Coded aperture imaging is analyzed in Fourier space and the conditions for obtaining artifact-free 3-D images are obtained. It is deduced that an infinite square array of coding apertures will obey these conditions. A finite array is considered and it is shown that, after a certain coordinate transformation has been performed, the finite aperture acts to bandlimit the spatial frequencies in the image. This result is used to deduce a sampling theorem for coded apertures which places limits on the artifact-free 3-D information that may be obtained. It is thus deduced that 3-D information with a resolution greater than the limits placed here may only be obtained by extrapolating the data to larger viewing angles.