A Fresnel zone plate is to be designed for a soft X-ray microscope operating at a…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

What an Instrument Can See, Ch Scalar diffraction theory, derived

Problem

A Fresnel zone plate is to be designed for a soft X-ray microscope operating at a photon energy

E=1200\ \mathrm{eV}

(use

hc=1239.84\ \mathrm{eV\,nm}

for the vacuum wavelength), with an overall diameter

D=50\ \mu\mathrm{m}

. The design target is a Rayleigh resolution of

25\ \mathrm{nm}

. ((a)) Using the Rayleigh resolution

1.22\,\Delta r_N

of a zone plate, where

\Delta r_N

is the width of its outermost zone, find the

\Delta r_N

required. ((b)) Using

N\approx D/(4\Delta r_N)

for the number of zones, find

N

. ((c)) Using

f=D\Delta r_N/\lambda

, find the focal length

f

. ((d)) The first-order efficiency of the plate is degraded if the illumination bandwidth exceeds

\lambda/\Delta\lambda\sim N

. Find the maximum photon energy spread

\Delta E

the beamline may deliver.