Wigner distribution function of volume holograms.

Based on a linear systems approach, we derive the Wigner distribution function (WDF) of a 4f imager with a volume holographic three-dimensional pupil; then we obtain the WDF of the volume hologram itself by using the shearing properties of the WDF. Two common configurations, plane and spherical wave reference volume holograms, are examined in detail. The WDF elucidates the shift variant nature of the volume holographic element in both cases.