Figure 4.

While there might be practical limitations to the number of zone plates that can be stacked together, one can obtain gains in first-order diffraction efficiency that go well beyond the simple thin zone plate expression of equation (1). In (a) we show the efficiency as a function of individual zone plate thickness and cumulative thickness t, where = zone plates are used with with a separation of = 10 µm (for = 45 µm, and = 25 nm for the first zone plate at 10 keV). A single gold zone plate with the optimum thickness = 2.0 µm would give = 32.7%, whereas much higher efficiencies can be obtained by using many more zone plates with slightly higher cumulative thickness. In (b) we show how the stacking of = 8 zone plates, each with a thickness = 0.5 µm, leads to differences in diffraction efficiency as one changes the separation distance between zone plates. Smaller separation distances are preferable but might be impractical, but even with larger separation distances like = 1000 µm one can still obtain an efficiency of = 36% if = 5 zone plates are used. All calculations were for gold zone plates at 10 keV.