One of the most promising objectives of observational
cosmology achievable in the next decade is an
extensive (
of the sky), accurate (
), detailed (angular
resolution <30') imaging of the Cosmic Microwave Background (CMB) anisotropies. A
precise reconstruction of the primordial fluctuation spectrum up to multipoles of order
(corresponding to angular scales 
) provides a unique
tool to gain new insights on fundamental issues
of physics and cosmology. Following the COBE-DMR
detection of anisotropy (
) at large (
) angular scales
(Smoot et al. 1992), an increasing number of
experiments have been performed with ground-based and
balloon-borne instruments at degree angular scales (e.g.,
Cheng et al. 1994; De Bernardis et al.
1994; Clapp et al. 1994; Gundersen et
al. 1995; Ruhl et al. 1995;
Netterfield et al. 1995, and
references therein). A second-generation space mission,
however, is required to fully image the CMB anisotropies with
sub-degree angular resolution (e.g. Danese et al. 1995). It
has been shown (e.g. Jungman et al. 1996) that accurate
full-sky maps with resolution <30' yield precise
determination of all key cosmological parameters, such as the
total and baryon density parameters 
and 
,
the Hubble constant 
, the cosmological constant 
.
These parameters and a statistical analysis on the detected
anisotropies will allow to trace structure formation
mechanisms and the thermal history of the universe, while
producing effective tests of inflation. A number of space
projects are under study in Europe and in the U.S.A. to
address this outstanding scientific goal (Mandolesi et
al. 1995; Bouchet et al. 1995;
Bersanelli et al. 1996; Janssen & Lawrence
1995; Wright et al. 1996).
An important aspect to consider in the design of the space-borne
instrument and observation technique is
the accuracy and reliability of the method for calibrating
the detected sky signals. In this
paper we analyze the calibration issue based on the
COBRAS/SAMBA
Low Frequency Instrument (LFI) concept.
The LFI concept and the COBRAS/SAMBA mission have been described elsewhere
Bersanelli et al. 1995, 1996; Mandolesi et al. 1995;
Muciaccia et al. 1996), and here we only outline the main
features. The LFI is an array of 28 corrugated horns, each
feeding two independent
receivers, at the focal plane of an off-axis optical system. The array works in four frequency
bands (centered at 31.5, 53, 90, and 125 GHz) with passively cooled (
K)
differential radiometers based on state-of-the-art transistor amplifiers. Different channels
have different angular resolution: 30', 18', 12' and 12' FWHM for the 31.5, 53, 90
and 125 GHz channels, respectively. The spacecraft is spin-stabilized with a spin rate of 1
rpm, and the telescope field of view is offset by 70
with respect to the spin axis. It will
operate from a Lissajous orbit around the L2 point of the Sun-Earth system, pointed in
anti-Sun direction during normal operation. In the baseline scan strategy the spin axis will
be re-oriented by 5' every 2 hours, to compensate for the Earth revolution and keep the
anti-sun position
(footnote: Pointing maneuvers up to 
arou
nd the anti-sun position are
allowed, and an optimized mission plan for best sky coverage is currently under study
(Mandolesi et al. 1996)).
Therefore, each detector observes the same sky circle, approximately 
wide, for two hours before each 5' step.
The output of the n-th radiometer channel
(
) will be a
time-dependent voltage 
, expressed in term
s of telemetry counts. The purpose of
calibration is to convert the signal strength from raw telemetry data into physical units. The
calibration is performed in terms of antenna temperature,
proportional to the received power per unit bandwidth. If a
linear receiver (the system is designed to be linear in its operating range) observes during a
scan two sources of known antenna temperatures and
at times 
and 
, the calibration constant, or gain,
is determined by:
In principle, each value 
is constant in
time; in practice, temperature
variations or intrinsic instrumental effects may produce drifts or time fluctuations. Thus one
wishes to measure the calibration constants as accurately as possible and as
frequently as possible during the mission, and/or monitor the stability of
with time.
Following Bennett et al. (1992), we use the term
absolute calibration to refer to a measurement of the
value of 
, and relative calibration to refer to a
measurement of its time-stability.
The calibrating signal can be provided by stable solid-state noise sources, a strategy
adopted by the COBE-DMR experiment (Smoot et al. 1990;
Bennett et al. 1992). However, for an experiment
like COBRAS/SAMBA the implementation of a suitable active
calibration system is likely to require some compromise in
instrument performance (either additional insertion loss in
the front-end low-noise amplifiers for internal sources, or
some level of distortion in the optical quality of the
telescope for external sources). In any case, it is important
to evaluate the accuracy achievable using celestial sources
which will be observed during the survey. In this work we
limit the analysis to calibration with celestial sources. In
Sect. 2 we study the accuracy which can be achieved in the
determination of 
using the CMB dipole, the spacecraft
orbital velocity and the signal from external planets.
The rest of this work deals with our ability to control
long-term variation of the instrumental response.
The LFI receivers (Bersanelli et al. 1995)
measure signals 
proportional
to the antenna temperature difference between the sky
at a given frequency, 
, and a stable internal load associated with each receiver
at a comparable effective temperature, 
:
Thus, both changes in 
and drifts in 
can perturb
the measured signal 
. The two effects, however, can be decoupled. Since in a time
interval 
min we can assume that the instrument response is stable, the signal difference between two sky regions
and 
observed in the same scan circle can be written as
which is independent of 
.
Thus one can recognize the effect of a
change in the calibration constant as a time-variation of the quantity 
,
i.e., a change in the signal differences corresponding
to two (or more) fixed regions of the
sky. On the other hand, a change in the observed signal 
which
leaves 
unchanged is the
signature of a thermal variation of the effective load
temperature 
. In Sects. 3 and 4, we discuss the
effects of long-term gain drifts (relative calibration) and
thermal baseline changes, respectively.