Comments on "The analysis of deployable umbrella parabolic reflectors"

In a recent paper (see abstr. B28664 of 1972), Ingerson and Wong show, using geometrical relations, that the entire deployable reflector can be thought of as being made up of an infinite number of parabolas. They give an expression for the focal length of this infinite collection of parabolas and then state incorrectly that `The infinite collection of parabolas has a continuous distribution of foci. Thus, if a primary feed is placed in focus for one parabola, it is out of focus for the rest of the collection´. This statement is evidently the result of improper application of geometrical optics (surface normals are not taken into account) and provides a wrong physical picture of the focusing and the axial defocusing in the umbrella parabolic reflectors