Optical systems with translational invariance
Utilization of telescopes has revolutionized the astronomy in the XVIIth century. Since the times of Galileo astronomers mainly use rotationally symmetric telescopes. However, already during the World War I Henri Chrétien introduced double-plane symmetric optical systems to create wide-angle optics for military use. These systems deform the image providing different magnifications in different directions of the image plane. For this property Chrétien called them anamorphic optical systems from the Greek anamorphoo (“to re-form” or “to transform”). Later anamorphic systems were used in the production of panoramic movies and for various wide field of view observations. Using novel technologies such as 3D printing, anamorphic optical systems may once again revolutionize the observational astronomy. In particular, they have potential to break current magnification records, which are reached by the James Webb Space Telescope and other greatest instruments of the epoch.
Such significant progress requires, however, the creation of theoretical foundations. In fact, aberrations (i.e. defects or inaccuracies in the image) get more complicated when breaking the rotational symmetry of the optical system. It is expected since the secondary waves are spherical according to the Huygens–Fresnel principle. Nevertheless, analytical calculation of aberrations for anamorphic systems is possible in certain approximations. One recently developed method is based on imitation of an anamorphic optical system by the pair of associated rotationally symmetric ones, which allows to derive the generalized ray-tracing equations. Roughly speaking, a cylinder is replaced by the two spheres, which imposes restrictions on the applicability of this method.
In a new scientific work carried out at the Faculty of Physics and Astronomy of the University of Wrocław the aberrations for cylindrically symmetric optical systems were obtained directly from the calculation of the optical path difference without the need for the above imitation. In addition, the translational invariance of these systems was used to derive generic properties of their aberrations. The researches at the University of Wrocław look forward to further theoretical and numerical investigations in this direction, and cooperation with the industry players on the way of manufacturing and testing the proposed solutions in laboratory and in space, using the small satellite platforms.
