5 Far sidelobes and beam resolution versus edge taper

COBE had to deal with rapidly changing local conditions--temperature variations in the instrument and surroundings, changes in the position of the Sun, Earth, and Moon with respect to the instrument, varying magnetic fields, etc. Differential measurement techniques were required.

The PLANCK orbit, design, and scan strategy reduce most such sources of error by orders of magnitude. For example, the largest systematic error for the COBE DMR was modulation of the ferrite Dicke switches by the Earth's magnetic field. The magnetic field at L₂ is orders of magnitude smaller than experienced by COBE; moreover, for the LFI instrument the effect of system susceptibility to variations in the solar magnetic field will be well below $1~\mu$K.

Further, with the PLANCK spin configuration there is no first-order process to induce spin-synchronous thermal variations. In COBE these produced effects only at the $1~\mu$K level, and in PLANCK the effects will be still smaller. The extreme thermal stability at L₂ means that the time scale of thermal drifts will be long compared to the 60s PLANCK spin period. The frequency dependence of the emissivity of the telescope surfaces and shields means that temperature stability requirements for PLANCK are driven by the HFI. For example, the HFI requirement for the temperature stability of the primary mirror is spin-synchronous variations of no more than $200~\mu$K, compared to the LFI requirement of 1mK (assuming that the mirror emissivity is that of vacuum deposited aluminum).

The primary environmental sources of error for the LFI are those due to imperfect off-axis rejection by the optical system of radiation from the Sun, Earth, Moon, planets, and Galaxy. These are variations in response as the spacecraft spins that cause errors. Jupiter is the strongest compact source that can actually pass into the beam, and data must be corrected or excluded when it falls within the $\simeq -56$ dB contour.

The radiation pattern at large angles from the main beam (sidelobes) is dominated by diffraction effects on the structure edges, that does not make negligible the response at large angles from the beam centre. Sidelobes introduce a contamination in sky temperature measured by the main beam due to the contribution of the sky signal entering the outer regions; this effect maybe significant principally owing to the Galactic emission, depending on the observed sky region, on the frequency and on the shielding efficiency. Further, the behaviour of the radiation pattern at intermediate angular scales from the beam centre has to be carefully considered.

The requirement on the rejection of radiation coming from directions far from the optical axis is stringent for PLANCK and does not pertain only to the telescope itself. Rather it is a requirement on the entire optical system, including the solar panel, shielding, telescope, and focal assembly components.

Since the far sidelobes of an antenna are largely determined by diffraction and scattering from the edges of the mirrors and from nearby supporting structures, they can be reduced by reducing the illumination of the edge of the primary. In the jargon of antenna design, this is called underilluminating the primary or, quantitatively, increasing edge taper, defined as the ratio of the power per unit area incident on the center of the mirror to that incident on the edge.

Of course, higher is the edge taper and lower is the sidelobe Galaxy contamination; on the other hand increasing the edge taper has a negative impact on the angular resolution. Results based on a simple computation performed in the parabola equivalent approximation are given in Table 4 for the LFI channels assuming beams located along the telescope optical axis. The spillover radiation is calculated as a ratio between the power outside the reflector and the total power emitted by the feed.

   

Table 4: Angular resolution, FWHM (in arcmin), directivity (in dB) and spillover losses at PLANCK LFI frequencies as function of the edge taper for the PHASE A Telescope. A simple parabola equivalent approximation has been used for these estimates that hold for beam located along optical axis only. The spillover has been calculated assuming a $\cos(\theta)^N$ feed pattern function: $\mbox{spill}_\% = 100 \times 0.9278^{ET \cdot 3.074 + 1}$where ET is the edge taper in dB

Edge Taper	15 dB	20 dB	25 dB	30 dB
		FWHM
30 GHz	32.5	34.6	36.8	39.0
44 GHz	22.2	23.6	25.1	26.6
70 GHz	13.9	14.8	15.8	16.7
100 GHz	9.8	10.4	11.0	11.7
		Directivity
30 GHz	51.1	50.6	50.0	49.5
44 GHz	54.4	53.9	53.4	52.8
70 GHz	58.4	58.0	57.4	56.8
100 GHz	61.5	61.1	60.5	59.9
		Spillover %
	2.9	0.9	0.3	0.1

Sidelobe structure sweeping across the Galaxy can produce artifacts in any direction, particularly, for LFI, at the lowest frequencies. From numerical simulations based on the optical results of De Maagt et al. (1998), objects of detailed works (e.g. De Maagt et al. 1998; Burigana et al. 1999b; Puget & Delabrouille 1999; Wandelt & Górski 1999), we find that the Galaxy straylight contamination at 30 GHz, defined as the signal entering from $\sim 1^\circ \div 2^\circ$ from the beam centre, shows a peak level at about 13 $\mu$K at low galactic latitudes, to be principally ascribed to the beam response at few degrees to the main beam, and maximum values of about $6~\mu$K at high galactic latitudes, to be principally ascribed to the radiation entering the main spillover at $\simeq 90$^ $^{\circ}\;$from the beam centre; the latter effect may be particular significant, contaminating the sky regions clean from relevant Galaxy contributions.

The PLANCK data will significantly improve our knowledge of galactic emission. Given a good characterization of the far sidelobes of the optical system before launch, a self-consistent reconstruction of both the Galaxy and the telescope radiation pattern could be made. But there will be residual errors in the reconstruction, and the purpose of PLANCK is to image the CMB, not the Galaxy. To ensure that the residual errors do not compromise PLANCK's primary science, we require that the level of galactic contamination be below the white noise level at 100GHz for 12months of observations, with a factor of two margin to allow for uncertainties in the level of galactic emission, over 50% of the sky. This can be translated into a requirement on the sidelobe levels outside the central beam, calculated for the actual positions of the feeds. The exact number depends on the details of the sidelobe pattern, but is in the range -60 to -70dB.