The theory of the Mesooptical Fourier Transform Microscope (MFTM) for nuclear research emulsion is given. The structure of the output signal produced by the MFTM for straight-line tracks of particles is analyzed, and the signal-to-noise ratio is estimated. Some algorithms for search for events on the basis of the output signals of the MFTM are described. Descriptive examples are given to show the topological difference between traditional optics and mesooptics. Experiments performed on the MFTM of the Joint Institute for Nuclear Research are described.