DAWN VIR CALIBRATION DOCUMENT
Version 2.4 (May 2014)
Written by: G. FILACCHIONE (INAF-IAPS, Rome), E. AMMANNITO (INAF-IAPS, Rome)
Document Change History
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Change Date Affected Portions Checked by Approved by
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Version 1.0 January 2011 A. CORADINI
(INAF-IAPS,
Rome)
Version 2.0 October 2013 Chapter 6 : added details M. GIARDINO M.C. DE SANCTIS
about the responsivity (INAF-IAPS, (INAF-IAPS,
formula. Rome) Rome)
Chapter 7 : added some M.T. CAPRIA
explanation about usage (INAF-IAPS,
of internal calibration Rome)
Chapter 8 : added details
about the dark current
subtraction procedure,
corrected CALIB directory
file names.
Version 2.1 November 2013 M. GIARDINO M.C. DE SANCTIS
(INAF-IAPS, (INAF-IAPS,
Rome) Rome)
M.T. CAPRIA
(INAF-IAPS,
Rome)
Version 2.4 May 2014 Chapter 8: added the M. GIARDINO M.C. DE SANCTIS
formula to calculate (INAF-IAPS, (INAF-IAPS, Rome)
the calibrated Rome) Rome)
reflectance factor M.T. CAPRIA
(INAF-IAPS,
Rome)
===========================================================================
1. INTRODUCTION
This document describes the algorithms used to calibrate VIR raw (EDR) data in physical units (RDR, spectral radiance), in order to give to the final user a detailed view of the method used to remove instrumental effects on the data.
A complete calibration campaign of VIR was performed at channel level in Selex Galileo (SG), Florence, immediately after integration and before delivery to Orbital for assemblage on the Dawn spacecraft.
In the SG calibration facilities were performed spectral, geometrical, flat- field and radiometric measurements. thanks to different measurements setups. A description of the methods used and results of these tests is described in De Sanctis et al. (2010). Furthermore in this phase were characterized the focal planes performances (including defective pixels, linearity and dark current at various operative temperatures), the instrumental thermomechanical stability, the data-commanding-telemetry handling and electrical interfaces.
In section 2 is described the experimental setup used for pre-lauch calibrations at SG; section 3 is devoted to the description of the spectral calibration; geometrical calibration is included in section 4; flat-field is described in section 5; section 6 contains a description of radiometric calibration; section 7 is about the internal calibration procedure and finally section 8 explain the algorithms used to convert raw data in spectral radiance or reflectance.
2. CALIBRATION SETUP
The basic setup used during the calibrations consists of an optical bench over which are housed a collimator, a reference target placed at its focal plane and a folding mirror used to move the collimated beam in the instrumental FOV along the azimuthal (sample) and zenithal (line) directions.
As VIR focuses at infinite distance becomes necessary to use a collimator to have a collimated reference beam impinging the optical pupil. The SG-developed collimator uses an off-axis parabola (D=250 mm, F=1020 mm, off axis angle=8°) which guarantees unobstructed beam, reduced aberrations and high spatial scale. For VIR the magnification ratio is equal to:
MR=F_VIR/F_collimator=152mm/1020mm=0.15
which means that 1 mm on the collimator's focal plane corresponds to 0.15 mm on the VIR detector. As VIR focal plane detector has 40 µm pixel pitch (square), this scale corresponds to 4 spatial pixels along both sample and line directions. The collimator's focal plane is equipped with an holder able to sustain several interchangeable targets (pinholes, test slits, MTF masks, matrix of 5x5 microlamps); these elements are used for the different calibrations. The collimated beam is folded towards the instrument thanks to a folding mirror placed over two computer controlled, micrometric mounts able to aim it at steps of 1 µrad along the azimuthal (scan parallel to VIR slit, along sample direction) and zenithal (scan perpendicular to the slit, along lines direction) angles.
In order to reproduce the operative conditions aboard the satellite, VIR is housed into a thermo-vacuum chamber. In these conditions, thanks to the internal cryo-cooler (operating on a Stirling cycle), it's possible to cold down the IR focal plane up to the operative temperature of about 70 K and the CCD at about 160 K.
The collimated optical beam reaches the spectrometer's pupil thanks to a CaF2 window housed in the front of the thermovacuum chamber. This window is characterized by an elevated optical transmittance in the 250-5100 nm spectral range.
All opto-mechanical devices placed on the optical bench are controlled thanks to a dedicated software (OCS, Optical Control System), while VIR is controlled thanks to a separate setup, consisting in the UT (Unit Tester) connected to the experiment through the Proximity Electronics Module (PEM). This system allows to send commands to the instrument, to start acquisitions only when all optical elements commanded by OCS are in the correct configuration and to receive back and record telemetries and scientific data.
3. SPECTRAL CALIBRATION
The spectral calibration concerns with a fundamental aspect of the functional requirements of a hyperspectral imaging spectrometer: the conversion of bands positions along the spectral axis of the detectors in wavelength units.
The spectral calibration is obtained through the following steps:
The following instrumental parameters are deduced from the spectral calibration:
As the instrument uses a diffraction grating which disperses the light according to a linear law we can assume SSI(n) = SSI; in this case the spectral calibration relation assumes the following expression:
λc(n) = λ0 + SSI • b
These quantities were measured during on-ground tests by acquiring several fine spectral scans using a monochromator as a source. The calibration setups used to define the spectral properties of VIR derives from a similar setup developed for VIRTIS/M aboard Rosetta and Venus Express missions (Ammannito et al. 2006; Filacchione 2006).
Two different configurations were used to characterize the spectral response, the first using a transmission method and the second using a diffusion method.
In the first case (transmission) on the optical bench, the source, the monochromator, the test slit and the collimator were present; using this set-up the level of the signal was high enough to stimulate VIR, but the alignment between the output slit of the monochromator and the test slit of the optical bench was difficult to achieve. In the second case (diffusion) on the optical bench were the source, the monochromator, a silvered diffusive target and the collimator; in this case the alignment of the system wasn’t critical, but the level of the signal was lower.
The monochromator scans different wavelengths, thus illuminating the diffusive screen. VIR acquires monochromatic images at each step. Therefore VIR is "simulated" at wavelength steps smaller than its spectral resolution. In this way it is possible to associate to each frame the wavelength of the input beam coming from the monochromator. Studying the profile over the lines of each illuminated band, it is possible to get the spectral response function of that particular band.
3.1 Transmission method
The transmission method was applied only to the visual channel. For each illuminated pixel, the spectral response Function, fitting a Gaussian-like function over the profiles measured during the spectral scans, was computed. With this setup the the intensity of the signal along the slit isn’t uniform. This could be related with a misalignment between the output slit of the monochromator, namely the test slit of the optical bench and the entrance slit of the experiment. Moreover a spectral shift along the slit is apparent, given that at every illuminated band a different central wavelength is found. The central wavelength and the spectral width of the illuminated bands are calculated by averaging such parameters over every illuminated sample. The central wavelength of the band is calculated by using a linear fit while the spectral width is given by a polynomial fit. A summary of the parameters calculated with the fits and their uncertainties are reported in the following table:
Spectral dispersion Spectral width
Model a • x + b a • x4 + b • x3 + c • x2 + d • x + e
Parameters a=1.89297 b=245.744 a=5.25E–11 b=-6.08E–8 c=2.74E–5 d=-0.0049 e=2.13
Sigma σa=0.00016 σb=0.041 σa=0.14E–11 σb=0.14E–7
σc=4.82E–5 σd=0.0068 σe=0.31
In the next table are indicated, for all the illuminated bands, the measured and calculated values of the central wavelength and spectral width. The measured values are averages computed over all the illuminated samples for a fixed band.
Band # λmeas λcal SWmeas SWcal
(nm) (nm) (nm) (nm)
79 395.125 395.289 1.89559 1.88451
80 397.049 397.182 1.89332 1.88290
81 398.964 399.075 1.88235 1.88131
82 400.860 400.967 1.87189 1.87976
83 402.761 402.860 1.86246 1.87824
84 404.662 404.753 1.87010 1.87675
157 542.828 542.94 1.87158 1.82947
158 544.925 544.833 1.84376 1.82947
159 546.835 546.726 1.83146 1.82949
160 548.742 548.619 1.82906 1.82952
161 550.640 550.512 1.82154 1.82956
162 552.548 552.405 1.84028 1.82961
163 554.454 554.298 1.84128 1.82967
237 694.480 694.378 1.81275 1.85861
238 696.323 696.271 1.86955 1.85922
239 698.219 698.164 1.84252 1.85983
240 700.101 700.057 1.85477 1.86045
241 702.000 701.950 1.86519 1.86107
242 703.898 703.843 1.85821 1.86170
317 845.842 845.816 1.91248 1.91559
318 847.74 847.709 1.91959 1.91639
319 849.647 849.602 1.92232 1.91720
320 851.542 851.495 1.91718 1.91800
321 853.447 853.388 1.91865 1.91881
396 995.282 995.361 1.97795 1.99122
397 997.171 997.254 1.98837 1.99243
398 999.063 999.147 1.99155 1.99365
399 1000.95 1001.04 1.98800 1.99487
400 1002.85 1002.93 2.00388 1.99611
401 1004.75 1004.83 2.00954 1.99735
From these measurements’ analyses we have noted the presence of a slight spectral shift occurring along the slit. In order to evaluate this effect we have repeated the calculation of the linear fit coefficients for other samples along the slit (at samples = 110, 140); the results at slit’s center (sample = 128) were previously discussed. This analysis demonstrates the presence of a change in the spectral calibration response when repeated on different points along the slit. The fit parameters with their errors on samples 110, 128, 140 are reported in the next table.
Sample# λmeas SWmeas
(nm) (nm)
110 246.76±0.56 1.8926±0.0022
128 245.83±0.30 1.8926±0.0011
140 245.40±0.19 1.8921±0.0007
The calculations demonstrate that the parameters are incompatible among them so the central wavelengths calculated with the coefficients indicated in the previous table cannot be used and another calibration approach is necessary. At the end of the post-processing analysis it is possible to conclude that the measurements of the spectral width are satisfactory while further measurements are needed to get the dispersion coefficients. Using the Transmission setup, in fact, they seem to be sample dependent. In the next paragraph the results obtained using the Diffusion setup data are discussed.
3.1 Diffusion method
The Diffusion method was used to characterize the spectral response of both Visual and Infrared channels. We use these measurements to determine the central wavelength of the Visual channel and both the central wavelength and the spectral width of the Infrared channel. Comparing these results with the similar profiles taken with the Transmission setup, it is apparent that the spectral shift among profiles taken at different samples is negligible. In this way it is verified that the effect is caused by the Transmission set-up characteristics (difficult to co-align VIR and test slit orientations) and is not due to the VIR malfunctioning.
By using the same technique discussed in advance, we have retrieved the best spectral dispersion and width values. For both channels, the central wavelength of each band b is retrieved through a linear fit while for the spectral width is used a polynomial fit.
Spectral dispersion Spectral width
VIS Model a • x + b a • x4 + b • x3 + c • x2 + d • x + e
Parameters a=1.89223 b=245.660 a=1.3E–10 b=-1.1E–7 c=1.89E–5 d=0.0047 e=1.6
Sigma σa=0.00033 σb=0.085 σa=8.1E–10 σb=7.8E–7
σc=0.26–5 σd=0.0037 σe=1.7
IR Model a • x + b a• x4 + b • x3 + c • x2 + d • x + e
Parameters a=9.4593 b=1011.29 a=-6.8E–10 b=8.23E–7 c=-2.09E–4 d=0.0021 e=13.9
Sigma σa=0.0011 σb=0.28 σa=2.3E–9 σb=1.6E–6
σc=3.80E–4 σd=0.0335 σe=1.2
We report in the next Table the measured and computed values of the central wavelength and spectral width for both channels. The measured values are averaged over all the samples for a given band.
VIS channel
Band λmeas λcal SWmeas SWcal
# (nm) (nm) (nm) (nm)
81 398.875 398.931 2.07338 2.03109
82 400.774 400.823 2.02554 2.03699
83 402.597 402.715 1.99148 2.04287
84 404.436 404.607 2.07068 2.04875
158 544.700 544.633 2.42099 2.44303
159 546.577 546.525 2.44812 2.44754
160 548.465 548.417 2.45310 2.45203
161 550.355 550.309 2.45829 2.45648
162 552.249 552.201 2.47181 2.46091
163 554.144 554.094 2.47652 2.46531
164 556.028 555.986 2.46822 2.46969
238 696.007 696.011 2.69859 2.70952
239 697.892 697.903 2.69611 2.7116
240 699.785 699.795 2.69541 2.71365
241 701.677 701.688 2.70452 2.71567
242 703.572 703.58 2.72082 2.71767
243 705.508 705.472 2.80885 2.71963
317 845.453 845.497 2.75994 2.79344
318 847.337 847.389 2.80736 2.79368
319 849.239 849.282 2.8061 2.79391
320 851.142 851.174 2.79165 2.79412
321 853.043 853.066 2.80487 2.79433
396 994.789 994.983 2.75589 2.80388
397 996.686 996.875 2.8257 2.80439
398 998.595 998.768 2.77639 2.80492
399 1000.46 1000.66 2.79735 2.80548
400 1002.28 1002.55 2.78868 2.80606
401 1004.22 1004.44 2.84745 2.80666
IR channel
Band λmeas λcal SWmeas SWcal
# (nm) (nm) (nm) (nm)
2 1029.3 1030.21 14.0742 13.9467
3 1038.77 1039.67 13.78 13.9478
103 1986.31 1985.6 12.9869 12.7654
104 1995.85 1995.06 12.7585 12.7477
105 2005.35 2004.52 12.6494 12.7299
106 2014.87 2013.98 12.5963 12.7122
208 2978.82 2978.83 11.4667 11.4689
209 2988.07 2988.29 11.2923 11.4666
210 2997.45 2997.75 11.6996 11.4645
211 3006.83 3007.21 11.5063 11.4626
212 3016.13 3016.67 11.337 11.461
315 3991.6 3990.98 12.7906 12.9028
316 4000.3 4000.44 12.6859 12.9335
317 4010.2 4009.9 13.5031 12.9647
367 4482.68 4482.86 14.9175 14.9333
368 4492.2 4492.32 15.1484 14.9807
369 4501.56 4501.78 14.8612 15.0283
370 4511.02 4511.24 15.1136 15.0763
At the end of the post-processing analysis it is possible to conclude that the measurements of the dispersion coefficients are good both for the visual and infrared focal planes, that measurements of the spectral width for the infrared focal planes are compliant with the specifications, and that the spectral width of the visual focal plane, the one computed with the transmission method, gives better results. The quality of the spectral calibration is checked observing the spectrum of a calibrated HgNe pencil lamp.
4. GEOMETRIC CALIBRATION
The geometrical calibration allows characterization of:
1. the field of view, hereafter FOV;
2. the instantaneous field of view (hereafter IFOV) of different pixels along and across the spectrometer’s slit directions (respectively sample and line directions).
We define the pixel function, PF(s), as the convolution of a unitary step function V (s) (representing the real pixel) with the instrumental response along the sample direction, INST(s):
PF(s) = V(s) ⊗ INST(s)
The slit function, SF(l), is given by the convolution of a unitary step function U(l) (representing the spectrometer’s slit response) with the telescope response along the line direction, TEL(l):
SF(l) = U(l) ⊗ TEL(l)
These two responses were measured during the pre-launch calibration campaign acquiring the signal produced by a test-slit, illuminated by a HgNe lamp, having an equivalent width narrower than the instrumental IFOV (the test slit aperture is 3.0 x 0.1 mm, corresponding to 12 x 0.4 pixels at VIR scale). This test-slit is placed at the collimator’s focus and it is moved at subpixel steps perpendicular and parallel to the VIR slit by moving the folding mirror. By using this method it is possible to measure the FWHM of the IFOV on three positions of the FOV (boresight: sample = 128, line = 128), position N: sample = 38, line = 218; position O: sample = 218, line = 38). For the VIS channel the FWHM of the pixel function is ranges over the 237.9–244.1 µrad interval while the slit function is 287.7–389.4 µrad; for the IR channel the ranges are 421.7–488.1 and 350.9–367.3 µrad respectively. These differences are caused by a residual of astigmatism in the optical design.
The determination of the FOV (nominally 3.6° x 3.6°) is possible through the imaging of a 5 x 5 array of microlamps placed at the focus of a collimator. This array was built to cover the entire FOV when placed at collimator’s focus: the presence of a regular grid of subpixel sources allows for evaluation of the imaging and geometrical performances of the experiment. The absolute position of each microlamp was measured with a theodolite placed on the pupil of the collimated beam; when compared to the relative positions of the lamps spots on the images it is possible to infer the dimensions of the instrumental FOV.
Moreover, this setup is particular useful in evaluating the presence of possible "spectral shift", e.g. a mismatch between the position of one monochromatic image with respect to another. This effect is particularly evident on VIRTIS-M on Rosetta, where it reaches a shift of about 8 spatial pixel (samples) between the first and the last image of the VIS channel. The cause of it is a slight misalignment among slit, grating grooves and focal plane orientation (for a full discussion of the spectral tilt and post-processing corrective methods the reader can refer to Filacchione 2006). For VIR several optical improvements were introduced on the grating design that allow drastically reducing this effect. The analysis of the 25 microlamps’ target allows verification that the spectral shift on the VIS channel reaches about 2 spatial pixels between the two spectral extremes of the range. This value comes from the analysis of the distribution of the microlamps position (in sample-line space) on the monochromatic images. As each microlamp has a subpixel dimension when seen by VIR through the optical bench setup, it is possible to measure the associate barycenter position through a 2D Gaussian fit; this procedure is done for each lamp and for every spectral band (432 images).
5. SPATIAL CALIBRATION: FLAT-FIELD
Flat-field is defined as the response of the instrument to a uniform source (Filacchione et al. 2006). It is used to homogenize the pixels’ response across the whole focal plane. In the case of imaging spectrometers using 2D detectors, flat field matrices contain, for each wavelength, the relative variation of the instrumental response with respect to the boresight (sample s* = 127).
The measurements of the VIS and IR flat-field matrices were calculated during the pre-launch tests by acquiring a spatially flat source placed on the focus of a collimator and aligned to the VIR boresight. The source used in the 0.25–2.5 µm range is a lambertian surface illuminated by a QTH lamp; this target is about 10 x 10 cm wide in order to completely fill the instrumental FOV. It is replaced by a blackbody source for the measurement of the flat-field in the 2.5–5.0 µm range. In both cases the flat field is retrieved through a spatial scan across these targets by moving the folding mirror at 1 IFOV step. This approach allows for observation of the same region of the target with each pixel (sample) of the detector, thus eliminating possible target non-uniformity from the flat-field matrices.
The resulting flat-field matrices for the two focal planes are given by the ratio of the signal measured at a certain position of the focal plane (b, s) with respect to the signal measured ad boresight (s = s*) and at the same band position b:
FF(b,s) = Ns(b,s) / Ns(b, s*)
Flat-field matrices are sensitive to the characteristics of the detector (single and clusters of defective pixels, dis-uniformities due to the production process) and of the optical layout (the two horizontal features at samples 80 and 150 are caused by the slit’s shape; several vertical features with a symmetry with respect to boresight are introduced by the grating design).
6. RADIOMETRIC CALIBRATION
As explained in the Flat-Field paragraph, the wide spectral range of the experiment can be explored only by using different sources (Filacchione et al., 2006).
For the radiometric calibration two different sources are necessary:
The input radiance is measured and verified through a laboratory radiometer, (Field-SpecTM spectroradiometer). Unfortunately as the optical pupil of the Field-Spec optics does not match entirely with the VIR pupil, the measured radiance can only be used as a relative value: the "shape" of the radiance, Rad, emitted by the target doesn’t change but the knowledge on the geometric factor (constant and uniform for each spectral channel) is not known. For this reason the overall calibration shall be tested in flight and complemented with specific observations of known targets, such as stars and planets. The lamps used are observed first with the spectroradiometer, and then with VIR. Knowing the value of input radiance, we can associate it with an average of 50 VIR acquisitions of the Spectralon™ target, taken at slit center, with an integration time ti = 10 s. The Responsivity, R, is therefore calculated by applying the following equation:
R(b, s*) = DN(b, s*) / (BB(b)*ti)
where R(b,s*) is the responsivity computed for each band b at the sample s*, DN(b,s*) is the raw signal in digital numbers acquired by the spectrometer for each band b at the sample s*, BB(b) is the radiance of the source measured by the reference spectroradiometer and sampled at the VIR spectral band b and ti is the integration time.
The expansion to the sample of the focal plane different from s* is possible applying the flat-field FF. In this way we retrieve the ITF (Instrument Transfer Function) array:
ITF(b, s) = FF(b, s) • R(b, s*)
The IR channel radiometric calibration is done acquiring directly the radiance emitted by a blackbody source placed at the collimator’s focus. The blackbody temperature is set at different values in order to have a good SNR on several spectral ranges and with different integration times (a summary of the acquisitions is given below). As reported in the next Table, only a limited spectral range can be used for the evaluation of the IR responsivity: for bands < Min Band the signal is very low and it includes only the readout offset and residuals of the dark current; for bands > Max Band value the signal is saturated. After this selection we reduce the signals in the restricted spectral range Min Band < band < Max Band; therefore the responsivity is retrieved by using only the signal intervals as indicated in following:
TBB (°C) ti (s) Min Band Max Band
50 0.2 250 438
1.0 238 280
2.0 238 255
5.0 170 240
100 0.2 238 281
1.0 148 239
2.0 140 195
5.0 120 170
200 0.2 110 174
1.0 80 120
2.0 70 105
5.0 65 95
300 0.2 60 100
1.0 40 68
2.0 35 58
5.0 0 37
350 0.2 0 78
1.0 0 52
2.0 0 35
The IR responsivity is computed by using
R(b, s*)=DN(b, s*) / BB(b) ti
where the blackbody radiance BB is given by Planck’s formula. Finally, applying
ITF(b, s) = FF(b, s) • R(b, s*)
to these data, it is possible to derive the responsivity for each pixel of the IR channel.
7. INTERNAL CALIBRATION
Instrumental performances can be checked during in-flight conditions thanks to the internal calibration sequence. VIR, in fact, can acquire reference signals thanks to the combined use of cover, shutter and VIS and IR lamps (Melchiorri et al., 2003). These lamps, housed on the side of the telescope illuminate the internal side of the external cover. The cover is placed near the entrance pupil of the instrument to minimize optical aberrations. The window of each lamp contains a transparent filter (holmium for the VIS, polystyrene for the IR) to introduce some well-shaped spectral absorption features on the overall spectrum. The signal coming from the two lamps can be used to:
- check the in-flight stability of the instrumental spectral response;
- check the in-flight stability of the flat-field;
- monitor the evolution of defective pixels (number and distribution);
- perform a check on the relative radiometric response of the instrument.
The internal calibration mode, implemented in the VIR on-board software, consist in the acquisition of a sequence of 35 frames: 5 electronic offsets, 5 backgrounds, 5 dark currents, 5 acquisitions of the IR lamp, 5 acquisitions of the VIS lamp, 5 dark currents and 5 backgrounds.
Even if the data acquired during this sequence are not used in the calibration pipeline, they are fundamental to follow the temporal evolution of the instrument and to monitor the overall performances in operative conditions.
8. HOW TO CALIBRATE VIR IN-FLIGHT DATA
From the Dawn Science Center (UCLA-JPL) the VIR team receives data and telemetry packets from the satellite. These packets are processed in the PI institution (INAF-IFSI, Rome, Italy) with a proprietary GSE (Ground Support Equipment) and converted in standard PDS (Planetary Data System) format. Thanks to a dedicated package scripts and routines and by using calibration files distributed with this archive, it is possible to convert raw data in physical units
A raw data cube contains uncalibrated signal Ns in DN; dark currents are periodically stored in the same raw data cube and in each data cube there is at least one dark current acquisition. The dark current must be subtracted from the original data in the raw cube before the conversion in physical units. The number and location of dark current frames in each raw cube is documented in the hkt table (shutter status, open if normal acquisition, closed if dark current acquisition). The same information alternatively can be found by reading the parameter DARK_ACQUISITION_RATE into the data cube label file.
If in a raw data cube there is only one dark current frame, the equivalent dark current frame is the same for every frame in the data cube and is equal to the only dark current frame acquired, If in a raw data cube there are more than one dark current frame, the equivalent dark current frame is the interpolation in time of two consecutive acquired dark frames. The dark subtracted frames are computed subtracting the equivalent dark current frame to the original frame in the raw data cube. At the end of this operation the dark current frames are removed and there will be a dark subtracted data cube with the same bands and samples number of the raw data cube and a number of lines equal to the original minus the number of dark current frames.
This is also the reason why calibrated cubes have a lower number of frames than corresponding raw cubes.
The counts stored in the PDS cube can be converted in physical units of spectral radiance Rad (W m-2 µm-1 sterad-1) by using the following equation:
S(λ(b), x, y) = N s (b, s, l) / (ITF( λ(b), s)* t i)
where:
- S(λ(b),s,l) is the cube calibrated in spectral radiance which have the same bands and samples number of the raw data cube and a number of lines equal to the original minus the number of dark current frames of the raw cube;
- λ(b) is the wavelength associated to band b according to spectral calibration tables of VIS and IR channels (files DAWN_VIR_VIS_HIGHRES_SPECAL_Vx.TAB and DAWN_VIR_IR_HIGHRES_SPECAL_Vx.TAB, respectively);
- s, l corresponds to sample and line location of the pixel in the dark subtracted cube;
- ti is the integration time of the observations (in seconds) as indicated in the PDS header of the file for VIS and IR channels;
- ITF( λ (b), s) is the Instrument Transfer Function matrix for VIS and IR channels (files DAWN_VIR_VIS_RESP_Vx.DAT and DAWN_VIR_IR_RESP_Vx.DAT, respectively).
At the same time, to calculate the calibrated reflectance factor, the equation is:
R(λ(b), x, y) = (S(lambda;(b), x, y) * ( pi*(ssd / K)2 )) / si
where
- R(λ(b), x, y) is the cube calibrated reflectance factor which have the same bands and samples number of the raw data cube and a number of lines equal to the original minus the number of dark current frames of the raw cube;
- K is the value of one astronomical unit expressed in km ( 149597870.7 ) ;
-ssd is the spacecraft heliocentric distance expressed in km, as read from the cube label file in the SPACECRAFT_SOLAR_DISTANCE field
- si is the solar irradiance for VIS and IR channels (files DAWN_VIR_VIS_SOLAR_SPECTRUM_Vx.DAT and DAWN_VIR_IR_SOLAR_SPECTRUM_Vx.DAT, respectively).
This calculus can be applied to high resolution acquisitions (432 bands times 256 samples); in nominal modes, where spatial and/or spectral resolutions are reduced, it is necessary to interpolate both spectral tables and responsivity matrices according to binning values.
In the CALIB directory the following calibration files are stored:
- DAWN_VIR_VIS_RESP_Vx.DAT, a 432x256 floating precision matrix containing the VIR-VIS Instrumental Transfer Function, including the VIS flat-Field.
- DAWN_VIR_IR_RESP_Vx.DAT, 432x256 floating precision matrix containing the VIR-IR Instrumental Transfer Function, including the IR flat-Field.
- DAWN_VIR_VIS_HIGHRES_SPECAL_Vx.TAB and
- DAWN_VIR_IR_HIGHRES_SPECAL_Vx.TAB, 432 row ASCII tables containing the wavelengths of the VIS and IR channels in High Resolution Mode.
- DAWN_VIR_VIS_WIDTH432_Vx.TAB and
- DAWN_VIR_IR_WIDTH432_Vx.TAB, 432 row ASCII tables containing the width of the VIS and IR channels in High Resolution Mode.
These files must be used for cubes collected in High Resolution Mode.
Cubes in Nominal Mode (x3 binning along bands) can be calibrated by using the following spectral calibration files:
- DAWN_VIR_VIS_NOMRES_SPECAL_Vx.TAB and
- DAWN_VIR_IR_NOMRES_SPECAL_Vx.TAB, 144 row ASCII tables containing the wavelengths of the VIS and IR channels in Low Resolution Mode.
- DAWN_VIR_VIS_WIDTH144_Vx.TAB and
- DAWN_VIR_IR_WIDTH144_Vx.TAB, 144 row ASCII tables containing the width of the VIS and IR channels in Low Resolution Mode.
"x" is a digit representing the version number of the file. The first release is "V1".
VIR data included in this release can be calibrated by using this basic pipeline. Further improvements, based on the use of the internal calibration sequences, will be included in the next future.
The actual ITF is also currently under improvement : calibrated values in the spectral range [2.534µm - 3.272 µm ] are still under verification, this is the reason why these values have been put to null into the ITF.
When the validation tests will be completed, the next versions of ITF will be released.
An alternative non-standard calibration procedure, based on external data derived from ground observations, can be found in [7].
9. REFERENCES
[1] E. Ammannito, PhD dissertation, Università degli studi di Padova, Centro Interdipartimentale di Studi e Attività Spaziali (CISAS), 2008. Available on line at http://paduaresearch.cab.unipd.it/760/1/tesi_online.pdf (in Italian)
[2] E. Ammannito, G. Filacchione, A. Coradini, F. Capaccioni, G. Piccioni,M.C. De Sanctis,M. Dami, A. Barbis, Rev. Sci. Instrum. 77, 093109 (2006)
[3] M.C. De Sanctis • A. Coradini • E. Ammannito • G. Filacchione • M.T. Capria • S. Fonte • G. Magni • A. Barbis • A. Bini • M. Dami • I. Ficai-Veltroni • G. Preti • VIR Team, 2010. The VIR Spectrometer. Space Sci Rev DOI 10.1007/s11214-010-9668-5
[4] Melchiorri, R., Piccioni, G., Mazzoni, A., 2003. Review of Scientific Instruments, vol. 74, number 8, 3796-3801.
[5] G. Filacchione, PhD dissertation, Università degli studi di Napoli Federico II, 2006. Available at ftp.iasf-roma.inaf.it/gianrico/phd/Filacchione_PHD_2006.pdf (in Italian)
[6] G. Filacchione, E. Ammannito, A. Coradini, F. Capaccioni, G. Piccioni,M.C. De Sanctis,M. Dami, A. Barbis, Rev. Sci. Instrum. 77, 103–106 (2006)
[7] M. C. De Sanctis , J.-Ph. Combe, E. Ammannito, E. Palomba, A. Longobardo, T. B. McCord, S. Marchi, F. Capaccioni, M. T. Capria, D. W. Mittlefehldt, C. M. Pieters, J. Sunshine, F. Tosi, F. Zambon, F. Carraro, S. Fonte, A. Frigeri, G. Magni, C. A. Raymond, C. T. Russell, and D. Turrini, Detection of widespread hydrated materials on Vesta by the VIR imaging spectrometer on board the Dawn Mission, The Astrophysical Journal Letters, 758:L36 (5pp), 2012 October 20