Greek ladder is a technique for approximating Cn by rational numbers where n is a positive integer and C is a positive real number. For the classical Greek ladder, the value isC. Based on the continued fraction theory and algebraic equation, the classical Greek ladder in a special case can be reduced to the generalized Fibonacci sequence. By means of proper switching and binary, ternary or quaternary phase modulation, here we have successfully designed the various kinds of nano-photonic devices to produce three-dimensional array foci whose focusing properties satisfy the above mathematical characteristics. With this technology, the diffraction-limited array foci are freely designed or distributed under the requirement at the desired multiple focal planes.

Three-dimensional array diffraction-limited foci from Greek ladders to generalized Fibonacci sequences.

An algorithm for the digital reconstruction of the Fresnel-coded gamma camera image consists of the spatial Fourier transform of the hologram after applying a quadratic phase shift. Background subtraction is implemented by use of positive and negative zone plates. Tomographic planes are reconstructed in 27 sec from a single zone-plate shadow image by successively varying a parameter in the reconstruction algorithm on a small computer system.

Reconstruction of the Fresnel-coded gamma camera images by digital computer.

In a photographic camera, the camera lens forms an image of the object and the image is detected by the photographic film. In the Anger camera described in Chapter 4, the pinhole aperture or the multihole collimator performs the imaging operation while a detector system consisting of a scintillation crystal and an arrangement of photomultiplier tubes detects the image. The detector system in the Anger camera is very efficient and records almost every X-ray or γ-ray photon that arrives with an energy within the preselected energy window. Unfortunately, the imaging system severely limits the number of photons that arrive. A collimator typically passes only 0.01% of the radiation emitted by the object. Since the statistical quality of the images formed in this way is dependent on the number of photons collected from a single element of the object, one needs to collect as many photons as possible. Patient-dose restrictions limit the number of photons available, while exposure time is limited by temporal-resolution requirements in a dynamic study, by image degradation due to patient motion, by patient fatigue, or by the expense involved in tying up a clinical instrument for extended periods.

Coded-Aperture Imaging

A method of imaging a three-dimensional object with the aid of coding and decoding using coherent point codes, whereby the object is recorded in two steps, each with a plurality of radiation sources of different orientation on the same recording material. Negatives of the two images are produced, after which the positive of one image is combined with the negative of the other image, the combined images being subsequently multiplied by means of point holograms formed with the aid of a reference wave and a multiplicity of light sources whose co-ordinates correspond to those of the point images of the two source arrays recorded by a pinhole camera, the two multiplied images being superposed in one plane, the coded images being decoded by changing their scale with the aid of two synchronously controlled zoom lenses whereby the coordinates of the point image function of an image of an object layer in the coded images are adapted to the points stored in the two point holograms.

Image coding and decoding using coherent codes

Digital filtering of scintigrams and an investigation into the application of the Fresnel zone plate in nuclear medicine

Coded aperture imaging of X ray or y ray emitting objects using on-axis Fresnel zone plate apertures was the original method suggested by Mertz in 1961. Since then other forms of coded aperture imaging have become more popular. We show in this paper that, under certain well-defined conditions, high quality images can be obtained with Mertz' original encoding method.

M. D. Tipton

Papers

Coded Aperture Imaging with On-Axis Fresnel Zone Plates