# Detector pointing

## Introduction and Summary

The overall geometry of the Planck focal plane is shown here:

The Planck focal plane.

In order to take full advantage of the Planck beams, we must know the individual detector pointing positions to a precision of better than several arcseconds, over the course of the entire mission.

Spacecraft pointing comes from the on-board star-tracker sampled at 8 Hz between repointings (Attitude History File, AHF). This is translated via a series of 3-dimensional rotations to a pointing for the centre of the focal plane and resampled to the HFI or LFI TOI data rate for convenience. We must then further rotate this focal-plane boresight pointing to the individual detector locations. Because neither the rotations from the star-tracker to the boresight nor those from the boresight to the individual detectors are known exactly a priori, we must calibrate them using flight data.

Specifically, measurements of HFI and LFI detector pointing are based largely on observations of the brighter planets, with information from the much more frequent observations of lower-flux Galactic and extragalactic high-frequency sources used to monitor and build a model of overall pointing drift. This long-term drift of the spacecraft attitude is due to changes in the moment of inertia of the spacecraft, and also includes specific events that may induce sudden changes, essentially random as far as our ability to predict their effects is concerned. In this delivery HFI used a model (described below) to follow the pointing drift continuously, while LFI used two different focal plane descriptions for the two time periods separated by operations perfomed on the instrument that modified the thermal behaviour; the two approaches are consistent to better than a few arcsec.

Note that for HFI the resulting pointing model cannot easily be directly compared to a physical/optical model; in particular, it includes a phase shift in the scan direction from the convolution and deconvolution of the detector transfer function, which is complex in the Fourier domain (see Planck-2013-VII[1]). This phase shift was not measured during normal operations, but a short campaign during which the spacecraft was spun at a higher rate will be used to determine these offsets in future data releases. Comparison with the initial optical model indicates that the in-scan change due to this phase shift is of the order of 1 arcminute. Note also that stellar aberration is corrected in all observations.

The final pointing model is measured to be better than 2 arcseconds rms in the co-scan and cross-scan directions averaged over ten-day periods, as shown below. Note that there are some larger hourly drifts of up to 10 arcseconds due to interference from the radiometer electronics box assembly (REBA), as discussed more fully in Planck-2013-VI[2].

## Stellar aberration

The corrected quaternions are interpolated using a spherical linear interpolation algorithm and transformed into Cartesian vectors, which we call "DPT". For each sample the stellar aberration correction is applied:

${\rm DPT} = {\rm DPT} - {v_{\rm sat} \over c },$

where vsat is the satellite velocity and c is the speed of light. After this operation the vector is normalized.

Finally the Cartesian vetor is converted into Ecliptic coordinates to give the detector pointing.

## Beam rotation

The rotation of the beam with respect to North is the angle ψ and is computed rotating the corrected quaternions Q.

The resulting rotation matrix represents the rotation of the beam, the angle ψ is then

$\psi = -\arctan (R[0][1],R[0][0]) .$

## Focal plane drift

The low-frequency pointing correction, known as PTCOR has been reworked to include satellite "wobble" angle corrections (difference between the satellite spin frame and the rigid body reference frame). This move was necessitated by problems in the measured wobble angles beyond the full mission for HFI (i.e., beyond Survey 5). We also observed that the long time scale features in the pointing correction were very well fit using a template constructed from the solar distance. This template was further augmented by including a linear component and breaks at times of known thermal disturbance onboard the spacecraft.

Measured cross-scan offsets after applying the low-frequency pointing correction (shown in orange).
Measured in-scan offsets after applying the low-frequency pointing correction (shown in orange).

## References

1. Planck 2013 results. VII. HFI time response and beams, Planck Collaboration, 2014, A&A, 571, A7.
2. Planck 2013 results. VI. High Frequency Instrument Data Processing, Planck Collaboration, 2014, A&A, 571, A6.

Attitude History File

(Planck) High Frequency Instrument

(Planck) Low Frequency Instrument