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The beam pattern and the polarization characteristics
of the radio telescope RATAN-600

E.K. Majorova, SAO RAS

Results ara presented of calculation of the Mueller matrix elements of the radio telescope RATAN-600 that connect the the Stokes parameters at the input and output of the antenna setup of the radio telescope. The computation is performed with allowing for the diffraction effects in the space between the primary and secontary mirrors and for limited width of the primary mirrow ring. The proportion of spurious linear and circular polarization from the antenna is estimated when modeling passage of extended across the beem pattern.

      The Mueller matrix elements was computed via formulas  [1]:

where are the beam patterns (BP) for main polarization and cross-polarization, when the field of the feed is vertically polarized and      are the beam patterns for main polarization and cross-polarization, when the field of the feed is horyzontally polarized.
     The matrix element    characterize the power BP of the radio telescope for an unpolarized source of radio emission, element   determine the BP of spurios circular polarization, element    characterize variations of the position angle of linearly polarized radiation. The BP were computed by the aperture method, proceeding from the fild distribution in the aperture of the primary mirror.    The components of the main and cross-polarization components of the electric field in the vertical aperture of the primary mirror was computed in Frenel diffraction approximation.   The field distribution in vertical apertute secontary mirrors was computed in the approximation of geometrical optics, proceeding from the BPs of the primary feeds. [2].

Fig.1.  The BP of RATAN-600 ()and the two-dimensional matrix elements () () at wavelength  32 cm, are computed in approximation of geometrical optics - (a) and in the Frenel diffraction approximation - (b) for different heights of observed sources h.

      For the vertification of computations accuracy a comparison was made of calculated and experimental relations between the maximum values of the BP () in different horizontal cross-sections and the shift value of the section in elevation with respect to the central cross-sections. The experimental relations was got from observations of brigth point cosmic sourses in the mode of transit of a sourses across the immovable BP of the telescope. The observations conducted for different heights of the sources with the focused antenna and in the presence of aberrations. In the process of the sourse  1830-211 (h=25o) observation the primary feed at wavelength   7.6 was at the focus of the antenna, the primary feed at wavelength  3.9 it was displaced from the focus by 7.8 

.2.  Maxsimum of values   of the BP   in different  horizontal  sections for the wavelength  7.6 cm - (a) and for the wavelength  3.9 cm - (b).  Curves 1 is computed in the Frenel diffraction approximation, Curves 2 - in approximation of geometrical optics, the triangles are the experimental values derived from observations of hte point source  1830-211 (h=25o).

      The calculations carried out with provision for the diffraction effects and also more correct allowance for thr vertical size of the reflected elements of the primary mirror made possible revision of the shape of the BP of the radio telescope RATAN-600 both in intensity and polarization. The power beem patterns of the radio telescope and the Mueller matrix elements computed with allowance made for these effects have a smaller extent in the vertical plane than those calculated in approximation of geometrical optics. The reduction of the solid angle of the BP proved to be the more considerable the lower elevation of the source and the longer of the wavelength. From this it follows that at long wavelengths the effect of confusion will be far weaker than it was assumed earlier. Allowance for the diffraction effects causes narrowing of the aberration-free zone of the radio telescope near zenith and disturbance of antisymmetry of the element with respect to the central horizontal section ( the maximum (minimum) values of the element in the upper half-plane differ from the minimum (maximum) values of the lower half-plane in magnitude).

Fig.3. The aberration curves at the wavelength  1 cm for h=90o. Solid lines - the diffraction approximation, dashed lines - approximation of geometrical optics.

     The portion of spurious polarization from antenna    as an expended sourse passes across the BP of the radio telescope was computed as the ratio of the maximum value of convolution of the element   wiht a Gaussian to the maximum value of convolution of the element   with the same Gaussian. The computations was carried for the case symmetrical and H planes of the BP of the primary feed and for case assymmetrical of the BP in the range of wavelengths   =132 cm. The calculation have show, that, when the BPs of the primary feed are symmetrical about the polarization, the portion of spurious circular polarization does not exceed 35%, the portion of spurious linearly polarization does not exceed 4%. The proportion of spurious polarization related to non-symmetry of the horn BPs in E and H planes is estimated. The calcucation have shown that the portion of spurious linearly polarization from the antenna at the wavelength 1 cm in the investigation of the relic background fluctuation with RATAN-600 (experiment "Cosmological gene") will not exceed 1% even at great displacements of primary feeds from the focus if the asymmetry of the horn BPs in E and H planes is not higher than 10%.

Fig.4.  Maximum values of elements at the wavelength  32 cm as dependent on the elevation of the source. The solid line refers to in the upper half-plane, the dashed line to in the lower half-plane.

[1]  Esepkina N.A., 1972, Astrophyz.Issled. (Izv.SAO), No.4, p.157.
[2]  Korzhavin A.N., 1979, Astrophyz.Issled. (Izv.SAO), No.11, p.170.