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A Zone plate is a simple mask with opaque and transmitting regions, which when correctly constructed is able to focus incident radiation. Essentially it is a flat lens that works by blocking certain parts of the incident radiation, unlike, say, a glass lens which uses all the light falling upon it. There are many possible choices for the zone plate. These include, amongst others, the Fresnel zone plates and Gabor zone plates.

A Fresnel plate is a binary plate. That is, it has a binary transmission function, either blocking or completely transmitting radiation. It is designed so that the distance from the principle focus, f, to any of the transmitting zones is such that only radiation of similar phase is let through. This is how the zone plate is able to focus radiation. By only allowing through radiation which will be in-phase at a desired point, constructive interference of the waves ensure a focus as this point is produced. Unfortunately the Fresnel zone plate has multiple foci at f/3, f/5, f/7... This results in a blurring at the principle focus. The zone boundary radii are given by

rj=r1√j, where j=1,2...,N,

and r1 is the radius of the first zone which is calculated from

r1=√fλ,

with λ being the wavelength of the illuminating radiation. This implies that the Fresnel zone plate is has a focus dependent on wavelength, unlike lenses. This is true of all zone plates.

A Fresnel zone plate may be positive or negative. A positive plate has a transmitting central zone, while a negative plate has an opaque central zone.

A Gabor zone plate has a continuous transmission function. It is the same pattern produced when scattered radiation from a point interferes with a plane wave. It is the hologram of a point. This means that upon illumination of a Gabor plate the point is reconstructed, but both virtual and real images exist. The transmittance of a Gabor plate at a radius r, is given by

t(r)=½{1±cos(πr² / r1²)}

where r1 is the same as defined previously. The choice of sign depends on whether a positive or negative zone plate is required. A negative plate is equivalent to the radiation undergoing a phase shift of π on passing through the zone plate.

The Gabor plate has the advantage over the Fresnel zone plate in that it has only the single pair of conjugate foci. One disadvantage of a Gabor zone plate is that the intensity of the radiation at the focus is less than with a Fresnel zone plate, it is also more difficult to manufacture.

Zone plates can be used to create holograms from incoherent radiation.

My apologies if your browser cannot display the equations correctly. They are:
r[j] = r * sqrt(j)
r = sqrt(f * l)
t(r) = 0.5 * (1 +/- cos ( pi * r^2 / r^2))

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