The formulae for the monochromatic radiation intensity at the Earth during the lunar occultation of an incoherent source are examined. It is shown that the oscillatory portion of the radiation intensity may be assigned an envelope amplitude and phase a+ each instant of time. Each complex number thus defined gives the amplitude and phase of one spatial Fourier component of the source brightness distribution. Resolution is limited by the maximum available spatial frequency, and is shown to depend on integration time, seeing, antenna aperture, bandwidth, and the signal-to-noise ratio of the observation. When observations are polychromatic, the monochromatic intensity is modified by a certain function of bandwidth and wavelength. This function is specified and theoretical occultation curves of a point source are given for various bandwidth-wavelength ratios. A new method of estimating a brightness distribution is illustrated by taking the inverse Fourier transform of the spatial Fourier components present in an occultation record of 3C 49. Restored distributions for the quasars 3C 273 and 3C 245 are also given. Source positions and/or lunar limb slopes may be determined from such distributions. When the width of single sources or the angular separation of double sources is all that is required, only the inner part of the envelope of the occultation record need be determined. Theoretical curves and envelopes are presented for use in comparisons with observed data.