The effectiveness of different types of diffractive optical element (DOE) for homogenizing partially coherent beams is analyzed, both analytically and numerically. The effectiveness is described by the homogenizing parameter, defined as the inverse of the normalized variance of the dose distribution. For an important class of DOEs designed with common discrete-Fourier-transform methods, it is found that the homogenizing parameter is only of the order of the number of coherence cells in the illuminating beam. However, for a different type of DOE that produces distinct beams under coherent illumination, the homogenizing parameter can be an order of magnitude higher. The inherent dehomogenizing effect caused by the limited temporal duration of the beam, a phenomenon sometimes referred to as dynamic speckle, is also considered.
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