“…Both ε and B are conserved in an ideal optical system but are degraded by Coulomb repulsion between electrons, which reduces B and increases ε. An even more useful measure is the coherent fluence: N c = N p λ 2 /ε 2 = πλ 2 B T/e, which is unaffected by electron acceleration, beam focusing or apertures, space charge, or pulse compression but is degraded by lens aberrations and stochastic interaction [43]. For diffraction-contrast images, N c ≈ 1 suffices, but for phase-contrast or diffractive imaging, N c > 10 is required, whereas current UED systems have N c << 1 (Bryan Reed, personal communication), hence the need for electron gun development, which includes maximizing the extraction field at the photocathode, ensuring low capacitance (for short pulses), and reducing the thermal emittance by using a low cathode temperature.…”