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A two-dimensional band-limited picture is scanned in such a way that the intensity and its directional derivative are sampled at equally spaced points along the scan lines which themselves are equally spaced. The sample points are then assumed to lie on a sampling lattice which consists of integral linear combinations of a pair of basis vectors. The necessary and sufficient conditions are then found such that a certain form of reconstruction formula will exist for a class of intensity functions characterized by the fixed bounded support of their Fourier transforms. These conditions relate this support to the reciprocal lattice of the sampling lattice. This is illustrated for the case of an isotropic support.