1303.5069.pdf

Astronomy & Astrophysics

manuscript no. calibration

January 22, 2014

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. Huffenberger

, A. H. Jaffe

, T. R. Jaffe

, 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. Maffei

, 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

, A. Zonca

(Affiliations can be found after the references)

Received XX, 2013; accepted XX, 2023

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 different 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 effective correction to limit their effect 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. Both these uncertainties lie in the range from 0.3% 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.

Cosmology: observations – Cosmic background radiation – Surveys – methods: data analysis

Corresponding

authors:

Perdereau

perdereau@lal.

in2p3.fr

, G. Lagache

guilaine.lagache@ias.u-psud.fr

arXiv:1303.5069v2 [astro-ph.CO] 21 Jan 2014

Planck Collaboration:

Planck

-HFI calibration and mapmaking

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.

CMB experiments can be calibrated using the dipole

anisotropy induced by the motion 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, cal-

ibration using the orbital dipole involves comparison of data

taken at large time separation (typically 6 months), and the pre-

cision 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 addressing 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 elec-

tronic chain, and for the present release have chosen to use the

solar dipole, based on the measurement of the solar dipole pa-

rameters from

WMAP

(Hinshaw et al. 2009), as the main cali-

brator 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

accurate calibration. Although we used the Galactic emission

as measured by FIRAS for the calibration of the

Planck

early

papers (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 effective correction.

We then detail the calibration for the 545 and 857 GHz chan-

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

be fixed (Sect. 5). We finally quantify the accuracy of the photo-

metric 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

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.

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 [

◦

]

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 efficiently 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 detector, 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 parameter

side

set to 2048 we use the same internal

resolution for building the HPR.

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

cessing, is mostly white at high frequency, with a “

” in-

crease at low frequency (Planck HFI Core Team 2011a). In such

a case, a destriping approach is well suited for the mapmak-

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

is represented by an offset, denoted by

, and a white noise part

, which is uncorrelated with the low-frequency noise. We may

then reformulate Eq. 1 as

Γ

(2)

where

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

tion 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 likelihood.

As there is a degeneracy between the average of the offsets and

the zero level of the maps, we impose the constraint

〈

〉

Tristram et al. (2011) have shown that with scanning and noise

like those of HFI, an accurate reconstruction of the offsets

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

Planck Collaboration:

Planck

-HFI calibration and mapmaking

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

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 detec-

tors,

–

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 offsets using

the whole mission data set, and then use these offsets to

compute the maps for the whole mission, as well as for re-

stricted time intervals (corresponding to each individual sur-

vey, and to the 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

values computed in each pixel. Overall, a total of about

6500

sky maps have been produced. We used this data set to evalu-

ate 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 inte-

grated in the FSL and zodiacal light (hereafter called

zodi

)

components, which vary in time, we have constructed tem-

plates for the combination of these components at frequen-

cies 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 differences between maps from the previous set and

maps from which the

zodi

and FSL have been removed. The

difference 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.

3. Photometric calibration of the low-frequency

channels: dipole-based calibration

3.1. ADC non-linearities and calibration

With

larger

data

set

than

that

analyzed

Planck HFI Core Team (2011b), we could ideally use an

orbital-dipole-based calibration, as described in Tristram et al.

(2011). However, the additional redundancies revealed new

systematic effects, ADC non-linearities and very long time

constants (of the order of a few seconds) with very low energy

content in the system’s response. The former induce apparent

gain variations with time. The latter shifts the CMB dipole

a few arcmin in the scan direction, and hence creates leaks

from the Solar dipole into the orbital dipole signal. These

systematic effects 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.

Effects 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 differ-

ence maps for one 143 GHz detector, built using the calibration

and mapmaking scheme presented in Planck HFI Core Team

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

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

stant gain assumption used to build these maps is incorrect.

Figure 1.

Differences between temperature maps built using data

from detector 143-1a, for Surveys 1 and 3 (top) and 2 and 4 (bot-

tom). 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

the orbital dipole,

about 10 times lower.

Planck Collaboration:

Planck

-HFI calibration and mapmaking

Intrinsic bolometer sensitivity variations cannot explain such

gain variations. The HFI bolometers have been precisely char-

acterized in flight using a dedicated sequence of

(

)

measure-

ments, 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 re-

sponse variations larger than 0.1 %. In addition, such variations

are corrected for within the HFI DPC pipeline. In our present un-

derstanding, these apparent response variations are the result of

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

ers (ADC) used in the bolometer read-out units. The variation

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 affect signals differently 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 difficult 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

. This is larger

than the required calibration precision of the 100 to 217 GHz

channels.

-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]

Figure 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 regularly every 64 steps.

In order to precisely correct all the data for this effect, 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

K, to obtain a clean ADC charac-

terization on Gaussian noise. Correcting this effect needs to be

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

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

tion 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 effective 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 coefficients

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 effective 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

Planck Collaboration:

Planck

-HFI calibration and mapmaking

200

400

600

800

Time [days since 14 Aug. 2009]

1.75

1.80

1.85

1.90

1.95

2.00

2.05

Gain [W/K

CMB

]x10

143-1a

gains with HFI maps

smoothed (50 rings)

smoothed & translated

Figure 3.

Solar dipole gain reconstructed ring-by-ring for one

HFI bolometer. The thin black line represent the raw values, and

the thick cyan line is a smoothed rendition with a width of 50

rings (about 2 days). We have indicated the conventional bound-

aries of the surveys as black vertical lines. The orange vertical

dashed lines indicate the interval in which we compute the gain

(computed between rings 2000 and 6000, or approximately

days 60 and 190). The red curve shows the smoothed gain varia-

tion shifted to match the repetition in Surveys 3 and 4 of the scan

strategy followed in Surveys 1 and 2 (note that the scan strategy

for Survey 5 differs from that of Survey 3). The grey band high-

lights a

excursion around the averaged gain

. The

observed

∼

1% variations explain the large-scale residuals seen

in Fig. 1.

for each bolometer independently. The problem finally reads

(

)

Γ

(4)

where

is the ring number. The unknowns are the offsets

, the

sky signal represented by

, and the gains

, sampled using one

value per ring. Since the orbital dipole is an absolute calibra-

tor, the solution for

should also fix the absolute photometric

calibration.

We take advantage of the low amplitude of the observed gain

variations to linearize this nonlinear problem, following an iter-

ative approach. Starting from an approximate solution for the

gains

and sky maps

, we determine the variations with re-

spect to these,

δ

and

, by solving :

(

δ

)(

(

)

Γ

(5)

≈

(

)

δ

(

)

Γ

(6)

The linearized Eq. 6 may then be solved for

δ

and

by a conjugate-gradient method. Using

δ

and

, the gains

and sky maps

can be updated. This process is iterated

until a satisfactory solution is reached. To initialize the it-

erations, we start from the constant gain solution. We stop

when the relative change in the

derived from Eq. 4 is low

enough ( in practice, when the change is less than

−

). This

approach is similar to the one used for the LFI calibration

(Planck Collaboration V 2014). It was successfully tested us-

ing the data set of Tristram et al. (2011), derived from simu-

lated timelines with a

Planck

-like scanning strategy, realistic

noise (both for the white and

components), Gaussian beams,

and delta-function bandpasses, for four 143 GHz polarization-

sensitive bolometers over about 12000 rings. Figure 4 presents

gains reconstructed with

bogopix

on simulated data, and com-

pares them with the constant input gain values. From these re-

sults, we see that the precision of the gain value reconstructed

for a single ring is about

5 %

(which is comparable with the

global precision of

−

for a constant gain for 12000 rings

found in Tristram et al. 2011). We computed the gain variations

2000

4000

6000

8000

10000

Ring number

0.96

0.98

1.00

1.02

1.04

Relative gain

Figure 4.

Example of results obtained with

bogopix

on the

simulated data set used in Tristram et al. (2011), where constant

gains biases were applied. The colours distinguish four different

bolometers. Dots correspond to individual measurements, and

the thick line is a smoothed representation of these results with a

50 ring width. We plot relative reconstructed gains, with respect

to their unbiased value. In this simulation, each bolometer’s data

was biased by factors of respectively 1.98 (blue) , 0.77 (green) ,

0.50 (black) and 0.07 % (orange) respectively which is precisely

reflected by the recovered

bogopix

value.

using single-detector data, thus neglecting polarization. As in

destriping (Tristram et al. 2011), gradients within the sky pix-

els used for

will limit the accuracy of the gain determination.

These gradients increase with frequency. Moreover, the ADC

non-linearity will induce biases in the signal used for the gain

determination. As this signal’s dynamic range increases with

frequency, we expect this bias also to increase with frequency.

For these reasons, we used

bogopix

to determine an effective

correction for the apparent gain variations only for frequencies

≤

217

GHz. To avoid the central part of the Galactic plane and

point sources, we used the mask used for destriping in the

Planck

Early Results paper (Planck HFI Core Team 2011b, Figure 32).

As shown in Fig. 5, the variations of the gains

found with

bogopix

follow nicely those from the solar dipole calibration

(

) in the regions where this signal is large. The lower level

of fast variations from

bogopix

in the time intervals where

the scan lies close to the Solar dipole equator and at the same

time close to the Galactic plane, indicates that the

bogopix

re-

sults are less biased for these rings. We observe apparent gain

variations on time scales of a few hour as well as months, with

amplitudes of 1 to 2 % maximum, largely uncorrelated from one

detector to another.

The averaged gain level determined by the two methods are,

however, different by 0.5 to 1 %, and the difference varies from

one detector to another. We believe this is due to the different

scales of the calibrating signals in the two methods: the absolute

scale of

bogopix

results is set by that of the orbital dipole, a

factor of 5 to 10 lower in amplitude that the solar dipole used in

the other method. These signals are thus affected to different de-

grees by the ADC non-linearities. In the simplest case, the effect

of the non-uniformity of the ADC digitization steps is a fixed

offset (positive or negative) added on top of the signal, when

this signal oversteps a given level, so the resulting calibration

bias will be lower for the largest calibration signal.