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The uniformity of focused laser beams, that has been modified with randomly phased distributed phase plates [C. B. Burckhardt, Appl. Opt. 9, 695 (1970); Kato and Mima, Appl. Phys. B 29, 186 (1982); Kato et al., Phys. Rev. Lett. 53, 1057 (1984); LLE Rev. 33, 1 (1987)], can be improved further by constructing patterns of phase elements which minimize phase correlations over small separations. Long-wavelength nonuniformities in the intensity distribution, which are relatively difficult to overcome in the target by thermal smoothing and in the laser by, e.g., spectral dispersion [Skupsky et al., J. Appl. Phys. 66, 3456 (1989); LLE Rev. 36, 158 (1989); 37, 29 (1989); 37, 40 (1989)], result largely from short-range phase correlations between phase plate elements. To reduce the long-wavelength structure, we have constructed phase patterns with smaller short-range correlations than would occur randomly. Calculations show that long-wavelength nonuniformities in single-beam intensity patterns can be reduced with these masks when the intrinsic phase error of the beam falls below certain limits. We show the effect of this improvement on uniformity for spherical irradiation by a multibeam system.
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