On Gabor’s Expansion Theorem*

As a generalization for optics of the well-known sampling theorem of information theory, D. Gabor proposed an expansion theorem. It relates to the number of independent solutions of the wave equation in a region defined by the object and by the aperture of an optical system.A proof of this theorem presents formidable difficulties. In this paper, a proof relating to important cases is established, and a more accurate estimate for the number of the independent solutions in the general case is given.