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17 September 2018 Abbe experiment with inclined grating
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Abbe theory considers the image formation process in an optical system (OS) in two stages: obtaining a spatial spectrum in a back focal plane and composing an output magnified image in an image plane. Abbe-Porter experiments are bright illustrations of this theory. This theory can be extended from two-dimensional (2D) case to three-dimensional (3D) one. It has to consider the grating inclined relatively the optical axis round the axis parallel to the grating slits. It makes possible calculations of the minimum resolvable period (MRP) of an OS as the functions of the angle of grating inclination. The paper presents the optical setup for observation of spatial spectrums and magnified images in case of the inclined gratings. It has been demonstrated that this spatial spectrum is in full compliance with the proposed theory. It has been also shown that the MRP exists in case of inclined gratings in full compliance with the theory. This experiment may be considered as one of the very interesting experiments for demonstration, understanding and explanation of the physical process of 3D image formation by an OS. Famous Abbe experiment becomes only the partial case and, of course, the most important case of this experiment with an inclined grating.
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Volodymyr Borovytsky and Oleksii Hudz "Abbe experiment with inclined grating", Proc. SPIE 10745, Current Developments in Lens Design and Optical Engineering XIX, 1074512 (17 September 2018);

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