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2000 - 20012
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Bölüm: Işık University, Faculty of Arts and Sciences, Department of Mathematics × Konu: Lenses ×

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  • Küçük Resim
    Yayın
    On the realization of optical mappings and transformation of amplitudes by means of an aspherical "thick" lens
    (Gustav Fischer Verlag, 2000) Hasanoğlu, Elman; Polat, Burak Deniz
    The constraints for the realization of a given optical mapping by means of an aspherical ''thick" lens are investigated by using the laws of geometrical optics. The analysis yields us a partial differential equation which the optical mapping functions must satisfy as a necessary and sufficient condition. It is shown that thick lenses, which convert plane waves to plane waves, can be considered as a pure amplitude element, An interesting feature of this equation is that it does not involve the lens profiles. The problem of realization is later discussed for some special mappings and graphical illustrations of the aspherical lens profiles for a linear mapping are presented.
  • Küçük Resim
    Yayın
    A method for calculating profiles of a dielectric thick lenses
    (IEEE, 2001) Hasanoğlu, Elman
    Hasanov and Polat (see International Journal of Electronics and Communications (AEO), vol.54, no.2, p.109-113, 2000) investigated the transformation of a plane wavefront to another plane wavefront after passing through a thick lens and described the class of optical mappings realizable by means of such lenses. However, it is desirable to describe the class of optical mappings and calculate the lens profiles for a more general case when incoming and outgoing wavefronts have arbitrary shapes. For two reflecting surfaces a similar problem has been solved by Gasanov (1991). The aim of this paper is to provide a method for calculating the profiles of symmetric thick lenses which realize an a priori given optical mapping between spherical and plane wavefronts. It is shown that this mapping may be chosen freely and be used for various purposes such as satisfying Abbe's sine law or Herscel's condition exactly. We have shown, that calculating the profiles of lenses can be reduced to solving two first-order differential equations which can be solved separately. It is also shown that the geometry of the problem provides a natural condition to control the accuracy for the numerical solution of the obtained differential equations