  An analysis of the homodyne tomography process that is often used to
determine the Wigner functions of quantum optical states is performed to
consider the effects of the spatiotemporal degrees of freedom. The homodyne
tomography process removes those parts of the input state that are not
associated with the mode of the local oscillator by tracing out those degrees
of freedom. Using a functional approach to incorporate all the spatiotemporal
degrees of freedom, we find that this reduction in the degrees of freedom
introduces distortions in the observed Wigner function. The analysis also shows
how the homodyne tomography process introduces a resolution that depends on the
strength of the local oscillator. As examples, we consider coherent states,
Fock states and squeezed vacuum states.
