4.1.4 Spectrophotometric Calibration for Point-Sources
This section describes the basic steps used to derive the flux calibration for point sources. It also serves as a guide for deriving your own flux calibration. For example, if you want to extract a point-source spectrum with an aperture that is not the default one, the calibration provided in e.g. SPICE will not be valid. This means that the translation from instrumental units (electrons/sec) to Jy will be incorrect. The default aperture is the full-slit for the high-resolution modules and a tapered aperture for the low-resolution modules. To use a non-default aperture, you will need to perform your own spectrophotometric calibration. Here is how to do it:
1. Download Post-BCD products for staring observations of standard stars (from Campaign 18 onward). The primary calibrator for the low-resolution modules is HR 7341, while that for the high-resolution modules is HR 6688 (ksi Draconis). For every high-resolution observation of HR 6688 AOR there will be another AOR observing the nearby sky. You will need to download that too.
Be aware that the bias voltage for the LL module changed in Campaign 45, while the bias for the LH module changed in Campaign 25. To do your own calibration, use only stars that have been observed with the same bias as your target. For example, if you are interested in LH observations performed in Campaign 30, you will need to download all the observations of HR 6688 from Campaign 25 onwards.
The pointing scheme of the telescope was substantially improved after campaign 17 (3-15 Jan 05). Some observations performed before campaign 18, but calibrated with later pipeline versions, will show significant order mismatches.
Table 4.4 AORs used to calibrate S18.18 SL data, PRE-33 campaigns.
Table 4.5 AORs used to calibrate S18.18 SL data, POST-32 campaigns.
Table 4.6 AORs used to calibrate S18.18 LL data, PRE-45 campaigns.
Table 4.10 AORs used to calibrate S18.18 LH data, POST-24 campaigns.
(*) Campaign 49 data not used in S18.18 calibration.
2. Subtract the sky from the standard star observations. For the low-resolution modules, the pipeline provides ready-made sky-subtracted products. The files are called bksub.fits, bmask.fits, and bkunc.fits, and are the result of subtracting nod2 images from nod1 images and vice versa. (For an explanation of these names see Chapter 6). To do something different, start with coa2d.fits, c2mask.fits, and c2unc.fits. For the high-resolution observations, you will always need to subtract the sky by yourself. For each high-resolution AOR, subtract the sky products called coa2d.fits from the standard star products of the same name. Add the uncertainty images (c2unc.fits) of the sky to those of the standard in quadrature. Perform a logical 'OR' operation between the c2msk.fits from the sky and that from the star.
3. Extract your spectra. Start SPICE and run it in batch mode over the sky-subtracted images of your standard star. The setup should be exactly the same as in you intend to use for your science target. The SPICE products you will need for the calibration are called *extract.tbl.
4. Combine all the individual *extract.tbl files. These files contain the instrumental spectra, in units of electrons/sec. The pipeline uses a clipped median to combine all the spectra, with the uncertainties propagated accordingly. The bit flag values are OR-ed. There are other possibilities: a clipped average has better noise characteristics, for example. Alternatively, one may combine all 2D images for each nod, and then extract a single image.
6. Obtain the polynomial correction. To do so, divide the averaged *extract.tbl by the model, and fit the result with the lowest-order polynomial possible. The pipeline uses polynomial fits of orders less than 3 for each individual order in each module. These are the 'fluxcons'.
7. Run SPICE on your science data, with the same setup as the calibrations. Obtain *extract.tbl products.
8. Divide the *extract.tbl products by the fluxcons. You can make SPICE use your calibrations to tune the spectra, in which case SPICE will take care of this step. Or you can do it in a separate script.
4.1.5 Spectrophotometric Calibration for Extended Sources
Extended sources need to be calibrated differently than point sources because the flux fills the slit. In principle, an extended source with a known surface brightness distribution and spectrum should be sufficient to derive the calibration. However such a source does not exist. Sources like the Moon are too bright for the IRS. The zodiacal background is another extended source which might be considered but it is weak and its spectrum and strength are not well known and vary from region to region. Thus an absolute calibration for extended sources is not possible. The best we can do is to derive an approximate calibration to give users an idea of the extent of the correction that may be required. To do this, we describe two correction factors in Sections 126.96.36.199 and 188.8.131.52 below: the Aperture Loss Correction Factor (ALCF) and the Slit Loss Correction Factor (SLCF). Both of these correction factors are built into the extended source capabilities of SPICE, SMART, and CUBISM.
184.108.40.206 The Aperture Loss Correction Factor (ALCF)
For an extended source we would like to extract light from the entire aperture. Hence FOR THE LOW RESOLUTION SLITS ONLY we first have to apply a correction for the aperture shape we adopted for point sources. This is called the aperture loss correction factor, or ALCF for short.
The first step in deriving the ALCF is to extract point sources using a flat-sided aperture with a width of 28 pixels. This is slightly smaller than the 32 or 33 pixels for the SL and LL modules and avoids the noise at the edges of the slits. The resulting extraction should be compared to the standard star models and a new fluxcon table should be derived. The ratio of the calibrated flat-aperture and standard extractions estimates the ALCF.
The differences between the flat-aperture and standard extractions are small, less than 10%. Figure 4.10 through Figure 4.17 show the comparison for a bright source in each of the SL and LL orders and at each of the nods. In these figures, the top panel shows the ratio of the extracted spectra in the 28-pixel flat aperture versus the standard expanding aperture. The second panel in each image shows the extracted spectrum with the open circles indicating the extracted signal from the flat-sided 28 pixel aperture. For SL2 and LL2, more light is being lost at the blue end of each order than at the red end. In other words, the change in the PSF is not linear and either the blue end PSF is wider or the red end PSF narrower than would have been expected. Secondly, note that the ratio for SL1 is nearly flat across the entire bandpass (except for the 14 micron bump). This means that the variation of the PSF from red to blue end is linear with wavelength for this slit in these orders. Beyond 35 microns, the signal to noise is extremely poor and therefore the calibration is highly uncertain.
Figure 4.10: Comparison between standard and constant-width extractions for Short Low 2, nod 1.
Figure 4.11: Comparison between standard and constant-width extractions for Short Low 2, nod 2.
Figure 4.12 Comparison between standard and constant-width extractions for Short Low 1, nod 1.
Figure 4.13 Comparison between standard and constant-width extractions for Short Low 1, nod 2.
Figure 4.14: Comparison between standard and constant-width extractions for Long Low 2, nod 1.
Figure 4.15: Comparison between standard and constant-width extractions for Long Low 2, nod 2.
Figure 4.16: Comparison between standard and constant-width extractions for Long Low 1, nod 1.
Figure 4.17: Comparison between standard and constant-width extractions for Long Low 1, nod 2.
220.127.116.11 The Slit Loss Correction Factor (SLCF)
The second correction that must be made is much more difficult. It is an estimate of how much light is lost or gained in the slit as a function of wavelength. For a star this correction is IMPLICIT in the calibration because the extracted spectrum is fixed to the model. Hence if we are losing 10% of the light at the blue end and 40% of the light at the red end, we already account for this. For an extended source, however, such corrections for light losses are meaningless because light also enters the slit from outside the slit. In the case of a spatially flat and spectrally flat source, the light losses from the slit should EXACTLY cancel the light GAINS into the slit and therefore there should be NO correction for slit loss. If one were to apply the standard fluxcon table that we have derived for stars, then the correction for the light loss must therefore be undone.
Note that the term "SLCF" is a misnomer because we are trying to reverse the correction already applied for light losses. But since the term has been in popular use, we continue its use here.
In principle the slit loss correction also depends on the brightness distribution of the source because the observations are a convolution of the beam profile and the source brightness distribution on the sky. But since the source brightness distribution for a given source is not known a priori, our correction can only be based on an approximation. The approximation we make is that the source is spectrally and spatially flat and it fills the slit uniformly. To recover an unbiased flux, you must multiply by an SLCF which is simply the fraction of the PSF which the slit admits, as a function of wavelength.