiance of the sources. In order to determine theexternal source radiance, O(r), the two functions S(r) andRE(r) must be identified. This can be performed with theclassical ‘‘two-source’’ calibration approach,11 which leads tothe following system of equations:�

M1ðrÞ ¼ SðrÞ�½O1ðrÞ þ REðrÞ�M2ðrÞ ¼ SðrÞ�½O2ðrÞ þ REðrÞ�

�ð3Þ

O1(r) and O2(r) are known (usually blackbody) spectra. Theabove system can be solved with respect to S(r) and RE(r):

SðrÞ ¼ M2ðrÞ �M1ðrÞO2ðrÞ � O1ðrÞ

REðrÞ ¼ O1ðrÞ �M1ðrÞSðrÞ

8>>><>>>:

ð4Þ

If a spectrum M(r) is measured (e.g., during Mars observation)and S(r) and RE(r) are known from the above expression, thenthe calibrated spectrum OM(r) can be obtained as:

OMðrÞ ¼ ½MðrÞ �M1ðrÞ�O2ðrÞ � O1ðrÞM2ðrÞ �M1ðrÞ

þ O1ðrÞ ð5Þ

Equation 5 highlights that OM(r) depends on both themeasured spectrum M(r) and the calibration parameters, sothe accuracy of OM(r) will be influenced by the uncertaintiesof the measured spectra and the reference sources.

UNCERTAINTY ANALYSIS AND OPTIMIZATIONOF CALIBRATION SOURCES

The uncertainty of the calibrated spectrum depends onvarious factors related to the calibration procedure or to theinstrument itself. Measurement repeatability is expressed by thenoise equivalent spectral radiance (NESR), which is the inputsignal that would produce a spectrum equal to that generatedby the detector noise. NESR is generally dependent onwavenumber. In our study a constant value, based on theaverage responsivity, was assumed because instrument perfor-mances were not yet fully defined. Because calibration isusually performed by averaging repeated measurements of thereference sources, the uncertainty affecting M1(r) and M2(r)measurements can be decreased by selecting the proper numberof averages N. The drawback to this procedure is resourceusage, so the trade-off between averages and desiredradiometric accuracy must be balanced. According to the ISO

(International Organization for Standardization) guide,12 theuncertainty of the calibrated spectra uOM(r) is obtained bypropagating the uncertainties of the quantities in the secondterm of Eq. 5. Under the assumption that all the uncertaintiesare uncorrelated, one obtains:

uOMðrÞ ¼ ]OM

]MuM

� �2

þ ]OM

]M1

uM1

� �2

þ ]OM

]M2

uM2

� �2"

þ ]OM

]O1

uO1

� �2

þ ]OM

]O2

uO2

� �2#

1=2

ð6Þ

uM, uM1, and uM2 are the uncertainties of the measured rawspectra, while uO1 and uO2 are the uncertainties due to thereference sources. Each term in Eq. 6 is, in general,wavenumber dependent. As previously mentioned, raw spectrauncertainty is related to NESR and can be reduced byaveraging. Uncertainties uO1 and uO2 are related to thereference sources and include emissivities and temperaturecontributions. In order to optimize the instrument calibrationand define the optimal reference sources, uOM(r) is the costfunction that must be minimized.

Looking at Eq. 6 one can identify three different sources ofuncertainty:

(1) Radiometric uncertainty in the target raw spectrummeasurement;

(2) Radiometric uncertainty in the calibration sources rawspectra measurements;

(3) Uncertainty in the computed reference calibration spectra,due to temperature and emissivity uncertainties.

In the following, the optimization process will analyze andminimize separately the contributions of these terms. The firstterm is expressed by the NESR and is unaffected by thecalibration process. Considering the uncertainty contributiondue to the calibration source measurements, named in thefollowing uOS, one can write:

uOSðrÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNESR2

N

MM �M2

M2 �M1

� �2

þNESR2

N

M1 �MM

M2 �M1

� �2s

ð7Þ

Equation 7 shows that the combined uncertainty uOS(r) isproportional to NESR and depends on the measured radiances.To verify increasing uncertainty with respect to NESR, Eq. 7was rewritten in terms of dimensionless ratios between the rawspectra of the calibration sources and that of the target (i.e.,Mars):

uOSðrÞ ¼ NESR

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

ðk2 � 1Þ2 þ ðk1 � 1Þ2

ðk2 � k1Þ2

s¼ NESR � u incffiffiffiffi

Np

ð8aÞ

k2 ¼M2

MM

¼ O2 þ RE

OM þ RE

ð8bÞ

k1 ¼M1

MM

¼ O1 þ RE

OM þ RE

ð8cÞ� Issues related to phase error correction are not addressed in this paper;each measured spectrum is considered to be phase corrected.

628 Volume 65, Number 6, 2011

k1 and k2 are wavenumber functions, though not explicitlyindicated, N is the number of measurements, and u_inc,introduced for writing convenience, expresses the errorincreasing with respect to NESR. In the following, N is set to1 to highlight how source selection (i.e., the factors k1 and k2)affects uOS(r). It should be kept in mind that RE can benegative because it contains the opposite of the detectorradiance.� Figure 1 shows the uncertainty increasing for a fewcombinations of k1 and k2 ratios.

The (expected) result is that uncertainty increases when themeasured radiances of the sources are similar, so this is acondition to avoid. On the other hand, if the radiance of thecold source is smaller than that of the target, the uncertaintyincrease always has a minimum, achieved for

k2 ¼ 2� k1 ð9Þ

If the condition in Eq. 9 is fulfilled, then u_inc is always 0.7.Other than this common result, the various minimumconditions are significantly different. The k2 range in whichu_inc is close to the ‘‘absolute’’ minimum enlarges as k1

decreases. Thus, having lower values of k1 is preferable sincethe achieved optimum is ‘‘more robust’’ with respect to changesin the target. Moreover, one can notice that until k1 is lowerthan 1, the uncertainty increase is always lower than 1 and aminimum exists. When the cold source is colder than thedetector, i.e., k1 , 0 (in the plot the case k1 ¼�1 has beenreported), the optimum is achieved with the second sourcehaving a radiance more than twice that of the target. Thiscondition might be undesirable because a large radiance of thecalibration source would impose sizing the detector chain onlyto cope with this large signal. Moreover, detector nonlinearitywould be more relevant in calibration. Nevertheless, it has to benoticed that even if Eq. 9 is not fulfilled, the uncertaintyincrease is limited: for instance, if k1 is lower than 0.8, havingk2 within the 1.2–2 range leads to an uncertainty increase lowerthan 0.8, a value that can be further reduced by averagingspectra. As a matter of fact, the minimum averages of thecalibration sources can be derived from the allowed uncertaintyincrease once the sources have been chosen, from Eq. 6.Neglecting the uncertainty of reference spectra, one can write:

uOM ¼ NESR

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ u inc2

N

r¼ NESR � ð1þ aÞ�N

¼ u inc2

ð1þ aÞ2 � 1ð10Þ

where a is the admissible uncertainty increase with respect toNESR. As discussed above, with one calibration source colderand one warmer than the target, the worst u_inc is 1. Even inthis non-optimal condition, by averaging ten spectra theuncertainty increase is lower than 5%.

In order to complete the radiometric error budget, theuncertainties coming from the spectra of the reference sourceshave to be considered: these can be computed by isolating inEq. 6 the O1(r) and O2(r) contributions:

uOREFðrÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðMM �M1Þ2u2

O2

ðM2 �M1Þ2þ ðM2 �MMÞ2u2

O1

ðM2 �M1Þ2

sð11Þ

uO1 and uO2 are the absolute uncertainties of the referencespectra. They can be computed by applying once more theprocedure of the ISO guide.11 The radiance coming from thecover, O(r), considering that it is a non-black sourceilluminated by the filament lamp, can be written as:§

Oðr; e; T; Ti;T‘Þ ¼ e1ðrÞ2hc2r3

eðhcr=kTÞ � 1

þ ½1� e1ðrÞ�2hc2r3

eðhcr=kTiÞ � 1

�

þF2hc2r3

eðhcr=kT‘Þ � 1 � ð12Þ

where e(r) is the spectral emissivity, T is the covertemperature, Ti is the source enclosure temperature, T‘ is thefilament lamp temperature, F is the geometric radiativeexchange factor between the filament lamp and the cover,and h, k, and c have the usual meaning of fundamentalconstants. In our configuration the ‘‘source enclosure’’ is theinterferometer enclosure; therefore, as shown by Eq. 12, wehave to cope with an uncertainty increase due to knowledge ofthe interferometer temperature. This is a direct consequence ofnot using the usual blackbody calibrators, which for this reasonshould always be preferred whenever possible. Temperaturesand emissivities of Eq. 12 will drive the uncertainty of thereference spectra, leading to:**

uO1 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi]O1

]e1

ue

� �2

þ ]O1

]T1

uT

� �2

þ ]O1

]Ti

uTi

� �2s

ð13aÞ

uO2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi]O2

]e2

ue

� �2

þ ]O2

]T2

uT

� �2

þ ]O2

]Ti

uTi

� �2s

ð13bÞ

ue(r) and uT, uTistand for the uncertainties of the emissivities

and temperatures of the sources, respectively. The emissivityuncertainty will be that achievable by the certificationlaboratory. As for the temperature uncertainties, they dependon the design of the sources and on the temperaturemeasurement. Once the above contributions are defined, theabsolute spectral radiance accuracy�� (ASRA) can finally be

� Writing the power balance at the detector incoming radiance is usuallyaccounted positive. So, if the instrument is observing a cold body, such asdeep space or a calibrator colder than the detector, the power balance isdominated by detector emission, leading to a negative radiance.

§ With a ‘‘non-black’’ calibration body, contaminating radiation might comefrom the reflection of the unbalanced beam. This leads to a ghost spectrumwith doubled wavenumber. In our analysis this effect has been discardedbecause, since the calibrating source is Lambertian despite its relevantreflectivity, the contribution is negligible.

** If the two sources are the same body at two temperatures then Eq. 11cannot be applied because uncertainties in the two sources becomecorrelated; the emissivity in this case has to be isolated as the samevariable in both expressions.

�� The adjective ‘‘absolute’’ may sound odd for a ‘‘relative’’ uncertainty butit depends on the usual distinction between the ‘‘absolute radiometricaccuracy’’ and the ‘‘relative radiometric accuracy’’. The latter considersonly the accuracy of the ratio between radiances at different wavelengthsin the same spectrum but not the accuracy of the measured radianceitself, as the former does.

APPLIED SPECTROSCOPY 629

computed:

ASRAðrÞ ¼ uOMðrÞ

OMðrÞð14Þ

ASRA is the typical performance index that must be matchedthrough the instrument design.

It can be noticed that the described optimization can beperformed only if the observed scenario OM(r) is known. Thisis a contradiction, especially for space-borne instruments,which are conceived to be ‘‘ready for the unknown.’’ However,the instrument design is always based on a given referencetarget assumed from existing knowledge of the target.

Summarizing, the described analysis guides the designer inthe calibration definition, highlighting the various contributionsto the overall uncertainty and, as a consequence, the possiblelevers on which one can act to match the radiometric accuracyrequirements. This procedure will be applied in the followingto design the MIMA calibration system.

DESIGN OF CALIBRATION SOURCES

The wavelength range covered by the two channels of theMIMA prevents the same calibration source from being usedfor both channels. Actually, the targets of the two channels arealso different because the SW is primarily devoted to solarabsorption spectrometry while the LW works out the Marsemission spectra. The usual solution to this issue would involvea blackbody for the LW channel and a filament lamp with adiffuser for the SW channel. This would require the capabilityof placing two different sources in and out of the instrumentFOV, but the only element that can be moved in such a manneris the instrument cover. At first a solution using different partsof the cover as different sources for the two channels wasconsidered, in particular a central disk reflecting the radiationof the lamp surrounded by a black surface that could bethermally controlled. The drawback to this kind of solution isthat the instrument responsivity depends on the source angularextension, so to obtain representative results calibration shouldbe performed with a source entirely filling the instrument FOV.

The concept of a ‘‘hybrid’’ cover that was partially reflectingand partially black led to the adopted solution whereby insteadof exploiting different portions of the cover surface, the fullarea was exploited with different behavior at differentwavelengths. The solution was borrowed from thermal controlmaterials where ‘‘Optical Solar Reflectors’’ (OSR) are widelyused to reflect the sun’s radiation while preserving highemissivity in the mid-infrared. The concept is quite simple: aquartz layer that is transparent in the visible–near-infrared(NIR) range but opaque in the mid-infrared (MIR) range isplaced on the top of a specular aluminum plate. Most of thesolar radiation is transmitted by the quartz and reflected backby the metallic surface underneath, so the system behaves as amirror for the sun’s radiation. In the MIR range, conversely,the quartz behaves almost as a blackbody. For our application,the different behavior in the NIR (specular) and in the MIR(black) was sought. Although the same concept could beimplemented with a specifically designed dichroic mirror, thesolution based on the silica layer was pursued because of itsadvantages in terms of proven stability in a space environmentand its reproducibility and cost effectiveness. A system basedon a custom-designed dichroic, however, would allow thealmost free selection of the wavelength range of reflection, andthe transition from reflection to transmission could be mademuch sharper, so it could be a solution in cases with differentrequirements.

The choice of using the cover as the source for the LWchannel derived from the possibility of accurately measuringthe emitter temperature, practically impossible if one wouldexploit, for instance, the emission in the MIR range of thewarm parts of the filament lamp. The calibration systemscheme is shown in Fig. 2. The internal surface of the cover ismade up of a stack of three components: a resistance filmheater bonded to an aluminum disk with a quartz plate (0.5 mmthick, sandblasted and aluminized on the rear surface) on thetop. The cross-section is shown in Fig. 2a, Fig. 2b shows thecover system integrated in the spectrometer, and the calibrationmechanism assembly is shown in Fig. 2c. The cover in thermalequilibrium with the Martian atmosphere (from thermal

FIG. 1. Uncertainty increase (u_incr) as a function of the ratios between the calibration sources and target raw spectra.

630 Volume 65, Number 6, 2011

analysis the temperature at instrument switch-on will be lowerthan �20 8C) acts as cold source for both channels. The hotsource is obtained by powering the heater and illuminating thecalibration surface by means of a filament lamp. The lamp ispartially collimated by an integrated parabolic mirror whoseprojected beam fully illuminates the cover. The OSR coatingprovides in the LW channel spectral range an averageemissivity of about 0.9; this is low if compared with the usual0.98–0.99 figures of calibration bodies. Moreover, because ofthe silica spectral features the cover is not expected to have flatemissivity within the instrument wavelength range. All thesefeatures affect the calibration accuracy so only ASRAcomputation can prove whether the conceived calibrationprocedure is acceptable or not. The cover emissivity wasevaluated in the design phase from the silica optical properties;once realized, the reflectivity was measured and the emissivityderived from it. Both are shown in Fig. 3.

The calibration uncertainty depends on the accuracy of thetemperature measurements of the reference sources. Twoplatinum resistance thermometers were inserted, respectively,in the center and at the border of the aluminum disk. The

measurement chain accuracy however, is not the onlyuncertainty source since temperature differences within thecalibrator area and drifts during the measurement time also leadto uncertainty. The matter was investigated using a thermalmodel of the cover, allowing prediction of the calibrationsurface temperature distribution and its evolution with time.The model considers the aluminum plate with the silica layeron top, glued along the border to the external frame of thecover, which is radiatively and convectively cooled by theMartian environment, with an atmosphere at �70 8C (worstcase assumption). The heater is a film resistor with uniformsurface power density and 0.5 W overall power dissipation.The predicted temperature distribution five minutes afterswitching on the heater is shown in Fig. 4.

The analysis shows that the maximum temperature differ-ence is within 0.6 8C, while temperature standard deviation islower than 0.2 8C. This result is in agreement with therequirements identified in the radiometric uncertainty budget.As previously mentioned the emissivity in the wavenumberregion 400–2000 cm�1 is between 0.7 and 0.9, while it falls tolower values at some spectral bands (see Fig. 3). Thecalibration procedure is not compromised by these gapsbecause the low emissivity regions are near the maximum ofthe blackbody emission. As far as the SW calibration strategy,the cover at 40 8C could not be used alone as the hot referencesource because above 3500 cm�1 its emitted radiance is oneorder of magnitude lower than that expected at Mars. Thus, thecover spectral range dominated by reflection was exploited toconvey the radiance of the filament lamp (nominal filamenttemperature of 1770 K). In this way the input spectrum iscomplemented in the high wavenumber region, providing forthe hot reference spectra radiances larger than those expectedfrom the target. The calibration procedure is schematized inFig. 5.

RADIOMETRIC ERROR BUDGETS

In order to match the scientific objectives of MIMA, aminimum absolute radiometric accuracy of 10% had to be

FIG. 2. (a) Cross-section of the calibrating system; (b) MIMA instrument with the cover rotated in the fully closed position; and (c) calibration system assembly.

FIG. 3. Measured reflectivity of the internal surface of the cover (black line),and the calculated emissivity (gray line).

APPLIED SPECTROSCOPY 631

achieved. LW and SW NESR were respectively estimated as4.8 3 10�7 and 2 3 10�7 (Wcm�1sr�1) on the basis of thedetector properties and instrument efficiency analyses. Giventhese constraints and accounting for the characteristics of thecalibration sources, the ASRA was computed under thefollowing additional assumptions:

(1) The temperatures of the hot and cold sources were obtainedfrom thermal analysis of the cover. The heater powerdissipation was sized to achieve in the ‘‘cold casecondition’’ a temperature larger than the largest expectedvalue of the Mars surface. The resulting calibration sourcetemperature range was from �80 8C to þ60 8C dependingon the environmental conditions. The cover at�20 8C wasused as the reference cold source, a worst ‘‘hot case’’among the expected temperatures at the start of observa-tions. On the other hand, the hot calibration source wasobtained from the cold operational case, with a wind speedof 20 m/s and a temperature of �70 8C. Under theseenvironmental conditions, the cover with the heater onreaches a temperature of about 40 8C (Fig. 4).

(2) The overall uncertainty in the calibrating body temperaturewas set to 0.5 8C to account for different contributions suchas non-uniformity, temperature drifts, and measurementchain uncertainty.

(3) Accounting for the stability of the lamp emission asobserved during laboratory tests, a filament temperatureuncertainty of 10 8C was considered.

(4) The relative uncertainty in the spectral emissivity mea-

surement was assumed to be 1% over the full instrument

range (2–25 lm).

(5) Mars surface temperature of 10 8C and albedo of 15% of

the average solar constant of 550 W/m2 were used to

evaluate the target radiance.

(6) The number of calibration spectra N was set to 10 (leading

FIG. 4. (a) Temperature distribution on the MIMA cover. (b) Temperature distribution over the calibrating surface.

FIG. 5. Hot and cold source generation schemes for the instrument channels. FIG. 6. Absolute radiometric accuracy for the LW and SW channels.

632 Volume 65, Number 6, 2011

to a maximum NESR increase of 5%, considered acceptablewithin the radiometric error budget).

(7) The non-uniformity of the instrument enclosure tempera-ture was set to 5 8C as a result of the thermal analysesperformed and considering that only one measurementpoint was available.

The computed ASRA curves for both channels are shown inFig. 6. The main result is that the radiometric accuracyrequirement is fulfilled in both cases. In particular, the LWchannel accuracy is always lower than half the allowed value,while for the SW channel ASRA is close to the 10% limit,especially in the low wavenumber region. This is due to thehigh reflectivity of the cover, which in the low wavenumberregion leads to significant reflection of the backgroundradiation, increasing the overall uncertainty. The majorcontribution to the uncertainty in this spectral range derivesfrom the non-uniformity of the background, which, asexplained, was set to 5 8C. Even if the instrument temperaturemeasurement were refined to reduce this contribution, theoverall accuracy would not dramatically improve because thetemperature lamp uncertainty gives comparable contributionsin the higher wavenumber range. Therefore, for what concernsthe SW channel, if a significantly higher accuracy wererequired a general re-design of the calibration system would benecessary.

CONCLUSIONS

The presented calibration system, conceived for an FT-IRspectrometer working in the 2–25 lm spectral range, hasproved capable of matching the mild requirement of 10%absolute radiometric accuracy. The proposed scheme is basedon a spectrally selective surface thermally controlled andilluminated by a filament lamp, which replaces the usualblackbody calibrators in the full spectral range. The mostremarkable characteristics of this calibration system are itslightness and compactness, making it probably the onlyfeasible solution given the mass, size, and power availabilityof the MIMA instrument. Optimization of the sourcetemperatures was carried out to minimize the uncertainty ofthe calibrated spectra. It has been shown that when using twocalibration sources with, respectively, smaller and largerradiance than that of the target, an optimal configuration canalways be found. Moreover, in the optimal configuration, theincrease in calibration uncertainty is always the same. A morerobust calibration system can be implemented if one source issignificantly colder than the target because uncertaintybecomes weakly affected by target radiance changes. The

drawbacks deriving from the use of calibration bodies withlarge reflectivity were considered, but for the analyzed case itwas shown that they can be effectively managed. Finally, itwas shown that for the considered instrument the increase inradiometric uncertainty due to the reflectivity of the calibrationsources is comparable to that due to their temperature stability.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support from the ItalianSpace Agency (ASI) under the research program ‘‘ExoMars, MIMA,’’ Prof.Sergio Fonti for the source reflectivity measurements, and the MIMAinstrument PI, Dr. Giancarlo Bellucci.

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