Showing papers on "Zone plate published in 1967"

Self-imaging objects of infinite aperture

Abstract: The necessary and sufficient conditions are derived in order that an infinite plane object, illuminated by a plane monochromatic wave of normal incidence, images itself without the aid of lenses or other optical accessories. This involves a solution of the reduced wave equation which does not satisfy the Sommerfeld radiation condition. The solution is obtained by requiring a geometrical-optics limiting condition as the wavelength λ goes to zero. Two cases of self-imaging are considered. The first case, called weak, deals with the faithful imaging of objects whose spatial frequencies are all much smaller than the (1/λ) value of the illuminating source. The conditions for this case demand that the two-dimensional Fourier spectrum of the object lies on the circles of a Fresnel zone plate. The second case, called strong, deals with the faithful imaging of objects for spatial frequencies up to the natural cutoff of 1/λ. Both doubly- and singly-periodic and nonperiodic objects are considered. For periodic objects the results are shown to agree well with the experimental and theoretical work to date, the latter of which has always employed the Fresnel–Kirchhoff diffraction integral with the parabolic approximation appropriate to Fresnel diffraction.

Resolving Power of a Zone Plate

Abstract: The resolution (Rayleigh criterion for resolution) of two point sources by a zone plate is analyzed with respect to the number of zones. It is determined that for N (number of zones) less than 200 the limit of resolution is greater than that of a lens with the same aperture diameter, D, if only the zones which contribute light with a positive phase to the point of observation are used, and less than that of the lens if only the zones which contribute light with a negative phase to the point of observation are used. But, in the former case the maximum value of the side lobe (secondary maximum, first ring) is less than that of an equivalent-diameter lens whereas for the latter case the maximum value is greater. For N greater than 200 the resolution and side-lobe values approach those of a lens in both cases.

Zone plate theory based on holography.

Abstract: A series representation developed from holography theory is used to determine the image distances and relative image intensities for three types of zone plates. The effect of nonlinearity in film reproduction on the hologram of a point object and the images produced by this hologram are discussed.

Photoelectric microcircuit components monolythically integrated with zone plate optics

Abstract: This invention concerns improved structures for the transformation of radiant energy into electric energy or vice versa. The improvement consists of combining a semiconducting microcircuit element with a zone plate optics into a compact integrated structure.

Fresnel zone plate generation.

Abstract: That old laboratory curiosity, the Fresnel zone plate, seems to have had always at least one peculiarity during its long history, i.e., the difficulty of making good zone plates with a large number of zones. In this laboratory, several methods of Fresnel zone plate fabrication were tried or considered. The object was to make a good zone plate composed of at least 1000 zones. Zone plate formation by Newton's rings was attempted, but the resolution in the system was not adequate for obtaining the large number of zones desired. The possibility of machine generation of the zone plate pattern was explored by contacting several companies which are engaged in this type of work. Also, one of the leading makers of custom reticles was consulted. All these possible sources could give no help in the making of any kind of template from which a thousand-zone zone plate could be made. Since drawing by hand or cutting through an overlay to make the entire pattern seemed far too arduous and time consuming, a combined graphical-optical method was devised for generating the zone plate pattern. A rotating shaft 15.24 cm long and 2.54 cm wide was pivoted at its center and rotated by a geared-down electric motor at approximately 10 rpm. A rectangular metal case containing a 30-W fluorescent lamp extending over the whole radius of the beam was used as a light source. A glass plate formed the top of the rectangular box facing the camera. Over this glass plate was stretched a sheet of Mylar upon which was drawn the Fresnel zone plate generating pattern in opaque and translucent zones. The pattern on the rotating beam was radially masked, as shown in Fig. 1, to balance

Fresnel zones and field ion microscopy

Abstract: It is shown that the pattern from a single‐crystal tip in a field ion microscope is a collection of Fresnel zone plates. The focal length of a zone is proportional to the interplanar spacing of the set of planes responsible for that zone.