Does electron holography energy-filter?

The contribution of inelastic scattering to off-axis electron holograms is considered. For a sample which introduces a single sharp energy loss δE, we find that this loss contributes time-independent interference fringes to the hologram provided δE<ΔE, where ΔE is the electron source energy spread. The relevance of this to two-beam lattice imaging at the Bragg condition is outlined, and the relationship between the uncertainty principle, the Van Cittert-Zernike theorem and the phase-space interpretation of coherence and Brightness reviewed.