A Fresnel zone plate is a diffractive element consisting of multiple concentric rings that alternate between transparent and opaque regions used to focus light or other wave-like objects. They were initially described in the 19th century by a French scientist named Augustin-Jean Fresnel, hence the name "Fresnel zone plates". Zone plates are used as imaging lenses with a single focus in photography instead of a lens or pinhole to create dazzling, soft-focus images. 

Instead of refraction or reflection, zone plates use diffraction. A zone plate is made up of a number of radially symmetric concentric rings called Fresnel zones that alternate between opaque and transparent states. Zone plates are circular diffraction gratings with increasing line densities in the radial direction. While the transparent rings pass through the even Fresnel zones, the opaque rings block the odd ones. Alternatively, the opaque rings block the even zones and the transparent rings flow through the odd zones. Light that strikes the zone plate will diffract around the opaque zones and act as a focusing lens. In order to create an image at the appropriate focus, the zones can be spaced so that the diffracted light interferes constructively there. Figure 1 represents a fresnel zone plate.

Figure 1: Fresnel Zone Plate

Let P be a point on a screen placed at a distance that has the brightest intensity of diffracted light (where the beams are brought into focus). Depending on where the light went through the zone plate, the phase of the light that arrives at the point P varies. The rings are selected so that at P, all of the phases of light passing through a transparent ring are within a certain range of  π. This indicates that none of the light passing through the transparent zones and arriving at P will cancel out. Although the light that has travelled through the inner and outer margins of a zone will be in anti-phase when it reaches P, this will be an incredibly minor component of the light. According to this, there is a half-wavelength path difference for light travelling to P from the zone's inner and outer boundaries.

Calculation of Fresnel Zone Plates

For a perfectly collimated beam, the fresnel number is given as

When Z > A, gives

Where A is the radial size of the beam 

Z is the distance from the beam to the observation point. 

The fresnel number decreases as Z increases. 

When the Fresnel number is low, about less than 1, the beam at the observation point is considered to be in the "far field" in comparison to the incident beam. Whereas, if it is greater than 1, the beam at the observation point is referred to as being in the "near field" in relation to the incident beam.

For non-collimated beams, if the observation point is closer to the focus, the converging beam will have an extremely low Fresnel number. Due to the absence of any zones where the observed phase reaches π, a completely spherical beam coming to focus will have a Fresnel number of zero. The Fresnel number increases as the observation point moves away from the focal region.

Applications of Fresnel Zone Plates

Fresnel zone plates are used in photography instead of a lens or pinhole. It has been proposed as a cheap alternative to gunsights or targeting lasers. Zone plates are used as imaging lenses, reflectors, and as laser focusing element that have variety of applications, such as micromachining, material processing, and scientific experiments.

Fresnel zone plates are often used in fluorescence microscopy for high-resolution imaging of small biological structures. They are also used in x-ray imaging to produce high-resolution images of objects which are useful for studying the internal structure of materials or in medical imaging applications.

Fresnel zone plates are used in optical experiments to study and observe the interference patterns produced by light. This can also be used to focus sunlight for solar energy collection that can be used to increase the efficiency of solar panels.