Planck 2013 results. VIII. HFI photometric calibration and mapmaking

A&A 571, A8 (2014)

DOI: 10.1051

0004-6361

201321538

ESO 2014

Astronomy

Astrophysics

Planck 2013 results

Special feature

Planck

2013 results. VIII. HFI photometric calibration

and mapmaking

Planck Collaboration: P. A. R. Ade

, N. Aghanim

, C. Armitage-Caplan

, M. Arnaud

, M. Ashdown

, F. Atrio-Barandela

, J. Aumont

C. Baccigalupi

, A. J. Banday

, R. B. Barreiro

, E. Battaner

, K. Benabed

, A. Benoît

, A. Benoit-Lévy

, J.-P. Bernard

M. Bersanelli

, B. Bertincourt

, P. Bielewicz

, J. Bobin

, J. J. Bock

, J. R. Bond

, J. Borrill

, F. R. Bouchet

, F. Boulanger

M. Bridges

, M. Bucher

, C. Burigana

, J.-F. Cardoso

, A. Catalano

, A. Challinor

, A. Chamballu

, R.-R. Chary

X. Chen

, H. C. Chiang

, L.-Y Chiang

, P. R. Christensen

, S. Church

, D. L. Clements

, S. Colombi

, L. P. L. Colombo

C. Combet

, F. Couchot

, A. Coulais

, B. P. Crill

, A. Curto

, F. Cuttaia

, L. Danese

, R. D. Davies

, P. de Bernardis

, A. de Rosa

G. de Zotti

, J. Delabrouille

, J.-M. Delouis

, F.-X. Désert

, C. Dickinson

, J. M. Diego

, H. Dole

, S. Donzelli

, O. Doré

M. Douspis

, X. Dupac

, G. Efstathiou

, T. A. Enßlin

, H. K. Eriksen

, C. Filliard

, F. Finelli

, O. Forni

, M. Frailis

, E. Franceschi

S. Galeotta

, K. Ganga

, M. Giard

, G. Giardino

, Y. Giraud-Héraud

, J. González-Nuevo

, K. M. Górski

, S. Gratton

A. Gregorio

, A. Gruppuso

, F. K. Hansen

, D. Hanson

, D. Harrison

, G. Helou

, S. Henrot-Versillé

C. Hernández-Monteagudo

, D. Herranz

, S. R. Hildebrandt

, E. Hivon

, M. Hobson

, W. A. Holmes

, A. Hornstrup

, W. Hovest

K. M. Hu

enberger

, A. H. Ja

, T. R. Ja

, W. C. Jones

, M. Juvela

, E. Keihänen

, R. Keskitalo

, T. S. Kisner

, R. Kneissl

J. Knoche

, L. Knox

, M. Kunz

, H. Kurki-Suonio

, G. Lagache

, J.-M. Lamarre

, A. Lasenby

, R. J. Laureijs

, C. R. Lawrence

M. Le Jeune

, E. Lellouch

, R. Leonardi

, C. Leroy

, J. Lesgourgues

, M. Liguori

, P. B. Lilje

, M. Linden-Vørnle

M. López-Caniego

, P. M. Lubin

, J. F. Macías-Pérez

, B. Ma

, N. Mandolesi

, M. Maris

, D. J. Marshall

, P. G. Martin

E. Martínez-González

, S. Masi

, M. Massardi

, S. Matarrese

, F. Matthai

, L. Maurin

, P. Mazzotta

, P. McGehee

, P. R. Meinhold

A. Melchiorri

, L. Mendes

, A. Mennella

, M. Migliaccio

, S. Mitra

, M.-A. Miville-Deschênes

, A. Moneti

, L. Montier

R. Moreno

, G. Morgante

, D. Mortlock

, D. Munshi

, J. A. Murphy

, P. Naselsky

, F. Nati

, P. Natoli

, C. B. Netterfield

H. U. Nørgaard-Nielsen

, F. Noviello

, D. Novikov

, I. Novikov

, S. Osborne

, C. A. Oxborrow

, F. Paci

, L. Pagano

, F. Pajot

R. Paladini

, D. Paoletti

, B. Partridge

, F. Pasian

, G. Patanchon

, T. J. Pearson

, O. Perdereau

, L. Perotto

, F. Perrotta

F. Piacentini

, M. Piat

, E. Pierpaoli

, D. Pietrobon

, S. Plaszczynski

, E. Pointecouteau

, G. Polenta

, N. Ponthieu

, L. Popa

T. Poutanen

, G. W. Pratt

, G. Prézeau

, S. Prunet

, J.-L. Puget

, J. P. Rachen

, M. Reinecke

, M. Remazeilles

, C. Renault

S. Ricciardi

, T. Riller

, I. Ristorcelli

, G. Rocha

, C. Rosset

, G. Roudier

, B. Rusholme

, D. Santos

, G. Savini

, D. Scott

E. P. S. Shellard

, L. D. Spencer

, J.-L. Starck

, V. Stolyarov

, R. Stompor

, R. Sudiwala

, R. Sunyaev

, F. Sureau

, D. Sutton

A.-S. Suur-Uski

, J.-F. Sygnet

, J. A. Tauber

, D. Tavagnacco

, S. Techene

, L. Terenzi

, M. Tomasi

, M. Tristram

, M. Tucci

G. Umana

, L. Valenziano

, J. Valiviita

, B. Van Tent

, P. Vielva

, F. Villa

, N. Vittorio

, L. A. Wade

, B. D. Wandelt

D. Yvon

, A. Zacchei

, and A. Zonca

ffi

liations can be found after the references)

Received 21 March 2013

Accepted 8 March 2014

ABSTRACT

This paper describes the methods used to produce photometrically calibrated maps from the

Planck

High Frequency Instrument (HFI) cleaned,

time-ordered information. HFI observes the sky over a broad range of frequencies, from 100 to 857 GHz. To obtain the best calibration accuracy

over such a large range, two di

erent photometric calibration schemes have to be used. The 545 and 857 GHz data are calibrated by comparing

flux-density measurements of Uranus and Neptune with models of their atmospheric emission. The lower frequencies (below 353 GHz) are

calibrated using the solar dipole. A component of this anisotropy is time-variable, owing to the orbital motion of the satellite in the solar system.

Photometric calibration is thus tightly linked to mapmaking, which also addresses low-frequency noise removal. By comparing observations

taken more than one year apart in the same configuration, we have identified apparent gain variations with time. These variations are induced by

non-linearities in the read-out electronics chain. We have developed an e

ective correction to limit their e

ect on calibration. We present several

methods to estimate the precision of the photometric calibration. We distinguish relative uncertainties (between detectors, or between frequencies)

and absolute uncertainties. Absolute uncertainties lie in the range from 0.54% to 10% from 100 to 857 GHz. We describe the pipeline used to

produce the maps from the HFI timelines, based on the photometric calibration parameters, and the scheme used to set the zero level of the maps

a posteriori. We also discuss the cross-calibration between HFI and the SPIRE instrument on board

Herschel

. Finally we summarize the basic

characteristics of the set of HFI maps included in the 2013

Planck

data release.

Key words.

cosmic background radiation – cosmology: observations – surveys – methods: data analysis

Corresponding authors: O. Perdereau, e-mail:

perdereau@lal.in2p3.fr

; G. Lagache, e-mail:

guilaine.lagache@ias.u-psud.fr

Article published by EDP Sciences

A8, page 1 of 25

A&A 571, A8 (2014)

Table 1.

Parameters of the solar dipole, as measured by WMAP

(Hinshaw et al. 2009).

Amplitude [mK

CMB

]

355

008

Galactic longitude [

◦

]

263

Galactic latitude [

◦

]

1. Introduction

This paper, one of a set associated with the 2013 release of data

from the

Planck

mission

, describes the processing applied to

Planck

High Frequency Instrument (HFI) cleaned time-ordered

information (TOI) to produce photometrically-calibrated sky

maps.

Cosmic microwave background (CMB) experiments can

be calibrated using the dipole anisotropy induced by the mo-

tion of the instrument relative to the cosmological frame. This

anisotropy is naturally separated into two components: we refer

to the component generated by the motion of Planck around the

sun as the

orbital dipole

, and that generated by the sun’s motion

relative to the CMB as the

solar dipole

In principle, the orbital dipole is the most precise calibra-

tor, as it depends on the very well known orbital parameters and

the temperature of the CMB, measured precisely by the COBE-

FIRAS experiment (Mather et al. 1999). However, calibration

using the orbital dipole involves comparison of data taken at

large time separation (typically 6 months), and the precision one

can achieve using this calibrator is thus directly linked to that of

the time stability of the data, and to the precision reached in ad-

dressing any time variable systematics. We have identified one

such systematic, induced by non-linearities in the analogue-to-

digital converters of the bolometers’ read-out electronic chain,

and for the present release have chosen to use the solar dipole,

based on the measurement of the solar dipole parameters from

WMAP (Hinshaw et al. 2009), as the main calibrator for the

100 to 353 GHz channels. These parameters are summarized in

Table 1.

At high frequency (

≥

500 GHz), the dipole becomes too

faint with respect to the Galactic foregrounds to give an ac-

curate calibration. Although we used the Galactic emission as

measured by FIRAS for the calibration of the

Planck

early pa-

pers (Planck HFI Core Team 2011a), we have now obtained a

better accuracy using planet measurements. Thus, the absolute

calibration of the two high-frequency channels is done using

Uranus and Neptune.

At all frequencies, the zero levels of the maps are obtained

by assuming no Galactic emission at zero gas column density,

and adding the cosmic infrared background (CIB) mean level.

The paper is organized as follows. We first summarize

the mapmaking procedure (Sect. 2). We outline the calibra-

tion method used for the CMB-dominated channels (100 to

353 GHz) in Sect. 3. We discuss in this section unexpected re-

sponse variations with time, and present an e

ective correction.

We then detail the calibration for the 545 and 857 GHz channels

(Sect. 4) and describe how the zero level of the maps can be fixed

(Sect. 5). We finally quantify the accuracy of the photometric

Planck

(

http://www.esa.int/Planck

) is a project of the

European Space Agency (ESA) with instruments provided by two sci-

entific consortia funded by ESA member states (in particular the lead

countries France and Italy), with contributions from NASA (USA) and

telescope reflectors provided by a collaboration between ESA and a sci-

entific consortium led and funded by Denmark.

calibration, and give basic characteristics of the delivered maps

in Sect. 6. Conclusion are given in Sect. 7.

2. Pipeline for map production

The products of the HFI mapmaking pipeline are maps of

and

, together with their covariances, pixelized according to

the

HEALPix

scheme (Górski et al. 2005) with a resolution pa-

rameter

side

2048. For a given channel, data sample

may be

described as

(

−

(

cos 2

sin 2

)

(1)

where

denotes the sky pixel with Stokes parameters

and

is the noise realization,

is the cross-polarization param-

eter (equal to 1 for an ideal spider-web bolometer and 0 for an

ideal polarization sensitive bolometer),

is the detector orien-

tation on the sky, at sample

, and

is the detector’s gain. Given

Planck

’s scanning strategy, reconstructing

and

requires

combining measurements from several detectors for most pix-

els. According to bolometer models, and given the stability of

the HFI operational conditions during the mission,

is not ex-

pected to vary significantly,

In order to deal e

ffi

ciently with the large HFI data set and the

large number of maps to be produced, we use a two-step scheme

to make maps from the HFI TOIs. The first step takes advantage

of the redundancy of the observations on the sky. For each detec-

tor, we average the measurements in each

HEALPix

pixel visited

during a stable pointing period (hereafter called

ring

), into an

intermediate product, called an HPR for

HEALPix

Pixels Ring.

Subsequent calibration and mapmaking operations use the HPR

as input. As we produce

HEALPix

maps with the resolution pa-

rameter

side

set to 2048 we use the same internal resolution for

building the HPR.

The in-flight noise of the HFI detectors, after TOI process-

ing, is mostly white at high frequency, with a “1

” increase at

low frequency (Planck HFI Core Team 2011a). In such a case, a

destriping approach is well suited for the mapmaking (Ashdown

et al. 2009). In this approach, the noise in a ring

is represented

by an o

set, denoted by

, and a white noise part

, which is

uncorrelated with the low-frequency noise. We may then refor-

mulate Eq. (1) as

Γ

(2)

where

represents the sky (which may be a 3-vector if polar-

ization is accounted for) in pixel

is the pointing matrix

(which makes the link between data samples and their positions

on the sky) and

Γ

is the matrix folding the ring onto samples.

From the above equation,

are derived through maximum like-

lihood. As there is a degeneracy between the average of the o

sets and the zero level of the maps, we impose the constraint

〈

〉

0. Tristram et al. (2011) have shown that with scan-

ning and noise like those of HFI, an accurate reconstruction

of the o

sets

requires a precise measurement of

for each

channel.

In addition, some signal components vary with time, adding

more complexity to Eq. (2). Such components include the zodi-

acal light emission, the CMB dipole anisotropy component in-

duced by the motion of the satellite with respect to the solar

System, and the far sidelobe (FSL) pick-up signal. Time vari-

ability of the former comes from the variation of the observa-

tion angle of the solar System region emitting this radiation, due

to the ellipticity and cycloid modulation of the satellite’s orbit.

A8, page 2 of 25

Planck Collaboration:

Planck

2013 results. VIII.

The FSL are discussed in Planck Collaboration VII (2014) and

Planck Collaboration XIV (2014). Accounting for these compo-

nents in the mapmaking process requires an accurate calibration.

Moreover, we need to take into account the low-frequency noise

in the calibration process, so both operations (mapmaking and

calibration) are interleaved.

For the production of the maps of the 2013 HFI data release,

we followed a four-step process.

1. We first build the HPR for all detectors, for three data sets:

all the data for each ring, and (for null tests) the data from

just the first or just the second half of each ring.

2. We then apply the following calibration operations to the

HPR:

–

solar dipole calibration, which sets the overall calibration

factors for the 100–353 GHz detectors,

–

planet calibration (Uranus and Neptune), which is used

to get the calibration factors for the 545–857 GHz

detectors,

–

determine the relative gain variations over time of the

100

−

217 GHz detectors, using the

bogopix

tool (see

Sect. 3.3).

3. For each data set we then do the destriping and projections,

using the

polkapix

tool that was thoroughly validated in

Tristram et al. (2011). We compute one set of o

sets using

the full mission (29 months) data set, and then use these o

sets to compute the maps for the full mission, as well as for

restricted time intervals (corresponding to each individual

survey, and to the 15-months nominal mission). Maps are

built by simple co-addition in each pixel of the destriped,

calibrated, and time varying component-subtracted signal.

We subtract the WMAP measured CMB dipole from all our

maps, using the non-relativistic approximation.

4. The zero-levels for the maps are set a posteriori.

We have produced single-detector temperature maps, as well as

temperature and polarization maps using all the detectors of a

single frequency and some detector subsets. We have also pro-

duced hit-count maps and variance maps for the

and

val-

ues computed in each pixel. Overall, a total of about 6500 sky

maps have been produced. We used this data set to evaluate the

performance of the photometric calibration. Note that the HFI

pipeline we have described is quite similar to that used for the

Low Frequency Instrument (LFI; Planck Collaboration II 2014).

In order to take into account the Galactic signal integrated

in the FSL and zodiacal light (hereafter called

zodi

) com-

ponents, which vary in time, we have constructed templates

for the combination of both components at frequencies where

Galactic emission in the FSL matters, i.e., 545 and 857 GHz,

and of

zodi

only at lower frequencies, as described in Planck

Collaboration XIV (2014). These templates are used to build

HPRs. We provide two sets of maps. The first set is built without

removing these spurious components, while the second set is the

erences between maps from the previous set and maps from

which the

zodi

and FSL have been removed. The di

erence

maps might be can be used to correct the HFI maps for specific

applications.

In the following sections we will describe the calibration

procedures and then assess their performance, and present some

characteristics of the resulting maps.

Fig. 1.

erences between temperature maps built using data from de-

tector 143-1a, for Surveys 1 and 3 (

top

) and 2 and 4 (

bottom

). In both

cases, large-scale features appear. Their amplitude and disposition on

the sky are compatible with residuals from the solar dipole, due to time

variations of the detector gain, of the order of 1 to 2%. These residuals

should be compared to the amplitudes of the solar dipole, 3.353 mK

CMB

and to the orbital dipole that is about 10 times lower.

3. Photometric calibration of the low-frequency

channels: dipole-based calibration

3.1. ADC non-linearities and calibration

With a larger data set than that analyzed in Planck HFI Core

Team (2011b), we could ideally use an orbital-dipole-based cal-

ibration, as described in Tristram et al. (2011). However, the

additional redundancies revealed new systematic e

ects, ADC

non-linearities and very long time constants (of the order of a

few seconds) with very low energy content in the system’s re-

sponse. The former induce apparent gain variations with time.

The latter shifts the CMB dipole a few arcmin in the scan di-

rection, and hence creates leaks from the solar dipole into the

orbital dipole signal. These systematic e

ects prevented us from

using the orbital dipole calibration. The very long time constants

were identified after correcting for the ADC non-linearities, and

have not yet been fully characterized yet. Both corrections will

be implemented in the

Planck

2014 data release.

ects of such ADC-induced gain variations are clearly

visible when comparing Survey 3 with Survey 1 or Survey 2

with Survey 4. As an example, in Fig. 1 we show survey dif-

ference maps for one 143 GHz detector, built using the cali-

bration and mapmaking scheme presented in Planck HFI Core

Team (2011b). Large-scale dipolar features, aligned with the so-

lar dipole, are prominent in these maps. This shows that the con-

stant gain assumption used to build these maps is incorrect.

Intrinsic bolometer sensitivity variations cannot explain

such gain variations. The HFI bolometers have been precisely

characterized in flight using a dedicated sequence of

(

)

A8, page 3 of 25

A&A 571, A8 (2014)

-400

-200

200

400

Output code -32768 [ADU]

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Transition position error [ADU]

Fig. 2.

Error on transition code positions measured on one chip around

the ADC mid-scale, on the ground on a spare ADC. The largest error

occurs at the sign transition, but errors of about 1 ADU also occur reg-

ularly every 64 steps.

measurements, during the post-launch verification phase and

end-of-life periods. The static bolometer models predict that

changes of their background during the observations could not

explain response variations larger than 0.1%. In addition, such

variations are corrected for within the HFI DPC pipeline. In our

present understanding, these apparent response variations are the

result of imperfections in the linearity of the analogue-to-digital

converters (ADC) used in the bolometer read-out units. The vari-

ation of the bolometer background with time and the unevenness

in the ADC quantization steps leads, at first order, to an apparent

gain variation in the electronic chain. These non-linearities may

also a

ect signals di

erently depending on their amplitude, for

example the solar and orbital dipoles.

Figure 2 shows the errors on the transition code positions

measured on a spare ADC chip around the mid-scale, which

is the most populated area. These “integrated non-linearities”

(INL) present a prominent feature in all channels: the central

step is always too narrow. In addition to this, the 64-code, nearly

periodic patterns contribute to the apparent gain variations, mak-

ing it di

ffi

cult to predict the consequence of such errors on the

reconstructed, demodulated bolometer signal. Such an INL ef-

fect has however been included in full mission simulations, and

it reproduces qualitatively the gain variation features observed in

real flight data, with an amplitude of about

1%. This is larger

than the required calibration precision of the 100 to 217 GHz

channels.

In order to precisely correct all the data for this e

ect, we

need accurate measurements of all the ADC INLs, together with

a good model for the bolometer raw signal (including systemat-

ics). Mapping the ADC response required more data than were

acquired before the end of the HFI cold lifetime, so a dedicated

campaign has been conducted over several months, at a focal

plane temperature of about 4 K, to obtain a clean ADC charac-

terization on Gaussian noise. Correcting this e

ect needs to be

carried out prior to the TOI processing steps, and will require

thorough checks of any products. At the time of writing, cor-

rection procedures are being intensively tested but they have not

been included in the 2013

Planck

data release.

In the absence of a full correction procedure, we had to de-

velop an e

ective method to address the apparent bolometer

gain variations that arise from the ADC non-linearities. In this

method, the absolute scale is fixed by the solar dipole, to en-

sure a better robustness against higher-order non-linearities, as

described in Sect. 3.2. Relative gains are determined using the

scanning redundancies, as explained in Sect. 3.3.

3.2. Solar dipole calibration

The photometric calibration of the 100–353 GHz bolometers is

based on the CMB dipole.

We estimate one value of the detector gain for each ring

through a template fit of the HPR data. We fit the coe

ffi

cients

of a linear combination of dipole, Galactic signal, and noise, ne-

glecting the CMB and the polarization:

(3)

Here

represents the HPR samples from ring

is the value

of the total (solar and orbital) kinematic dipole,

is a model

for the Galactic emission, and

is the white component of the

noise. For simplicity, we used a non-relativistic approximation,

as explained in Appendix A.2. We do not take into account the

smearing of the dipole by the instrumental beam in our proce-

dure, as justified in Appendix A.3. We simultaneously fit three

parameters:

, the gain of the kinematic dipole;

, the gain of

the Galactic model; and

, a constant accounting for the low-

frequency noise.

As the satellite scans circles on the sky, the ratio of the

dipole and Galactic signal amplitudes varies. We use a Galactic

model to obtain a measurement of the dipole gain, even in

rings where the dipole amplitude is low. However, imperfec-

tion of that model may lead to bias in the dipole gain. To

reduce this bias, we exclude pixels with a Galactic latitude

lower than 9

◦

. Because we calibrate on the kinematic dipole,

we do not use the gain

in what follows. Pixels contami-

nated by point sources listed in the

Planck

Catalogue of Compact

Sources (Planck Collaboration XXVIII 2014) are also excluded.

The best model we have for the sky emission at the HFI fre-

quencies being HFI measurements themselves, we use HFI sky

maps at the detector frequency as a Galactic model, as shown in

Appendix B.

Results of the gain estimation for each ring are shown in

Fig. 3 for one detector (143-1a) . We can see that the gain esti-

mate is less accurate on some ring intervals. This is due to the

Planck

scanning strategy: these intervals correspond to epochs

when the

Planck

spin axis is orthogonal to the dipole direction.

We can also see the apparent ring-by-ring gain variations, of the

order of

1%, explained in Sect. 3.1. To show this more clearly,

the figure compares the ring-by-ring variations reconstructed in

Surveys 1 and 2 with those from Surveys 3 and 4.

The final gain value for each detector, hereafter denoted by

, is defined as the average of these estimates between rings

2000 and 6000, between which the individual measurements for

each ring have a dispersion of less than 1%.

3.3. Effective correction and characterization

In order to handle time variation of the bolometer gains, we

set up an e

ective correction tool, called

bogopix

(Perdereau

2006). We start from Eq. (2), but take explicitly into account the

orbital dipole

, which is time-variable, and also fit the gains

for each bolometer independently. The problem finally reads

(

)

Γ

(4)

where

is the ring number. The unknowns are the o

sets

, the

sky signal represented by

, and the gains

, sampled using one

A8, page 4 of 25