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    A method for extracting object related information from in-line holograms using Wigner distribution
    (1990) Özgen, Mehmet Tankut
    In this thesis, a method based on Wigner distribution is developed to find the three-dimensional coordinates of particles directly from their in-line hologram without reconstruction. If a one-dimensional discrete hologram signed is subtracted from unity and the discrete-time Wigner distribution of the resulting signal is computed then a two-dimensional real sequence is obtained which can be displayed as an image carrying coordinate information about the objects encoded in the hologram. In order to analyze three-dimensional object distributions, the idea described above is adapted to the case of twodimensional holograms in the following way. A two-dimensional hologrcim is digitized in an image processing system, then, one of its rows or columns is selected and a DC level shift is given to thcit row or column. The discrete-time Wigner distribution of the resulting one-dimensional signal is computed and displayed as a two-dimensional image. If this is done for a sufficient number of rows and columns of the hologram then a set of images is obtained which contaixas the total information about the coordinates of particles encoded in the hologram.