#### What is in this article?:

- Obtaining Beam-Pointing Accuracy with Cassegrain Antennas
- Feed displacement effects
- Pointing errors from hyperbola rotation
- System analysis

**August, 1967**

Cassegrain antenna specifications never seem to define the specific relationship between reflector deflection characteristics and those of the feed system components. Yet, such relationships seriously affect antenna pointing accuracy. This article defines and develops from a system standpoint these pointing-accuracy interrelations.

**Pointing-accuracy factors**

The Cassegrain system geometry is shown in Fig. 1. All possible misalignments (not restricted to the plane of the paper) are indicated. The variables that affect pointing accuracy are: 1. The rotation of the reflector; 2. The translation or lateral displacement of the feed phase center; and 3. The translation and rotation of the subreflector.

**Reflector beam deviation analysis**

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Best-fit-reflector motion for a Cassegrain antenna with feed system fixed is the same as for a focal-point feed system.

Referring to Fig. 2, the reflector pointing error, θ_{p}, results from the anti-symmetrical deflection characteristic of the parabolic reflector. Best fitting of the anti-symmetric deflections of the reflector causes beam shift and beam deviation. Consequently, both vertex translation (*δv*) and focal point translation (*δfp*) from the original focal axis occur.

Since the radius of the curvature of the upper half of the reflector for gravity deflections (at the horizon position and in the deflected shape) is less than that of the lower half, the best-fit axis of the entire reflector shifts from the original design focal axis is shown. This effect is also produced by differential wind and thermal loadings and from surface manufacturing and alignment tolerance deviations.

The best-fit rotation of the reflector axis, θ_{1}, is:

Relating the best-fit reflector axis to the design focal axis is accomplished by “translating” the focal point of the best-fit parabola an amount –*δfp*, which results in a counter-clockwise beam deviation angle (θ_{2}) of:

where *K *= RF beam-deviation factor. This is the equation normally associated with beam deviation in a focal-point feed system with feed motion.

The resultant beam deviation, θ_{p}, is:

Substituting,

This is the equivalent to the best fit or average rotation of the reflector aperture plane from its initial undeflected position.