Zone Plate - Design and Manufacture

Design and Manufacture

To get constructive interference at the focus, the zones should switch from opaque to transparent at radii where

where n is an integer, λ is the wavelength of the light the zone plate is meant to focus and f is the distance from the center of the zone plate to the focus. When the zone plate is small compared to the focal length, this can be approximated as

.

For plates with many zones, you can calculate the distance to the focus if you only know the radius of the outermost zone, r _N, and its width, Δ r_N:

In the long focal length limit, the area of each zone is equal, because the width of the zones must decrease farther from the center. The maximum possible resolution of a zone plate depends on the smallest zone width,

Because of this, the smallest size object you can image, Δl, is limited by how small you can reliably make your zones.

Zone plates are frequently manufactured using lithography. As lithography technology improves and the size of features that can be manufactured decreases, the possible resolution of zone plates manufactured with this technique can improve.

Unlike a standard lens, a binary zone plate produces intensity maxima along the axis of the plate at odd fractions (f/3, f/5, f/7, etc.). Although these contain less energy (counts of the spot) than the principal focus (because it is wider), they have the same maximum intensity (counts/m^2).

However, if the zone plate is constructed so that the opacity varies in a gradual, sinusoidal manner, the resulting diffraction causes only a single focal point to be formed. This type of zone plate pattern is the equivalent of a transmission hologram of a converging lens.

For a smooth zone plate, the opacity (or transparency) at a point can be given by:

Binary zone plates use almost the same formula, however they depend only on the sign:

where r is the distance from the plate center and k determines the plate's scale.