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Some geometric transformations cannot be implemented exactly with continuous holographic optical elements (HOEs), since the grating vector field defining the element is not irrotational. In this paper, a new method is presented to implement such transformations. An element is produced by replacing the rotational part of the grating vector by a set of spiral phase dislocations. The method can cope with general transformations, and it is used to produce a HOE to implement a non-rotationally symmetric intensity transformation. The phase dislocations show up as holes in the intensity of the image of the HOE. The results are discussed.
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Carl Paterson (1994) studied this question.
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