The smoothing of the spatial illumination of an inertial confinement fusion target is examined by its spatial frequency content. It is found that the smoothing by spectral dispersion method, although efficient for glass lasers, can yield poor smoothing at low spatial frequency. The dependence of the smoothed spatial spectrum on the characteristics of phase modulation and dispersion is examined for both sinusoidal and more general phase modulation. It is shown that smoothing with non-sinusoidal phase modulation can result in spatial spectra which are substantially identical to that obtained with the induced spatial incoherence or similar method where random phase plates are present in both methods and identical beam divergence is assumed
