A beam homogenizer that minimizes undesired intensity variations at the output plane caused by sharp breaks between facets in previous embodiments. The homogenizer includes a hologram made up of irregularly patterned diffractive fringes. An input beam illuminates at least part of the hologram. The hologram transmits a portion of the input beam onto an output plane. In doing so, the energy of the input beam is spatially redistributed at the output plane into a homogenized output beam having a preselected spatial energy distribution at the output plane. Thus, the illuminated portion of the output plane has a shape predetermined by the designer of the homogenizer.