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Sections of nonrotational aspheric surfaces can be useful in a variety of optical situations. In several examples, image-forming objectives, as for photographic or electronic camera products, are described in which suitably located asymmetric pairs of refractive surfaces are devised, such that relative rotation about a displaced axis of one with respect to the other can be used to produce a focusing effect that is satisfactory for imaging purposes over reasonable fields of view and for practicable apertures and achromatic corrections. Taylor expansions about assignable reference points in any given surface of a sequence, together with suitable coordinate systems, can be employed to relate performance to shape parameters.

A family of two-mirror correctors has been devised in a more advanced form than that obtained by Paul in 1935. These correctors can be used in combination with any paraboloidal telescope of even the largest size and will yield a greatly enlarged photographic field without the need for refracting elements of any kind. Such correctors will be of particular use in the ultraviolet, and for space-borne telescopes into the far ultraviolet, with performance limited only by diffraction over angular fields appreciably larger than available heretofore.

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