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The beam-deviation formula for the feed system, θFS, obtained from the combined effects of feed translation (θc), hyperbola translation (θht), and rotation (θhr), is:

Substituting,

where δc and δht, and δhr are positive displacements in the + Y direction (Cartesian coordinate system).

The beam deviation formula for the Cassegrain system as an assembly is:

Substituting,

Once a reflector structure has been designed for minimum weight commensurate with its stress and surface accuracy requirements, its pointing error can be minimized. This can be achieved by the proper selection of deflection characteristics for the feed cone and hyperbola components. This becomes clear once it is realized that feed-cone and hyperbola motions are nothing more than different forms of focal-point motion identical to feed motion for a primary-feed system. Consequently, component weights, surface accuracy, and pointing accuracy can each be optimized individually utilizing the system equations here developed.

Pointing-accuracy criteria for each Cassegrain-system component have been developed. The individual effects can be isolated and the most significant parameters detected.

The most significant parameters that affect beam pointing are the rotation of the parabola and translation of the hyperbola. Feed-cone translation has an approximate 20 percent effect on beam pointing; hyperbola rotation, approximately a 10 percent effect. The magnification factor also has a significant effect.

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