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1 May 2012 Improvement method of the optical MTF by using Bayes' theorem and application results to a rod lens optical system
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Gradient-index (GRIN) lenses have excellent optical properties that are not generally observed in the case of homogeneous lenses. Hence, GRIN lenses are used to fabricate new optical elements that have promising applications in optical information processing and optical communication. For example, it is widely used for scanner, fax machines and copiers etc. One of the low cost fabricating methods of these lenses involves pulling up the core fiber vertically from a polymer solution whose refractive index has been adjusted to the desired value. But in fact, the refractive-index distribution is not ideal because of several factors in manufacturing. When a GRIN lens has the refractive-index distribution which is not ideal, it degrades modulation transfer function (MTF) extremely. In this paper, we studied the picture reconstruction by using Bayes' theorem. Bayes' theorem is applied to the degraded picture obtained in an experiment with the plastic rod lens, and as a result MTF has extremely improved. First, spatial distribution of point spread function (PSF) is calculated from the refractive index distribution inside a rod lens. The 4096 PSFs of spatial distributions are obtained by this calculation. By applying image processing using the Bayes' theorem, MTF becomes about 92.9% after the application, even if MTF is 23.3%. These researches show that Bayes' theorem is very effective in image restoration.
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Kotaro Okada, Shuma Horiuchi, Shuhei Yoshida, Zenta Ushiyama, and Manabu Yamamoto "Improvement method of the optical MTF by using Bayes' theorem and application results to a rod lens optical system", Proc. SPIE 8436, Optics, Photonics, and Digital Technologies for Multimedia Applications II, 843611 (1 May 2012);

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