Zone plate

A concentric diffractive focusing element with successive zone boundaries chosen to differ by half a wavelength of optical path to a focus. Alternating transmitting and absorbing zones suppress cancellation between neighboring half-period zones. For an incident plane wave, the paraxial boundaries satisfy $r_j^2=j\lambda f$. The outermost zone width controls the finest transverse scale, and the focal length varies with wavelength.

For uniform coherent plane-wave illumination, an ideal binary amplitude zone plate transmits alternate Fresnel half-period zones. If $N_o$ complete odd zones are open, every one contributes approximately twice the unobstructed axial complex amplitude, in the same phase, and $I_f/I_0\simeq 4N_o^2$. This is a local light intensity gain relative to removing the plate and outer stop. It differs from comparison with a finite clear aperture: an aperture containing an odd integer number of half-period zones has axial intensity $4I_0$, giving plate-to-aperture ratio $N_o^2$. Neither gain is a total power efficiency.