Blockage of the aperture field of a Cassegrain antenna by support struts for the secondary mirror has two adverse effects. One is the reduction of the aperture efficiency by an amount approximately equal to twice the fractional area blocked. The other is the increase in antenna noise temperature due to scattering of the radiation into the feeds from ambient surroundings. If the total aperture blockage is, say 3%, the aperture efficiency is reduced by ~6% and the increase in noise temperature could be as much as 9 K. For the extremely low receiver noise temperatures anticipated for the mmA the latter effect may be the more significant.

The overall strut geometry is determined largely by the mechanics of the structure. It is required to be stiff enough to avoid bending under wind loading and gravity (except, possibly for a homology component). It should also not have any resonances at frequencies that may be excited by the drive system or wind. The size and general arrangement for the struts must therefore be optimized structurally, but the detailed shape can be designed to minimize scattering of radiation at large angles to the boresight where it may fall on ambient temperature surroundings.

Some design aspects are examined below to estimate blockage and noise degradation.

II. Mechanical Considerations

Generally the support for a secondary mirror comprises a number of struts of uniform cross-section passing through the primary and attached to a mount supporting the secondary. The lowest natural mode of the whole support structure is generally a twist round the optical axis. In some antennas such as the JCMT and Voyager spacecraft, the support structure is similar to those of optical telescopes, with the supports arranged as triangular frames. This gives higher rigidity but also greater blockage [1]. Other antennas such as the OVRO 10-m and the NRAO 12-m have guy wires added to give torsional stiffness. The rotational mode may be excited if there are large azimuthal accelerations when the antenna is at high elevations but there should be little coupling with secondary mirror nutation and wind loading, for example. If a CFRP structure is used the natural damping will be higher than for a steel structure. Optically, the first order effect of this rotation is zero since the secondary mirror is nominally on the rotation axis. Small pointing shifts could result from asymmetry, and path length changes appear as a second order effect.

The stiffness of the structure depends on the strut dimensions. Torsional stiffness is proportional to the strut depth (radial direction), the cube of the width (azimuthal direction) and the inverse of the length. Since shadowing is not affected by the strut depth this may be quite large. The most critical choice is the width which strongly affects the blockage and stiffness.

Conventional structures use two, three, or four struts. The 2-strut solution is worse in the sense that it requires guy wires which stress the structure asymmetrically, but there are not major differences between the 3- and 4-strut solutions. For a given torsional stiffness the 3-strut solution has ~17% lower blockage. The choice of the number of struts may also be influenced by the symmetry of the backing structure.

For minimum blockage with a given strut width the fixture points should be at the rim of the primary mirror to avoid blockage of the spherical wave. This has been used on smaller antennas (e.g., OVRO 5-m, BIMA 6-m), but is not necessarily a good structural solution for larger antennas (e.g., OVRO 10-m, NRAO 12-m, JCMT 15-m, VLBA 25-m, Bonn 100-m), and an attachment diameter of 0.5–0.8 of the primary mirror diameter is more common. However, since the strut length is reduced, the strut width may be decreased for the same stiffness and the blockage penalty is minimized. Narrower base attachment makes the structure much more rigid as the bending stresses are decreased in favor of longitudinal compression stress.

Following the above arguments we choose a structure with three struts (Figs. 1, 2), radially oriented, and the base attached at about R_s = 0.325D, where the dish diameter D, is 10 m. The angle to the vertical, b , is about 44º, giving a horizontal distance from the focus, R_f, of about 0.58 m. No attempt has been made to optimize the structure as this will be part of the detailed structural modeling. However, the values are probably reasonable from the mechanical point of view. The struts are thicker in the radial direction than in the azimuthal one as this has no effect on the blockage. The strut profile is discussed later. Fig. 1 shows a rendered view of the design assumed for this study, and Fig. 2 gives the coordinate system and parameters referred to further on.

Fig. 2. (a) Parameters of the antenna and secondary mirror referred to in the text. The strut width, w, is given in the azimuthal direction. (b) coordinate system for the calculations.

III. Blockage and Spillover

For the short wavelengths of the mmA a geometrical optics calculation of the blockage is sufficiently accurate. When the struts are not attached at the rim of the primary they block both the plane wave from the aperture and the spherical wave from the secondary to the primary. The plane wave shadow is the projection of the struts on the aperture plane, and appears as radial shadows of the same width as the struts. The spherical wave shadow starts at the base of the strut and broadens out to the edge of the aperture [2]. The width at the edge depends on the distance of the strut from the prime focus along the geometrical edge ray. To keep this narrow, the top of the supports should be as far out from the axis as is structurally reasonable. In this strawman design we also taper the strut width, w, from about 80 mm at the base to about 50 mm at the top which gives a useful increase in stiffness with a small increase in blockage.

We have computed the blockage analytically, as well as using the Ray Trace Rendering capabilities of AutoCAD to determine the shadowing in the aperture plane (Fig. 3). The bitmap can be imported into Mathcad to calculate the area lost to blocking. This method can be used for any support geometry desired. With a secondary mirror diameter of 700 mm the total shadowing is ~2.6 % (2.8 % with aperture weighting). Of this, the struts contribute ~1.9 % (1.8 % with weighting). The maximum possible contribution to the antenna noise temperature by strut scattering is therefore ~5.5 K, though even with non-ideal structures we expect much less than this.

Fig. 3. AutoCAD ray tracing of the aperture plane shadow.

There have been several publications that predict the distribution of scattered radiation but these have generally been concerned with struts having widths comparable to a wavelength [3]–[6]. Rusch et al. [3] show that the scattering of a plane wave by a cylindrical member is in a conical pattern, with the cone axis along the strut and the cone half-angle equal to the angle of the strut to the plane wave direction. This is illustrated in Fig. 4. The distribution of the radiation round the cone is complicated, but it may be shown that it approaches the geometrical optics limit for short wavelengths. Provided the strut has the same cross-section over its length the scattering will still be in this conical pattern and only the variation of amplitude around the cone changes.

Instead of assuming cylindrical members, we take struts with a triangular inner surface. This profile has been proposed and used in several antennas, mainly as a retrofitted modification (see [4]–[7], for example). Fig. 5 gives the strut profile and the relevant dimensions.