Diffraction in the near-forward direction is examined for the localized model of an off-axis focused Gaussian beam scattered by a sphere when the beam is translated off-axis either in the scattering plane or perpendicular to it. The results are analyzed using the Fraunhofer diffraction approximation. We also obtain various Debye series contributions to the exact GLMT co-polarized VV and HH scattering amplitudes and cross-polarized VH and HV scattering amplitudes, and discuss their interpretation. Time-domain scattering is also considered for both the exact GLMT scattering amplitudes and our approximation to them, for which the sum over azimuthal modes is evaluated analytically. It is found that although the approximation accurately reproduces the overall magnitude of the scattered intensity, it is not as accurate in reproducing the phase of high-frequency oscillations in the intensity.