We present equilateral hyperbolic zone plates with variable focal length, which are formed as moire patterns by a mutual rotation of two identical basic grids. Among others, all principal zone plates, except of the spherical one, can be used as these basic transmittances. Three most important advantages of the proposed moire zone plates are: a constant aperture of the created element during the mutual movement of basic grids, lack of aberrations due to their undesired mutual lateral displacements and high diffraction efficiency of the binary phase version. To obtain clearer moire fringe pattern, a radial carrier frequency can be added additionally to the transmittances of basic grids. The destructive interference between both arms of the focal cross of the equilateral hyperbolic moire zone plate can be obtained by a constant phase shift introduced in the transmittances of the basic grids. Potential applications of discussed elements are indicated, including the most promising one in the three-point alignment technique.

Equilateral hyperbolic moiré zone plates with variable focus obtained by rotations

There are given equations describing the basic grids, which superimposed with themself, create the moire pattern in the form of the spherical, equilateral hyperbolic, and linear zone plates. All cases are derived for mutual displacements performed by translations along the axes of the coordinate system and by rotations. A family of basic grids set up a complete set of solutions. Moire zone plates can serve as imaging elements with very long, variable focal length, and have an application in alignment in the technique of three points.

Fresnel zone plate moire patterns and its metrological applications

The paper presents a proposal of multiorder varifocal moire zone plates, which change their focal length because
of the lateral displacement of their two components with transmittances described by a cubic profile. The newly
introduced element turns out to be an intermediate solution of the hitherto existing elements, which are the
refractive Alvarez lens and its diffractive counterpart. Some of the expected properties of multiorder varifocal
moire zone plates are discussed, as well as reasons, because of which this newly introduced set of elements can
be of interest in practical applications.

Multiorder varifocal moiré zone plates

Design of equilateral hyperbolic zone plate moire pattern formed by a mutual rotation of two basic grids is studied in detail. The advantages of this zone plate moire pattern are analysed in comparison with solutions for other moire zone plates. Two most important advantages are: a constant aperture of the element during the mutual rotation of basic grids and a lack of aberrations due to their undesired displacements. The applicability of considered moire pattern for the three point alignment technique is mentioned.

Salvador Bar

Papers

Varifocal equilateral hyperbolic zone plates obtained by rotational moire