PubMed · 5278906
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J H Carter. 1971. A nomogram to solve thin lens problems.. https://doi.org/10.1097/00006324-197103000-00011
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The set of paraxial optical systems is the manifold of the group of symplectic matrices. The structure of this group is nontrivial: It is not simply connected and is not of an exponential type. Our analysis clarifies the origin of the metaplectic phase and the inherent limitations for optical map fractionalization. We describe, for the first time to our knowledge, an image girator and a cross girator whose geometric and wave implementations are of interest.
A new theoretical model of the Lau effect is presented. The transmittance of a diffraction grating can be expressed in an equivalent form as the sum of transmittances of thin cylindrical lenses. Therefore it is possible to explain the Lau effect on the basis of the well-known imaging properties of lenses. According to the given approach, the Lau fringes are created by overlapped images of the first grating that are formed by a set of lenses corresponding to the second grating in the setup. The theory leads to an exhaustive description of the Lau-effect parameters. In particular, one can indicate the shape of the Lau fringes and localize planes of the fringes dependent on the axial distance between gratings and their periods.