Gaussian-apodized apertures are investigated for the purpose of reducing the diffraction background of a small-angle scatterometer. The farfield irradiance distributions of weakly truncated and untruncated Gaussian beams are compared. The envelope of diffraction ringing is shown to decrease proportionately with the level of truncation in the pupil. Spherical aberration and defocus are shown to have little effect on the higher-order diffraction rings of Gaussian-apodized apertures. A method is presented for determining the scattered irradiance level for a given bidirectional reflectance distribution function in relation to the peak irradiance of the point spread function. An example is provided that demonstrates that the small-angle diffraction background can be reduced by orders of magnitude as compared with a scatterometer with an unapodized pupil. Analysis of the point spread function is provided from 0 to 16 arcmin for an exit pupil diameter of 25.4 mm and A = 0.6328 Am. The numerical methods utilized to obtain these results are discussed.