Confocal Paraboloids: Some Comments William B. Wetherell and Matthew P. Rimmer

Itek Corporation, Lexington, Massachusetts 02173. Received 11 June 1974. The afocal optical system made up of confocal1 parabo­

loids represents an interesting phenomenon: most lens designers are aware of the concept; many use it routinely for applications such as laser beam expanders2; yet few designers seem to recognize its full powers. The few liter­ature citations are incomplete and in obscure sources. No geometrical optics texts of which we are aware treat con­focal paraboloids at all. For this reason, we welcomed Rosin's Letter.3 Annable's reply (above) and Rosin's brief rejoinder lead us to add our own comments.

First things first: confocal paraboloids were not men­tioned in our paper on two-mirror aplanats,4 but only be­cause they fell outside its intended scope. We are aware of the special properties of confocal paraboloids and have considered them for applications discussed below.

There are two principal reasons why confocal parabo­loids are seldom cited. First, the concept as applied to visual telescopes is both hoary with age and faulty. Mer-senne first proposed the confocal mirrors telescope (using spherical mirrors) in 1639,5 only 31 years after Lippershey invented6 the refracting telescope. Its faults as a visual telescope lie in its pupils—if the confocal paraboloids are of useful magnification, either their exit pupil will be in­accessible or the field of view will be drastically restricted by vignetting. Second, most nonvisual applications (ex­cept laser beam expanders, which do not use the wide-field correction) require a real focus. Thus the confocal paraboloids will be part of a more complex optical system and will generally not be discussed separately.

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Fig. 1. Confocal paraboloids in the form of an eccentric pupil afocal Gregorian telescope, with focusing objective.

Our principal interest has been in the eccentric pupil Gregorian design variant shown in Fig. 1. (We under­stand that J. Titus of Honeywell has also made extensive use of this configuration, although we can cite no refer­ences.) Its most attractive features are its z-shaped opti­cal path, which lends itself well to baffling against stray light, and the fact that physical stops can be placed at the prime focus image and at the image of the aperture stop. The latter allows use of a Lyot stop to reduce diffracted light from sources outside the field of view. Thus confo­cal paraboloids used with a focusing objective combine to form a lens system with a moderately large field of view and a very high rejection ratio for stray light from outside the field of view, in a relatively small package. This con­figuration is also useful in laser communication systems, where stray light control is more important than the large field of view.

The confocal parabolic Cassegrainian configuration de­scribed by Rosin3 can also be used in an all-reflecting wide-field objective, if inverted and combined with one or two additional mirrors. This design is analogous to the inverted telephoto lens so common in 35-mm photography and has the same size disadvantages. Fields of view ap­proaching 20° have been achieved with variants of this de­sign. One intriguing possibility it suggests is a convert­ible focal length reflecting objective, in which the confocal paraboloids form a removable wide-field attachment. Curvature of field in the confocal paraboloids will re­strict the allowable magnification of the attachment, how­ever.

Confocal paraboloids are fully corrected for all orders of spherical aberration, for third and fifth order coma, and for third order astigmatism. They are not corrected for curvature of field, distortion, or the higher order field ab­errations related to coma and astigmatism. (Note that curvature of field means that confocal paraboloids are not afocal for off-axis image points.) Distortion and higher order astigmatism are affected by stop shifts, but the other aberrations are not. The magnitude of the uncor­rected aberrations is strongly dependent on magnification. A Gregorian version will show less distortion than a Cas-segrain version of the same magnification, but its field curvature and higher order aberrations will be larger. These higher order aberrations are one of the strongest factors limiting performance in the eccentric pupil config­uration of Fig. 1. They cannot be balanced out in the fo­cusing objective, because it is not symmetric about the same axis as the paraboloids.

References 1. We prefer the term confocal (analogous to concentric) to the

term afocal used by Rosin and Annable. Confocal paraboloids are, in fact, not afocal for off-axis field points.

2. W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969), p.53.

3. S. Rosin, M. Amon, and P. Laakman, Appl. Opt. 13, 741 (1974).

4. W. Wetherell and M. Rimmer, Appl. Opt. 11, 2817 (1972). 5. L. C. Martin, Technical Optics (Pitman, London, 1950), Vol. 2,

p. 72. 6. L. Bell, The Telescope (McGraw-Hill, New York, 1922),

Chap. 1.

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