Questions to E-OAT:
Q7 Calibration Requirements
Instrumental calibration requirements for Euclid NIS slitless spectroscopy
Jeremy R. Walsh
Harald Kuntschner
Martin Kümmel
Space Telescope European Coordinating Facility
ESO
1. Wavelength calibration
In Section 3.1.3.1 of the Euclid Science Requirements Document, the accuracy for spectroscopic
redshift of each galaxy based on measurement of at least one emission line is required to be
<0.001(1+z). Given that the spectroscopic resolution is specified to be R=500 over the full
wavelength range (1.0-2.0 micron), then assuming 2 pixel resolution, this translates into an absolute
wavelength accuracy of <1 pixel.
From experience with HST ACS and WFC3 slitless spectroscopy this accuracy can be routinely
achieved. Kuntschner et al. (2009a) deals generally with the wavelength (and flux) calibration of the
WFC3 slitless spectroscopy modes and the details of the calibration for the near-IR slitless grism
modes can be found in Kuntschner et al. (2009b) for the G102 grism and Kuntschner et al. (2009c)
for the G141 grism.
The factors that enter into the wavelength determination are:
1. Fidelity of the dispersion solution across the full detector area
2. Estimation of object positions on the associated direct image
3. Transfer of the wavelength zero point from direct to grism image
4. Determination of the position of the emission line
In order to push below the 0.001 wavelength accuracy barrier, particular attention has to be paid to
items 1 and 3. Item 2 is well covered by object fitting techniques on direct images and provided
sufficient exposure is given to the associated direct image, then the effect of signal-to-noise on the
object determination should be a negligible contribution. Item 4 depends on the signal-to-noise of
the emission line measurement and the quality of contamination estimates. A systematic effect can
also arise from the mis-match in position of the centre of an object derived from a direct image filter
band (that includes continuum and line) as compared to the actual position of the peak in the single
emission line employed for the redshift determination. This systematic will affect the redshift
measurement and leads to a further source of uncertainty encompassing points 2 and 3, but will be a
small effect except for well-resolved sources. Points 1 and 3 are dealt with in more detail below.
Figure 1. Typical appearance of a slitless spectrum, as example an HST WFC3 G141 spectrum of the flux
standard star GD153. The position of the direct image (circled) is superposed from a separate image taken
through an F140W filter.
The dispersion solution across the detector area is expected to be relatively stable (or
reproducable), as it is sensitive to the grism repositioning and any changes in relative position of
components, such as resulting from thermal changes or outgassing of structural parts. Thus
achieving an excellent <0.0005 accuracy 2D solution of the dispersion across the field from ground
tests is mandatory. The necessary in-orbit routine monitoring of any changes in the low order
components can be achieved by observing objects with a number of emission lines across the
wavelength range (such as a compact planetary nebula at multiple positions over the field). This
technique has been employed for the WFC3 near-IR grisms and Fig.1 shows typical in-orbit slitless
spectra of a flux standard with the G141 grism. Figure 2 shows that the typical field for a compact
planetary nebula, which is in the Milky Way in the case of Hubble 12 (Hb 12), can be quite crowded
with fainter targets. However the compact PN is bright so a high quality extraction can be achieved
and is shown diagramatically in Fig. 3. A number of bright and fainter emission lines can be
distinguished and fitted even in this R=200 spectrum so that a 2nd order polynomial of wavelength
v. pixel offset from the position of the direct image (see Fig. 1) can be well fitted. For Euclid NIS,
with planned spectral resolution of 500, the spectra will allow more lines to be resolved leading to
higher accuracy (in Angstroms) in the determination of the dispersion solution, although the
accuracy in pixels is expected to be similar.
Figure 2. A WFC3 G141 slitless image with the compact planetary nebulae Hb 12 (PN G111.8 -02.8), used
for in-orbit wavelength calibration, as the prominent spectrum in the middle of the image.
Figure 3. Example of WFC3 G102 observations of the planetary nebula Vy2-2 and the source spectrum
extraction with the ST-ECF slitless extraction software aXe. The left panels show an example of a G102
dispersed image (top) together with its associated direct image in the F098M filter (bottom). The right panels
show the combined, aXedrizzled stamp image from the entire dataset (top) and the extracted one-dimensional
spectrum (bottom) with the identification of prominent emission lines.
The transfer of object positions to wavelength zero point is one of the fundamental areas where
slitless spectroscopy differs from slit spectroscopy, the other being the modulation of the spectral
resolution by the object size (since it is the object that defines the slit width and orientation in
slitless spectroscopy). There are two operational checks that can be performed that enable
monitoring of the wavelength zero point on a frame-by-frame basis. The first is use of the zeroth
order to check any shift of the spectra with respect to the direct image reference position. Zeroth
orders are usually weak, since in a well-designed grism, most of the power should be in one of the
first orders; the other disadvantage is that zeroth order is slightly dispersed so the position depends
on the object colour within the grism 0th order throughput. The second technique is to use common
objects with known, or at least expected, spectral features with which to cross correlate and thus
provide a contemporaneous check of the wavelength zero point. In practice late-type Galactic stars
(K and M spectral types) have strong features in the red and near-IR so can be used. Figure 4
shows a model of an M star (Teff 3200K) at the binning and resolution of Euclid NIS illustrating the
suitability of such stars for wavelength calibration. Practice of this method in the Hubble Legacy
Archive project on ACS slitless spectroscopy (Kuemmel et al. 2010, in prep.) shows that
improvements to an rms of about 0.5 pixels can be achieved. Several elaborations can be
contemplated, such as:
preparation of a set of ground-based well-observed late type stellar templates observed at a
spectral resolution ~3000 (to ensure telluric lines are resolved) and spread over the sky or chosen
so that the orbit track often passes these targets;
if available, use of Gaia classification and radial velocities of stars (Wilkinson et al. 2005) in order to
select those best suited for the cross-correlation. This option would allow good template matches
and rejection of possible halo stars with high radial velocities. However in a given field a small
fraction of stars would belong to the halo and thus possibly have high radial velocities, so an
interative procedure could be developed to exclude stars with large cross-correlation residuals.
Figure 4. Spectrum of a model atmosphere appropriate to an M star (Teff = 3200K) at the binning and
resolution of the Euclid NIS slitless spectroscopy. Model kindly provided by Stefan Uttenthaler.
One factor which can lead to catastrophic redshift determination is contamination of spectra,
whereby a line from another object is mistaken for belonging to a given object or a zeroth order is
mistaken for an emission line. Since the position of the zeroth order can be predicted to sub-pixel
accuracy from the known optical properties of the grism and the optical set-up, the latter should
not prove a serious impediment. Note, however, that objects outside the detector but still within
the instrument field of view will produce spectra, including zeroth orders on one side of the detector
(along the dispersion axis), so the catalogue of objects producing spectra on a given grism image
should include the detector surroundings.
Experience with ACS and WFC3 spectra demonstrates that absolute wavelengths to 0.5 pixels can
be achieved by employing the above precautions. Improving on this figure will require excellent
ground and in-orbit calibrations and robust methods for monitoring contemporaneous wavelength
zero point, that should be designed into the survey strategy.
Calibration overheads
A high precision (to 0.0005*lambda) derivation of the dispersion solution all over the field is
required from ground testing. Checking of this solution can be achieved by multiple exposures of a
point source with emission lines (compact planetary nebula or Be type star for example) in orbit.
Probably this calibration does not need much repetition (say 4 times in first year, twice per year
there-after) depending on the degree of stability demonstrated in-orbit by Euclid NIS. There are
only two bright compact PN with well-observed spectra in the near-IR. It would be prudent to
increase this number to say ten distributed around the sky to allow ready calibration early in the
orbital life of Euclid. This is only a small ground-based observational programme well suited to
medium sized telescopes with IR spectrometers.
Monitoring of the zero point, independent of the contemporaneous wavelength zero point checks by
K and M stars during the course of normal science observations mentioned above, could be
achieved by return to a single source or field of sources (matched to the size to the slitless field),
such as a single emission line source or a field of emission line sources (e.g. PN or compact HII
regions in a nearby galaxy) or a field of stars with well-studied spectra e.g. an open cluster. Careful
choice of targets and some ground-based spectroscopy of chosen targets would be necessary to
establish these calibrations.
It is concluded that very satisfactory in-orbit calibration strategies exist without resort to a
wavelength calibration lamp on the spacecraft.
2. Flat fielding
Since a slitless spectrum can occur anywhere on the detector, and the flat-field correction has to be
performed for each pixel as a function of incident wavelength; this leads to the use of a flat-field
cube
whereby the wavelength behaviour of the flat-field is described for each pixel by the 3rd dimension
in
addition to the two spatial dimensions of the detector (see Fig. 4). To characterize the wavelength
dependent behaviour, a series of direct image flat-fields taken at various central wavelengths is
used. The wavelength information in a set of direct image flat-fields of differing central wavelength
can be fitted by a polynomial to the series of wavelength dependent flat-field values for each pixels.
The flat-field cube then contains the polynomial coefficients in the third dimension. This method has
been successfully applied to ACS and WFC3 slitless data; more details can be found in Kuemmel et
al. (2009). Fig.4 shows how the the polynomial orders of the wavelength fit to the flat field for an
ACS flat field cube are stored in a FITS file.
Figure 4. The structure of the FITS flat-field calibration file which is used by aXe to construct, at each pixel
coordinate (i,j) a proper flat-field coefficient F F (i, j, x) = a0 + a1 ∗ x + a2 ∗ x2 + ... + ai ∗ xn , where x is a
normalized value obtained with x = (λ − λmin )/(λmax − λmin ) and λ is the wavelength of the pixel
(i,j).
In practice such a flat field cube can be established by on-ground calibration preferably with a
monochromator illuminating the instrument so that the detailed behaviour of the flat field with
wavelength can be modelled. However since the ground calibration illumination is often not identical
to that in-flight, the zeroth order (wavelength independent) plane of the flat field cube can be
adjusted by comparison with an on-orbit flat field, such as established by rastering a stellar field
across the detector in direct imaging with a filter within the passband of the grism (c.f. van der
Marel et al. 2003).
Figure 5. Example flat field cube - the four coefficient images of an HST ACS HRC/G800L flat-field cube. In
the region (top left) obscured by the coronographic finger, the coefficients have been reset to a value of 1.0
for all images.
In addition a 'super-sky' is required since the background in slitless spectroscopy is high and
presents some structure imposed by the detector and the dispersing element. This can be
established by median combination of many in-orbit science grism exposures and has been
demonstrated for ACS and WFC3 data. The temporal variation of this super sky (depending on sun
and earth angles for example) can be established to improve the 2D subtraction of the dispersed
background.
It is not necessary to provide a flat field calibration lamp for on-orbit use.
3. Flux calibration
There do not appear to be any requirements for flux calibration accuracy. Perhaps 10% is a fair
level. This can be achieved with a rudimentary photometric calibration on the ground and use of
spectrophotometric standards for in-orbit calibration. A set of primary spectrophotometric
standards has been developed for HST and JWST (Bohlin et al. 2001) and one of these could be
included once in the in-orbit calibration. Since this set of primary standards is small, then other
standards will be required for more continuous monitoring. If available, a set of stars from the Gaia
catalogue could be selected over the sky to achieve a more time-continuous flux calibration
monitoring. Depending on the requirements, a similar temporal frequency for flux calibration as for
checking of the wavelength zero point could be contemplated. If Gaia flux calibration is reliable to
the required level, the Gaia catalogue could be employed to choose both wavelength zero point and
standards with well-known spectral types in each field during the data reduction. Flux calibration
would thus rely on having well determined spectral types so that the near-IR flux distribution could
be assumed, since Gaia wavelength coverage does not overlap with Euclid NIS.
References
Bohlin, R. C., Dickinson, M. E., Calzetti, D., 2001. Spectrophotometric Standards from the FarUltraviolet to the Near-Infrared: STIS and NICMOS Fluxes. AJ, 122, 2118
Kümmel, M., Walsh, J. R., Pirzkal, N., Kuntschner, H., Pasquali, A., 2008. The Slitless
Spectroscopy Data Extraction Software. PASP, 121, 59
Kuntschner, H., Kümmel, M., Walsh, J. R., Bushouse, H., 2009a. Calibrating the WFC3 grisms.
ST-ECF Newsletter, 47, 4
Kuntschner, H., Kümmel, M., Walsh, J. R., Bushouse, H., 2009b. WFC3 SMOV proposal 11552:
Calibration of the G102 grism. WFC3 ISR 2009-18
Kuntschner, H., Kümmel, M., Walsh, J. R., Bushouse, H., 2009c. WFC3 SMOV proposal 11552:
Calibration of the G141 grism. WFC3 ISR 2009-17
van der Marel, R., 2003. Determination of Low-Frequency Flat-Field Structure from Photometry of
Stellar Fields. ACS ISR 03-10
Walsh, J. R., Pirzkal, N., 2005. Flat-field and sensitivity calibration for ACS G800L slitless
spectroscopy modes. ACS ISR 05-02
Wilkinson, M. I., et al., 2005. Sectroscopic survey of the Galaxy with Gaia- II. The expected
science yield from the Radial Velocity Spectrometer. MNRAS, 359, 1306