Spatial coherency originates from the fact that the illumination is never perfectly parallel and is actually slightly convergent at the best imaging condition, which can be described as having a distribution of different illumination tilts. The effect of illumination tilting on the phase contrast transfer function (PCTF) is to cause a phase shift about the y-axis and, in the same way as for the temporal coherency, the PCTF is averaged over this tilt distribution. The envelope function for the spatial coherency (Es) can be given by,
The Es has a defocus term, C1(Δf), which can be affected by the operator unlike the temporal coherency.
Note that the overall envelope function is affected by the angular spread α of the electrons incident at any specific point in the object plane because of the limited spatial coherence originated from the finite source size. Figure 3692 shows the separate effects of the temporal (Et) and spatial (Es) coherence envelopes on the phase contrast transfer function.
Figure 3692. The effects of the temporal (Et) and spatial (Es) coherence envelopes on the phase contrast transfer function.