Zone plate

A Fresnel zone plate, also called zone lens or movie form, is a plate mounted on the concentric rings. The zones differ in their transparency and / or in its optical path length. In one case, the radiation is diffracted by the annular columns and reinforced by constructive interference in deprived areas. In the other case, the black areas shown in the adjacent figure are replaced by a transparent material exactly a certain thickness, which causes a phase shift of the light wave of 180 °, so that the transmitted radiation at the focal point of these zones may also interfere constructively.

Except for light zone plates are used for focusing X-ray radiation as the X-ray lenses are very inefficient. For a long time producing so-called refractive X-ray lenses has even been thought impossible.

The Fresnel zone lens has in common with a Fresnel lens, only the inventor. Both were developed by Augustin -Jean Fresnel. The Fresnel zone lens can be viewed as a cross section through the Fresnel zone, which explains its name.

In a zone plate with binary gradation, ie completely transparent alternately with totally absorbing ( top image), the incident light is on many real and virtual foci distributed (see below). In order to concentrate the light on the two focal points of the 1st order, is only a sinusoidal contrast change required (lower panel ). The appropriate lens is similar to the diffraction image of a circular disk. Differences in the distances of the maxima result from the different imaging way: There is so-called Fraunhofer diffraction with radiation from infinity (which is focused by lenses) before, here the so-called Fresnel diffraction.

Calculation of the zones

For constructive interference in a focus, the radii of alternately transparent and absorbing zones in the " quadratic approximation ", the following equation must satisfy:

For the following applies:

And applies to the width of the narrowest of the outermost zone

This width corresponds to - up to a factor of 1.22 - the achievable spatial resolution with a zone plate in microscopy when it is used in its first order of diffraction. Here we see that the achievable with a zone plate resolution does not depend on the wavelength. 2008, the smallest zone widths in the X-ray microscopy unused micro- zone plates around 20 nm When using the zone plate in its m-th diffraction order is the achievable resolution but again higher by a factor m. These statements on the resolution are valid as long as the location resulting computational resolution is not smaller than the wavelength of the radiation used.

It will also be: the width of the outermost zone decreases linearly with the diameter of the zone plate. Because the length of the zones, but increases linearly with the diameter, the area of ​​the zones is constant - as long as the above-mentioned quadratic approximation applies.

For infinitely large zone numbers n such relationship to the zone radius and the zone width does not apply. The zone width then tends to a constant width. For g = f is this smallest achievable zone width.

Example

A green glowing object ( λ = 500 nm) at a large distance ( g » f) to be imaged by a zone plate whose inner radius = 10 mm ( n = 1). For m = 1 is the first focal point is located at 50 m ( spacing plate ) image, for m = 2 in case of 25 m, for m = 3, at 17 m. The zone plate is an order of magnitude smaller (inner radius of 1 mm), the focal lengths are smaller by two orders of magnitude, in the example, 0.5 m, 0.25 m, etc.

Application

Are zone plates in the X-ray optics, used especially in the X-ray microscope for focusing, since there is no collection lenses covering the frequency range with wavelengths of less than about 0.5 nm, because the absorption is too high in them. X-ray, the refractive index of all the electron transparent material is minimally smaller than 1, so that a single focusing lens ( biconcave ) shows minimal focusing. In particular, below 0.1 nm wavelength, the absorption is so low that an experimentally usable but focusing is achieved by a series of ultra-thin successively connected converging lenses, with so-called "compound refractive lenses ".

In photography zone plates may be used instead of a lens. With a zone plate optics captured images have a characteristic appearance. The hole of the camera obscura = 1 can be interpreted as an internal part of a zone plate of order m.

Measuring the roughness of a surface ( distance measurement) see Conoscopic holography

Importance in holography

The Fresnel zone plate was after its invention actually only a physical curiosity and even without application. However, with the invention of holography in 1948 came the zone plate to a whole new meaning. The Fresnelplatte in fact corresponds to a large extent the hologram of a single pixel when it is used as the reference wave during the hologram generating a plane wave or a spherical wave also. The only difference is that the hologram, in contrast to the shown on the right amplitude zone plate, has the only transparent and absorbing zones, continuous and there are no abrupt transitions transmission.

The relationship becomes clear when one considers that the Fresnel plate also acts as a diverging lens and a converging lens, ie, it has both virtual and real focal points - like a hologram which can reconstruct real and virtual image when the the hologram recording used reference wave or its complex conjugate is illuminated.

Since complex objects are nothing more than collections of pixels, one can understand the interference pattern as a superposition of a large number of Fresnel zone plates.