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The principles established for periodic objects in parts I and II are extended to non-periodic objects. The basis for the extension lies in the possibility of introducing a virtual lattice, which can be treated as in parts I and II when working with a primary wave field that has zero amplitude outside a given spatial region. Thus it becomes possible to form an image without the use of a lens in a manner similar to holography but based on different principles. A reference wave (as used in holography) is not required. The new principle can be applied in a number of variations, some of which are discussed.