Map-making

Map-Making and photometric calibration

Introduction

This page will give an overview of the map-making and photometric calibration procedures used by the HFI DPC to build detector and frequency maps. This processing and its performances are described in the the HFI DPC Paper and the the HFI DPC Calibration co-Paper [which will be completed prior to this page].

To build HFI maps, we work under destriping approximation, where the noise is assumed to decompose into two components : white noise plus low frequency drifts. Using the sky redundancy, the low frequency component is modelled as one constant, or offset, per pointing period. To speed up the ulterior processing we first build intermediate products, by taking advantage of redundancies : we average signal and detector orientation on healpix pixels visited during each fixed pointing period,which we call hereafter 'ring'. This intermediate product is called HPR for healpix pixel ring. This new dataset is used as input in the following steps.

Photometric calibration

dipole calibration (100 to 353 GHz)

For the 2013 data release, the calibrator for the CMB frequency was the Solar dipole, as measured by the WMAP team. We use a two component template fitting procedure, performed for each detector independently,to determine ring by ring a estimation of the dipole gain. We average these estimation for a subset of rings in the first survey (2000 to 6000) in which the dipole's amplitude is high enough with respect to that of the sky template, to get a single dipole gain per detector. The two fitted component are the Solar dipole and a sky template. We used the PSM for thermal dust emission at the detector's frequency as a first approximation of the sky template. Using the HFI channel map as a template brings negligible change in the averaged gain, but reduces the systematic ring-to-ring dispersion of our estimation.

Several pieces of evidence led to the conclusion that out bolometers presented apparent gain variation in time, after comparing the 3rd scan of the sky with the first one. This was later (mid-2012) explained by inequalities in the steps of the ADC used in the bolometer's electronic chain. These devices had to be characterized using warm data after thet end of the HFI observations. This process is still on-going (01/2012).

In the mean time we used an empiric correction, looking for a gain estimation and an offset per ring. This amounts at solving the non-linear equation : [math] \displaystyle{d\ =\ g_i.S + O_i + n} \label{nlequat}[/math]

where d is s the detector measurement, both S the sky signal, g the detector gain, O the offset (for ring no i) are the unknowns to be determined, and n the noise. We linearized this equation starting from the constant gain approximation, to get a measurement of the apparent time-varying gains for each bolometer independently. The limitations of this process are intrinsic signal variability from one observation to the other, like polarization or intra-pixel gradient. This procedure was thus only used for the 100 to 217 GHz detectors, for which the dipole signal is brighter and galactic signal (and polarization). A mask was used to removed the inner part of the Galactic plane.

[TBC : give precision]

Higher frequency calibration (545 and 857 GHz)

For the two highest frequencies, we calibrate the response using dust spectra measured by FIRAS. We use analytic fits to these spectra to extrapolate the dust signal within each detector's bandpass. These extrapolation are used to build nside=8 maps. We build on the other hand uncalibrated maps the we convolve with the beam of the FIRAS instrument. Finally we may derive one gain K and zero point Z per detector.

[math] \displaystyle{d_{FIRAS} = K.d_{HFI}}+Z \label{fircal}[/math]

While the gains are used only for the two highest frequencies, the zero point Z are used for all frequencies.

[TBC : give precision]

Building of Maps

Using the photometric calibration parameters, we build maps in two steps :

• we determine the destriping offsets using the full mission data
• we build the maps, using these offsets, by inverting the photometric equation :

[math] \displaystyle{d_i = g(I^p+\eta [Q^p cos(2\psi_i) + U^p sin(2\psi_i)]) + n} \label{photeq}[/math] where d is the destriped and calibrated signal at the HPR level. Detector's data are combined with an inverse noise weights derived from each detector's NEP. Q and U maps are build whenever possible. We propagate the white noise by building the 3x3 (or 1x1 if only I is reconstructed) covariance matrices in each pixel. At each frequency we build maps combining all detectors and independent detector sets. We use the offsets build for the full mission for building maps for each scan survey. We also build maps from the two independent halves of each rings. Altogether, more than 6000 m,aps are built at each release.

Noise properties

Map noise properties can be evaluated using several methods, thanks to the high level of observation redundancies. We can use the maps built from the difference between the first and second half of each rings, or compare individual sky scans, of detector sets with each other.

Low resolution (nside = 8 to 32 ?) pixel-to-pixel noise covariance matrices are build using an analytic approach from the measured noise power spectra.

Zodi correction

At the highest frequencies, Zodiacal emission is visible

Zodiacal Emission is removed from the 353, 545 and 857 GHz channels. It is described in the HFI DPC Paper, but a synopsis of the procedure is as follows:

• During each survey, a large fraction of the sky has observations which all fall within a week of each other. That is, during a single survey, most pixels are observed during a short, well-defined period. The contribution from Zodiacal Emission to the total brightness seen, then, is well defined.
• We use the the COBE model of the Zodiacal Light to make predictions for this Zodiacal emission for those pixels observed over a span of one week or less, and use GRASP models of the beams to predict the emission from the Galaxy given our sidelobes.
• We fit the survey difference maps with these model templates to estimate the emissivity of each Zodi component and sidelobe at the Planck wavelengths.
• We reconstruct each ring of the the full mission using the combination of the COBE geometric model with the emissivities determined above and the sidelobe models.
• We remove the reconstruction above from each ring of data.
• We then make maps as described previously in this section.

Far Sidelobe Correction

The far sidelobe correction is described in the section above. Note that this correction is done only for the 857 and 545 GHz channels, as it is not seen at longer wavelengths.

CO Correction

This is described in the the CO Paper