Calibration of AstroSat/UVIT Gratings and Spectral Responses
JJ. Astrophys. Astr. (0000) :
Calibration of
AstroSat / UVIT Gratings and Spectral Responses
G. C. Dewangan Inter-University Centre for Astronomy and Astrophysics (IUCAA), SPPU Campus, Pune, India. * Corresponding author. E-mail: [email protected] received 7 November 2020; accepted 20 December 2020
Abstract.
AstroSat / UVIT carries two gratings in the FUV channel and a single grating in the NUV channel.These gratings are useful for low resolution, slitless spectroscopy in the far and near UV bands of a variety ofcosmic sources such as hot stars, interacting binaries, active galactic nuclei, etc. We present calibration of thesegratings using observations of UV standards NGC 40 and HZ 4. We perform wavelength and flux calibrationand derive e ff ective areas for di ff erent grating orders. We find peak e ff ective areas of ∼ . at 2325Å forthe − ∼ . at 1390Å for the − ∼ . at 1500Åfor the − ≈ .
6Å in the − − ≈ / NUV gratings and all broadband filters. We have generated spectral response ofthe UVIT gratings and broadband filters that can directly be used in the spectral fitting packages such as
XSPEC , Sherpa and
ISIS , thus allowing spectral analysis of UVIT data either separately or jointly with X-ray data from
AstroSat or other missions.
Keywords.
Ultraviolet astronomy – ultraviolet telescopes — ultraviolet detectors — calibration
1. Introduction
The Ultra-Violet Imaging Telescope (UVIT; Subrama-niam et al . 2016; Tandon et al . 2017; Tandon et al .2020) is one of the four co-aligned payloads on-board the Indian multi-wavelength space observatory
AstroSat (Agrawal, 2006; Singh et al ., 2014). UVITis a twin telescope system, one of them is designedto observe in the far ultra-violet band (1300 − − − ff er in having di ff erent photo-cathodes as perthe wavelength band, and operate simultaneously. Thebeam splitter and the mechanical mounting of the tele-scopes cause the NUV channel field to be invertedand rotated by 33 ◦ with respect to the FUV channelfield. Each channel is equipped with a set of filtersthat allow selection of bands with spectral coverage of ∆ λ ∼ − ∆ λ ∼ − ∆ λ ∼ − − . − on CaF2 substrates of 4.52 mm thick-ness. The dispersion in the detector plane caused byeach grating is 12Å arcsec − and 6Å arcsec − in thefirst and second order, respectively, at 1350Å. One ofthree gratings is mounted on the NUV channel filterwheel while the other two gratings are mounted on theFUV channel filter wheel such that their dispersion axesare nearly perpendicular. Such an orthogonal arrange-ment of FUV gratings helps in avoiding contaminationof nearby sources in the grating images. A source alongthe dispersion arm of the main target in one FUV grat-ing image will cause contamination while the disper-sion arms will be well separated in the other FUV grat-ing image due to the orthogonal arrangement. The FUVgratings and the detector are designed to maximize thee ffi ciency in the m = − ffi ciency in the m = − et al . (2017); Tandon et al . (2020).The UVIT gratings have been described with di ff erent © Indian Academy of Sciences 1 a r X i v : . [ a s t r o - ph . I M ] F e b J. Astrophys. Astr. (0000) :
Figure 1 . FUV / NUV Grating images of NGC40. The negative grating orders are marked. The image sizes are ∼ . names, in Table 1 we list all the IDs to avoid any con-fusion when using di ff erent resources. Here we referthe gratins as FUV-Grating1 (FUV-G1), FUV-Grating2(FUV-G2) and NUV-Grating (NUV-G).In this paper, we present calibration of the UVITgratings. Some of the results derived in this paper arepresented in Tandon et al . (2020). Here, we presentthe calibration of the UVIT gratings, some results ofwhich can be found in Tandon et al 2020. Our updatedwork here results in minor changes to the wavelengthand flux calibrations, and also includes additional grat-ing orders. We describe the calibration method, de-rive additional calibration products and discuss cross-calibration between the gratings and broadband filters.The paper is organized as follows. We describe theUVIT data and the reduction in Sec. 2., extraction ofone dimensional (1d) grating spectra in Sec. 3., andwavelength calibration in Sec. 4.. We derive e ff ectiveareas and perform flux calibration in Sec. 5., and dis-cuss cross-calibration between the gratings and broad-band filters in Sec. 6. In Sec. 7., we derive instrumentalresponse in the form of a product of redistribution ma-trix and ancilliary response that can be directly used inpopular spectral fitting packages in X-ray astronomy.Finally we summarize our results in Sec. 8..
2. Calibration observations and data reduction
We used UVIT observations of NGC 40 and HZ 4,these observations are as listed in Table 2. The plan-etary nebula NGC 40 has a rich set of UV emissionlines and is well suited for wavelength calibration. Thewhite dwarf HZ 4 is a well-established spectrophoto-metric standard with nearly featureless spectrum, andis appropriate for flux calibration (e.g., Bohlin et al .1990). HZ 4 has also been used for the photometriccalibration of UVIT filters (Tandon et al ., 2017; Tan- don et al ., 2020)We used the Level1 data from the observationslisted in Table 2. We used the UVIT pipeline CCDLAB(Postma & Leahy, 2017) to process the Level1 data.The pipeline performs corrections for field distortion,centroiding bias, flat field, pointing drift and accountsfor frames rejected due to cosmic rays or missing fromthe level1 data. We used the VIS images to generatedrift series which could then correct for the pointingdrift in each orbit. We generated cleaned images foreach orbit, aligned and merged them for each grating,as shown in Figure 1. The x,y coordinates in these im-ages represent 1 / / ≈ .
413 arcsec wide. The images show the undispersedzeroth order image together with the dispersed ± ± m = − m = − FW H M ∼ et al ., 2017).For the calibration and analysis of the UVIT dataprocessed with the CCDLAB pipeline, we have de-veloped a software package UVITTools in the Julialanguage (Bezanson et al ., 2012). We have used thispackage extensively here. We also used the FTOOLS ,Sherpa (Freeman et al ., 2001) and XSPEC (Arnaud,1996) packages for generating response files and fitting https://heasarc.gsfc.nasa.gov/lheasoft/ . Astrophys. Astr. (0000) : Table 1.
UVIT Grating parameters
Parameter FUV-Grating1 FUV-Grating2 NUV-GratingFilter Wheel Slot number 4 6 4IDs in APPS 4 - grating1 (FUV) 6 - grating2 (FUV) 4 - grating (NUV)IDs in CCDLAB FUV Grating1 FUV Grating2 NUV GratingThis paper FUV-G1 FUV-G2 NUV-GIDs in Tandon et al . (2020) FUV1 FUV2 NUVIDs in Tandon et al . (2017) 2nd FUV grating ( m = − λ – – 2100Å m = − λ ∼ ∼ .
6Å 14 .
6Å 33Å
Figure 2 . NUV Grating image of NGC 40 with the gratingorders marked. The extent along the dispersion directionand the width along the spatial direction used to extract the1d spectrum is shown as the rectangular region covering the m = − the data.
3. Extraction of 1d spectra
It is clear from Fig. 1 that the dispersion axes are notexactly aligned to either of the x or y axis. We mea-sured the tilt angle relative to the x-axis and found thatthe dispersion axes can be represented by the linear re-lations y = mx + c where m = tan θ , c = y o − mx and x and y are the pixel coordinates of the centroidof the zero order image. We list the tilt angles in Ta-ble 3. The linear relations define the spectral trace i.e.,the centroids of the cross-dispersion spatial profiles ateach pixel on the dispersion axis. There is no additionalsignificant distortion in the dispersion direction, so spa-tial profile fittings to trace the dispersion direction is notrequired.We define coordinates along the dispersion direc-tion as the pixel coordinates relative to the zero orderposition. We examined the grating images visually anddetermined the range of coordinates for di ff erent grat-ing orders. These ranges are listed in Table 3. We useda 50 pixel width along the spatial direction centered onthe trace defined by the linear relations and summedthe counts to generate 1d spectra of a source of interest.Figure 2 shows the region used for the extraction of 1dspectrum of NGC 40 in the m = −
4. Wavelength Calibration
The raw 1d spectra shown in Figures 3 are not in phys-ical units. In order to convert the relative pixel coordi-nates along the dispersion direction, we used the emis-sion lines from NGC 40. We measured the emissionline positions by fitting Gaussian profiles along withlow order polynomial for the continuum. We then iden-tified the strong emission lines in the UVIT spectra us-ing the emission lines listed in Feibelman (1999) basedon
IUE observations. We then fitted the following lin-ear relation between the line wavelengths and the rela-tive pixel numbers. λ (Å) = a + bX , (1)where X is the pixel coordinate along the dispersion di-rection relative to the zero order position. The best-fitlinear relations are shown in the right panels of Fig-ures 3 for the blazed orders of FUV and NUV gratings.The slope and intercept of the best-fitting linear disper-sion relation are listed in Table 3. We converted thepixel coordinates in the raw grating spectra to wave-length in Angstroms using the above dispersion rela-tions.
5. Flux Calibration and E ff ective Area curves Flux calibration is the process of converting the ob-served count rate to flux density as a function of wave-
J. Astrophys. Astr. (0000) :
Table 2.
UVIT / Grating observations of NGC 40 and HZ 4
Target ObsID Date of Observation Grating Exposure Time (s) window sizeNGC 40 C02 010T01 900000 2016-12-07 FUV-G1 1194.0 350 × × × × × × Table 3.
Parameters for 1d spectral extraction and the coe ffi cients of the linear dispersion relation Grating Tilt angle ( θ ) Order Range in relative Pixel coordinate (X) Linear dispersion relationIntercept ( a ) Slope ( b )FUV-G1 358 . ◦ − −
629 to −
413 43 . − . . ◦ − −
323 to − − . − . . ◦ − −
624 to −
426 31 . − . . ◦ − −
313 to −
228 45 . − . . ◦ − −
545 to −
336 45 . − . Table 4.
The coe ffi cients of the best-fitting polynomials to the e ff ective areas of UVIT gratings Coe ffi cient FUV-G1 FUV-G2 NUV-G m = − m = − m = − m = − m = − c . − . . − . . c − . . − . . − . c . . . − . . c − . . − . × − . × − − . × − c . × − − . × − . × − − . × − . × − c − . × − . × − − . × − . × − − . × − c . × − − . × − – – 6 . × − c – 2 . × − – – − . × − λ . . . Astrophys. Astr. (0000) : c o un t s / s FUV Grating1, order=-2
625 600 575 550 525 500 475 450
Pixels number from 0th order S i g m a P i x e l nu m b e r f r o m t h o r d e r Wavelength (Å) D a t a - M o d e l c o un t s / s FUV Grating2, order=-2
620 600 580 560 540 520 500 480
Pixel number from 0th order S i g m a P i x e l nu m b e r f r o m t h o r d e r Wavelength (Å) D a t a - M o d e l c o un t s / s NUV grating -1 order
525 500 475 450 425 400 375 350
Pixel number from 0th order S i g m a P i x e l nu m b e r f r o m t h o r d e r Wavelength (Å) D a t a - M o d e l Figure 3 . The UVIT grating spectra of NGC 40 (left panels) and pixel-wavelength calibration (right panels) of the blazedorders (top panels: FUV-G1, m = −
2; middle panels: FUV-G2, m = −
2, bottom panels: NUV-G, m = − J. Astrophys. Astr. (0000) :
NUV Grating, order=−1 E ff ec ti v e A r ea ( c m ) D a t a − M od e l −2−1012 Figure 4 . The m − = − ff ective area,the best-fitting polynomial and the residuals. length. The background-subtracted net count rate is re-lated to the incident flux density f λ [ergs cm − s − Å − ]as C ( X ) = (cid:90) R X λ A λ f λ (cid:18) λ hc (cid:19) d λ (2)where C ( X ) is the net count rate at X along the disper-sion direction, R λ X gives the probability that a UV pho-ton of wavelength λ gets detected at X , A λ is e ff ectivearea of the spectrometer accounting for the collectingarea of the telescope, reflectivity of the mirrors, grat-ing e ffi ciency, detector quantum e ffi ciency and attenua-tion e ffi ciency of any other optical element. Thus A λ istelescope area corrected for all losses. In principle, A λ can be determined from pre-launch lab measurements,however, the various e ffi ciencies generally change withtime during and after launch. Hence, A λ is generally de-termined or corrected based on observations of standardsources with well measured fluxes. Eqn. 2 is appropri-ate for the photon counting data from UVIT, and canbe written in matrix form with λ , X now representingwavelength and spectral bins, C X = (cid:88) λ R X λ A λ f λ λ hc (3)In the case of dispersive spectrometers such as theFUV / NUV gratings with suppression of order-overlap,the response matrix can be assumed to be diagonal.Hence R X λ = λ and X follow the dispersion re-lation. Thus, f λ = C λ ( hc /λ ) A λ , (4) where C λ is the count rate spectrum.To determine the e ff ective areas of the gratings, weused the UVIT grating observations of spectrophoto-metric standard HZ4 (whose UV spectral flux valueswere obtained from spectrum file hz4 stis 005.fits avail-able at HST-CALSPEC ). We matched the wavelengthsbins of C λ measured with UVIT gratings and the spec-trum by linearly interpolating the standard spectrum.One can then calculate the e ff ective area of the UVIT-gratings using Eqn. 4. However, we note that HZ 4shows strong absorption lines at 1216Å (Ly α ) and1400Å, and the spectral resolution of the standard spec-trum measured with IUE in the far UV band is su-perior compared to that of the UVIT grating spectra.We therefore smoothed the HZ4 standard spectrum tomatch the UVIT grating spectral resolution. We usedGaussian kernels with widths that resulted in smoothe ff ective areas using Eqn. 4 for di ff erent grating orders.The e ff ective areas thus derived are shown in Figure 4for the − − ff ective ar-eas with low order polynomials of the form A λ = (cid:80) c n ( λ − λ ) n so that the observed count rate spectrumcan be converted to the fluxed-spectrum by dividing thebest-fitting polynomials using Eqn. 4. The best-fittingcoe ffi cients are listed in Table 4, and the best-fittingpolynomials are shown in Fig. 4 and Fig. 5.
6. Cross-calibration between gratings and broad-band filters
The flux densities measured by broadband filters attheir mean wavelengths must be the same as those mea-sured by the gratings at the same wavelengths if themean wavelengths represent the e ff ective wavelengthsof the filters. Small discrepencies may be expected asthe mean wavelengths of the UVIT filters are not de-fined to filfil the above condition (private communica-tion with S. N. Tandon). Nevertheless it is useful tocompare the flux measured with the gratings and broad-band filters. As mentioned earlier, gratings introducedistortion making the PSF slightly poorer. Hence, thesame sizes for the extraction regions i.e., the spatialwidth along the cross-dispersion direction in the caseof grating observations and the diameter of the circu-lar region in the case of broadband filter observations,may not provide the same flux densities. Therefore it isimportant to cross-calibrate the gratings and the broad-band filters. . Astrophys. Astr. (0000) : FUV Grating1, order=−2 E ff ec ti v e A r ea ( c m ) D a t a − M od e l −1012 Figure 5 . The m = − ff ective areas, the best-fitting polynomials and theresiduals. Wavelength (Å) f ( e r g s c m s Å ) FUV-Grating1FUV-Grating2NUV-GratingFilters
Figure 6 . A comparison of flux densities at various wavelengths derived from the FUV / NUV broadband filters and gratingobservations of HZ 4.
J. Astrophys. Astr. (0000) :
For this purpose, we used the calibration informa-tion and count rates already derived by Tandon et al .(2020). For HZ 4, we used their corrected count ratesthat were derived after applying corrections for flat fieldand saturation e ff ects. We converted these count ratesto flux densities using the unit conversion (UC) factorswhich we calculated from the ZP magnitudes listed inTable 3 of Tandon et al . (2020). We derived the UC fac-tors from the ZP magnitude as follows (Tandon et al .,2017), UC = − . ( ZP + . λ mean , (5)where UC is in ergs cm − s − Å − and λ mean is in Å.The flux density f λ in ergs cm − s − Å − is f λ = CPS × UC , (6)where CPS is the count rate in counts s − . In Table 5,we list the net count rate from (Tandon et al ., 2020), theUC factors and flux density calculated using Eqn. 5 andEqn. 6 for HZ 4.In order to check possible calibration di ff erencesbetween the flux densities derived from the gratingsand broadband filters, we plot FUV / NUV grating spec-tra and flux densities derived for di ff erent filters in Fig-ure 6. It is clear that, except for the F148W (CaF2-1)filter, the flux measurements agree very well betweenthe gratings and the broadband filters. The F148Wflux density is ∼
25% lower compared to that mea-sured with the FUV gratings. The discrepancy is ata level of 2 . σ . In comparison to the standard spec-trum ( hz4 stis 005.fits) used for the calibrationof gratings, the F148W flux density is also lower by ∼ ff ective areas from (Tandon et al ., 2020) and theFUV-G1 and NUV-G spectra. The predicted count ratesare listed in Table 5. It is clear that the observed andpredicted count rates agree very well. This shows theimportance of using e ff ective areas as discussed below.Based on the above analysis, we recommend a cross-dispersion width of 50 pixels for spectral extractionof point sources. In case of poor tracking correctionand extended sources, a larger cross-dispersion widthshould be used.
7. Grating spectral responses and multi-wavelengthspectroscopy
Working with data from di ff erent instruments onboard AstroSat require tools and techniques to faciliate jointanalysis of multi-wavelength data. In particular, thebroadband spectral coverage of
AstroSat , from near UVto hard X-rays, requires tools for simultaneous fitting ofspectral models to the multi-wavelength data. Due tothe complex interactions when X-rays go through thedetector material, the response function of X-ray detec-tors are generally complex, and the X-ray spectral datacannot be directly converted to the source spectrum.X-ray spectral analysis begins with an assumed sourcespectral model which is then folded with the instrumentresponse that results in model spectral data which isthen compared with the observed spectral data. Thesource spectrum is thus inferred from the best-fittingmodel. Grating spectrometers, such as the UVIT grat-ings, have much simpler response functions, and onegenerates a fluxed spectrum directly from the observa-tions using the dispersion relation and the wavelength-dependent e ff ective area or sensitivity curve as de-scribed in the previous section. The source spectralproperties are inferred from the fluxed spectrum aftercorrecting for the instrumental spectral resolution. It ispossible to treat the photon counting data from UVITsimilar to the X-ray data that are also photon count-ing by generating appropriate spectral responses in theform of a redistribution matrix (RMF) and ancillary re-sponse file (ARF), and use Eqn. 7 below which is sim-ilar to Eqn. 2 to infer the source spectrum. One canthen perform joint spectral analysis of UVIT and X-raydata from SXT, LAXPC and CZTI. In the following, wegenerate the count spectrum (i.e., distribution of pho-ton counts in di ff erent spectral channels), redistributionmatrix and ancillary response for UVIT gratings andbroadband filters. Such an approach is more accuratethan directly converting the count rates to flux densitieswith unit conversion factors and zero point magnitudesfor various filters as the latter quantities depend on thespectral shape. The unit conversion factors and zeropoint magnitudes are derived for the particular spectralshape of the spectrophotometric standard HZ 4 and areunlikely to be strictly correct for objects with di ff erentspectral shape.For the UVIT gratings, we constructed a countspectrum (counts vs spectral channels) from the uncal-ibrated 1d spectrum (counts vs relative pixel coordi-nates) in the same format as the X-ray spectral PHAfiles. For this purpose, we added a positive integernumber to the relative pixel coordinate and convertedto spectral channels (I) which start from 1. This countspectrum is related to the source spectrum in a way sim- . Astrophys. Astr. (0000) : Table 5 . The unit conversion factor (UC) for UVIT filters, and the observed count rate, flux density and predicted count ratefor HZ 4 in di ff erent filters. Filter λ mean UC HZ 4(Å) (ergs cm − s − Å − ) Obs. CPS a f λ b Pred. CPS c F148W CaF2-1 1481 (2 . ± . × − . ± .
062 21 . ± . . ± . × − . ± .
068 19 . ± . . ± . × − . ± .
068 15 . ± . . ± . × − . ± .
11 5 . ± . . ± . × − . ± . . ± . . ± . × − . ± .
067 7 . ± . . ± . × − . ± .
013 37 . ± . . ± . × − . ± .
022 27 . ± . . ± . × − . ± .
019 5 . ± . a Observed count rate in counts s − . Errors on the observed CPS are less than 2%. b In unit of 10 − ergs cm − s − Å − . c Predicted count rate using the e ff ective areas provided in (Tandon et al ., 2020) and the FUV-G1 and NUV-Gspectra of HZ 4 shown in Fig. 6. N o r m a li ze d c oun t s s − k e V − −3 −3 −3 D a t a / M od e l Energy (keV) − × − × − ν F ν ( e r g s c m − s − ) Wavelength (Å)
Figure 7 . Comparison of count PHA spectrum of Fairall 9 with instrument response and fluxed PHA spectrum with diagonalresponse.
Left panels:
Count PHA data (black open circles), flux PHA data (red filled circles), the same powerlaw fittedto the both datasets and the data-to-model ratios.
Right panel:
Unfolded spectra using a powerlaw of photon index,
Γ = N E = AE − Γ ) and unit norm at 1 keV. Both the count PHA and fluxed spectra were extracted from the − J. Astrophys. Astr. (0000) : ilar to Eqn. 2, D ( I ) = T (cid:90) R ( I , E ) A ( E ) N E dE + B ( I ) , (7)where D ( I ) is the source + background count in spectralchannel I , B ( I ) is the background counts in channel I , T is exposure time. R ( I , E ) is the redistribution matrixand A ( E ) is e ff ective area at energy E , N E is the photonspectrum of the source.The redistribution matrix R ( I , E ) represents thespectral response which is Gaussian with an FWHMthat is the same as the spectral resolution of the grat-ing spectrometers. To measure the spectral resolutionof UVIT gratings, we fitted Gaussian profiles to theemission lines observed from NGC 40 and derived theFWHM = .
63Å (FUV gratings, m = − m = − ff ective area with the redistribution matrixas in Eqn. 7 and created the grating response matrixwhich is the product R ( I , E ) A ( E ). The responses thuscreated for each calibrated grating order are compatiblewith the X-ray spectral fitting packages such as XSPEC(Arnaud, 1996), Sherpa (Freeman et al ., 2001) and ISIS(Houck & Denicola, 2000). The source and backgroundPHA files along with the spectral response can directlybe used in one of the above spectral fitting packages.This is helpful for joint UV / X-ray spectral modeling.We also created single channel response matrices forthe broadband filters using the updated e ff ective areasprovided in Tandon et al . (2020). These response filesalong with the grating or filter spectral PHA data in thefits format give complete flexibility to treat and analyzethe photon counting UVIT data in a way similar to theX-ray photon counting data.Another way to use the UV grating spectra and pho-tometric flux in the joint UV / X-ray spectral analysis isto convert the fluxed spectra in PHA format and gen-erate diagonal responses using the FTOOLS package.However, this has the disadvantage of not consideringthe actual spectral response of the instrument. Hence,the uncertainty associated with the UC factor for theparticular spectral shape of the standard star for a givenbroadband filter will enter into the spectral fitting. Inthe case of grating spectra, the derived spectral linewidths will not be free of instrumental resolution as theinstrument spectral response is not being used.We demonstrate the equivalence of these two ap-proaches as follows. For this purpose we used UVITgrating observations of a Seyfert 1 AGN Fairall 9 (Ob-sID: G06 157T01 9000000). We processed the Level1 data in the same way as in the case of NGC 40 andHZ 4. We generated an m = − f λ Vs λ of Fairall 9 for the FUV-G2 inthe m = −
8. Summary & Conclusion
We calibrated the two FUV gratings in the orders − − − ff ective areas for thegrating orders which can be used for spectral calibra-tion of any source observed with the UVIT gratings.We also checked the cross-calibration between the grat-ings and broadband filters and found excellent agree-ment in flux measurements for all broadband filters ex-cept the FUV filter F148W. We provide the updatedUC and ZP for this filter. We also generated the spec-tral response files for the gratings and the broadbandfilters that can be directly used for spectral analysisusing XSPEC, Sherpa or ISIS. A software package UVITTools for the analysis of UVIT data processedwith the CCDLAB pipeline has been developed.
Acknowledgments
The author is grateful to Shyam Tandon for numerousdiscussions on various aspects of UVIT, and allowingto use the calibration data. The author is thankful toPhil Charles and Shyam Tandon for their suggestionson the submitted version of the manuscript. This pub-lication uses the data from the AstroSat mission of theIndian Space Research Organisation (ISRO), archivedat the Indian Space Science Data Centre (ISSDC). Thispublication uses UVIT data processed by the payloadoperations centre at IIA. The UVIT is built in collabo-ration between IIA, IUCAA, TIFR, ISRO and CSA.
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