Generalized holography and computational solutions to inverse source problems

The inverse source problem for oneand two-dimensional coherently radiating sources is studied within the framework of generalized holographic imaging. It is shown that the image field produced from a generalized hologram of a one-dimensional source contains a complete description of the source. For such sources, structure larger than one-half wavelength is accurately imaged, whereas information on smaller scales can be obtained from a linear operator applied to the image field. The image fields of two-dimensional sources are shown to contain only partial information about these sources. It is shown, however, that perfect imaging is possible for the class of sources satisfying the homogeneous Helmholtz equation. This class is shown to be identical with the class of minimum energy sources recently encountered in connection with the inverse problem for three-dimensional sources. For noisy images there are serious practical limitations on source detail obtainable from any imaging system; the generalized hologram achieves near-ideal performance when the image is noisy.