Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits

B.D. Smith (ibid., vol.MI-4, p.15-25, 1985; Opt. Eng., vol.29, p.524-34, 1990) and P. Grangeat (These de doctorat, 1987; Lecture Notes in Mathematics 1497, p.66-97, 1991) derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeat's inversion formula is mathematically different from Smith's one, they have similar overall structures to each other. The contribution of the present paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeat's inversion formula and Smith's one can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam back projection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeat's intermediate function is exact for any complete orbit, whereas that based on Smith's intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies.     

Phase-retardation and full-polarization analysis of soft-x-ray synchrotron radiation close to the carbon K edge by use of a multilayer transmission filter

We have produced a multilayer transmission filter with 100 periods of Cr/C to achieve a significant phase retardation while maintaining good transmission for photon energies just below the carbon K edge. This device was installed into a polarimeter behind the SX700/3 monochromator at the Berlin synchrotron radiation laboratory, BESSY. The phase-retardation properties were observed as theoretically predicted. Agreement between experiment and calculation could be obtained by introduction of a rather small interface roughness in the simulation code (σ = 0.65 nm rms). An observed phase retardation of 5° was sufficient to permit, for the first time we believe, a complete and unambiguous polarization analysis of soft-x-ray synchrotron radiation (265-eV photon energy) with primary standards.     

Measurement of optical waveguide scattering loss: an improved method by the use of a Coblentz mirror

Light scattered from optical waveguides is collected by a Coblentz mirror, which provides a stable, accurate, and relatively high signal-to-noise ratio measurement. The scattering loss of the waveguides is analyzed from the measured scattered-light-power distribution functions, and the results show that the attenuation coefficients of the waveguides can be expressed by the derivative of these scattered-light-power distribution functions, which can be calculated from a least-squares fit to the measured scattered-light-power distribution functions.     

Thermal feedback control techniques for transistor-transistor logic triggered CO(2) laser used for irradiation of biological tissue utilizing infrared fiber-optic radiometry

A fiber-optic radiometer is used to monitor and control, in real time, the temperature of samples of biological tissue irradiated with a CO(2) laser. Several control algorithms are investigated and the optimal control mode is obtained. A silver halide infrared fiber is used both to deliver the CO(2) laser radiation needed to irradiate the target and to deliver the thermal radiation emitted from the target back to the radiometer. Such a system can be useful in medical applications of CO(2) lasers.     

Scalable optical hypercube-based interconnection network for massively parallel computing

Two important parameters of a network for massively parallel computers are scalability and modularity. Scalability has two aspects: size and time (or generation). Size scalability refers to the property that the size of the network can be increased with nominal effect on the existing configuration. Also, the increase in size is expected to result in a linear increase in performance. Time scalability implies that the communication capabilities of a network should be large enough to support the evolution of processing elements through generations. A modular network enables the construction of a large network out of many smaller ones. The lack of these two important parameters has limited the use of certain types of interconnection networks in the area of massively parallel computers. We present a new modular optical interconnection network, called an optical multimesh hypercube (OMMH), which is both size and time scalable. The OMMH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the torus (constant node degree and size scalability) networks. Also presented is a three-dimensional optical implementation of the OMMH network. A basic building block of the OMMH network is a hypercube module that is constructed with free-space optics to provide compact and high-density localized hypercube connections. The OMMH network is then constructed by the connection of such basic building blocks with multiwavelength optical fibers to realize torus connections. The proposed implementation methodology is intended to exploit the advantages of both space-invariant free-space and multiwavelength fiber-based optical interconnect technologies. The analysis of the proposed implementation shows that such a network is optically feasible in terms of the physical size and the optical power budget.     

Signal-to-noise ratio of nonlinearity recorded holograms of diffuse objects

A nonlinear model for holographic recording materials is used to evaluate the signal-to-noise ratio in diffuse-object holograms. A comparison of this model with the linear model proposed by Upatnieks and Leonard [J. Opt. Soc. Am. 60, 297 (1970)] shows that our model justifies the experimental results obtained for dieletric holograms at high density before bleaching.     

Development and field demonstration of a hardware-compressive fiber-optic true-time-delay steering system for phased-array antennas

We describe the design, fabrication, testing, and antenna-range demonstration of a photonic wavelengthmultiplexed true-time-delay steering system for use with broadband phased-array antennas. The prototype system is based on a unique hardware-compressive architecture and can drive 16 antenna elements over the 0.35-2.1-GHz band with 6-bit angular resolution over a ±45° scan angle.     

Shadow Doppler technique for sizing particles of arbitrary shape

The output from a linear diode array is used in a modified laser Doppler velocimeter to measure the size and shape of irregular particles. The sizing accuracy for transparent and opaque particles between 30 and 140 μm is better than 10%. The inaccuracy caused by trajectories that lay at angles of less than 24° to the axis of the array was less than +5%, and a further inaccuracy of +5% was caused by defocusing of the particle from the center of the velocimeter measuring volume by up to ±500 μm. The advantages of the shadow Doppler technique over other techniques for sizing irregular particles, such as amplitude systems with pointer volumes, are that the shadow Doppler technique records shape, the optical arrangement is more robust, less precise alignment is required, and the equipment can be constructed at low cost.