Equivalent Prisms Research Articles

Rotationally Reconfigurable Single-Element Prism for Enhancing Scanning Flexibility of Risley Prism Antenna System

In this letter, we propose a rotationally reconfigurable single-element prism that is compatible with the typical Risley prism antenna system. It consists of a pair of rotating decentered phase plates operating at 30 GHz. The equivalent prism angle can be continuously changed between 0° and 14° by simply rotating these two phase plates. An all-dielectric low-cost prototype has been designed, fabricated, and measured, which demonstrates the peak realized gain of 21 dBi can be achieved with a gain variation less than 0.9 dB within the reconfigurable angle range of 0°–14°. Besides, the combination of phase distribution of two rotating phase plates can be used as a new mechanism avoiding using first-order paraxial approximation to realize two-dimensional beam scanning.

Mid-Miocene uplift and tectonic-sedimentary evolution of the Taiwan accretionary prism: Constraints from sedimentary records in the Hengchun Peninsula, southern Taiwan

The young Taiwan orogenic belt is a classic example of a modern arc–continent convergence zone, which displays a longitudinal transition from active collision in the north to oceanic subduction in the south. However, the timing of its initial exposure above the sea level and the early-stage uplift mechanism has been a point of much debate. Here we applied major and trace element, Nd isotope and heavy minerals analysis on the Miocene sedimentary rocks from the Hengchun Peninsula to trace sediment provenance and to further constrain the tectonic-sedimentary evolution of the Taiwan accretionary prism. Results show that the Hengchun mudstones (∼11.6–6.5 Ma) are characterized by higher CaO (1.42 wt %) and MgO (2.57 wt %) contents, Cr/Zr (0.52) and Co/Th (1.58) ratios, and less negative ϵNd (t) values (−12 to −7) than those from the Chinese passive continental margin sediments. It indicates that the Chinese mainland was not exclusive sediment contributor for the Hengchun sediments. Combined with the high content of Cr-spinel heavy mineral (mean value ∼ 28.2%) in the Hengchun Miocene sandstones, and the presence of mafic lithic grains and N-MORB-type mafic rocks of 26-22 Ma in the Hengchun Peninsula, it is clear that the subducting South China Sea oceanic lithosphere should be also considered for the origin of the Hengchun sediments. The most likely source of these oceanic clasts being transported to the Hengchun Peninsula is the equivalent prism to the north, which had involved oceanic fragments during the subduction process. Consequently, Taiwan accretionary prism should have been already partly exposed prior to ∼11.6 Ma, considerably earlier than most previous estimates and the onset of arc-continent collision. Underplating of seamounts and/or the thinned Chinese continental margin beneath the overlying Taiwan accretionary prism, together with wedge extrusion tectonics, may have played an important role for this early-stage uplift, which now is also observed in the sandbox experiments, marine observation and analogue modeling. Our study not only better integrates the subduction and then erosion history of the South China Sea oceanic crust with sedimentary records in Taiwan, but also signifies a modern example from Taiwan that highlights the importance of soft exhumation mechanism in worldwide plate convergence zones relative to hard collision.

The Prism: Recursive FIR Signal Processing for Instrumentation Applications

This paper provides the mathematical background for the precise, repeat integral signal monitor (Prism), a signal processing network node used in a variety of sensing and instrumentation applications. The key operation is a double Fourier-style integration, which can be implemented recursively using sliding windows and precisely using Romberg integration. The Prism generates one or two outputs; if two are generated, they are orthogonal, analogous to an analytic signal, from which sinusoid properties, such as frequency, phase, and amplitude, can readily be derived. The Prism outputs are finite impulse response (FIR), but the calculation is recursive, resulting in a low computational cost which is independent of filter length. This paper compares the Prism’s computational efficiency with both a least squares FIR filter design and an equivalent Prism filter implemented as a conventional convolution. The advantages of the Prism include design simplicity, low computational cost, and a linear phase response, making it a useful network node for a wide range of instrumentation and signal processing tasks.

Comparison of Residual Stresses in Inconel 718 Simple Parts Made by Electron Beam Melting and Direct Laser Metal Sintering

Residual stress profiles were mapped using neutron diffraction in two simple prism builds of Inconel 718: one fabricated with electron beam melting (EBM) and the other with direct laser metal sintering. Spatially indexed stress-free cubes were obtained by electrical discharge machining (EDM) equivalent prisms of similar shape. The (311) interplanar spacings from the EDM sectioned sample were compared to the interplanar spacings calculated to fulfill stress and moment balance. We have shown that applying stress and moment balance is a necessary supplement to the measurements for the stress-free cubes with respect to accurate stress calculations in additively manufactured components. In addition, our work has shown that residual stresses in electron beam melted parts are much smaller than that of direct laser metal sintered parts most likely due to the powder preheating step in the EBM process.

Stable Reduction to the Pole at Low Magnetic Latitude by Probability Tomography

AbstractReduction to the pole (RTP) has played a key role in the interpretation of magnetic anomalies. In order to overcome the unstableness of RTP at low magnetic latitude, there are varieties of methods of RTP. We propose a new method of inversion by probability tomography that allows stable reconstruction of the RTP field with a high fidelity even at the magnetic equator. The inverse model for RTP calculation consists of a set of juxtaposed equivalent prisms. This inversion carries on gradually by imagery of the residual magnetic anomalies and realizes the complexity mapping from the probabilistic model to the geophysical model under the condition of tomography. The processing of inversion does not need to solve linear algebraic equation system. The construction of probabilistic model, inversion for physical properties and appraisal can be organically integrated together to speed up the process of inversion, so that the speed of inverse calculation can be compared with the probability tomography. The computations of the model and practical field data demonstrate the effectiveness of the method that the equivalent source construction offers a stable means for reducing a set of magnetic data to the pole at the equator even with noise.

Visible-wavelength super-refraction in photonic crystal superprisms

We demonstrate the fabrication of superprism devices in photonic crystal waveguides with excellent transmission through 600 rows of 160nm diameter holes. Broadband spectral and angular measurements allow mapping of the chromatic refractivity. This shows the ability of such devices to super-refract by more than 1°∕nm close to the principal band gaps, 10× more than equivalent gratings, and 100× more than equivalent prisms. Simple theories based on plane-wave models give excellent agreement with these results.

Optical Switch Utilizing Total Reflection of (Pb, La)(Zr, Ti)O3 Ceramics

We have previously proposed an optical deflector which consists of a (Pb, La)(Zr, Ti)O3 (PLZT) rectangular solid and triangular electrodes on its top and bottom surfaces. Applying DC voltage to both electrodes, the refractive index of the material covered by the electrodes increases and becomes different from that of the remaining part of the plate. Therefore, the part covered by the electrodes works as a prism. By increasing the applied voltage, total reflection takes place at the boundary between the part covered by electrodes and the remainder of the plate. We propose here an optical switch utilizing this total reflection, the electrodes of which are divided into three parts. By applying voltage to two of the three electrodes, the shape of the equivalent prism can be changed. Thus, the output optical beam can be deflected and switched either to the left or right. Since the beam travels straight without voltage application, it is found that this device works as a 1×3 optical switch.

The precipitate Ω phase in Al-Cu-Mg-Ag alloys

The combined addition of small concentrations of Ag and Mg to Al-Cu alloys promotes precipitation of a phase, designated Ω, that forms as thin, hexagonal-shaped plates on matrix {111} α planes. The structure, morphology and composition of this phase have been examined in two quaternary alloys using transmission electron microscopy, electron microdiffraction and energy dispersive X-ray spectroscopy. Electron microdiffraction patterns from the precipitate phase may be indexed in accordance with an orthorhombic structure ( a = 0.496 nm, b = 0.859 nm, c = 0.848 nm) and the orientation relationship between precipitate and matrix lattices is such that (001) Ω∥(111) α and [010] Ω∥[101̄] α. The morphology of the precipitate phase is consistent with the intersection point group ( 2 m ) defined by symmetry elements common to the two lattices in the observed orientation relationship. The plate shape parallel to (111) α is determined by a pinacoid parallel to the common 2-fold axis, [010] Ω. The hexagonal form in this plane is defined by four equivalent prism facets with a common direction perpendicular to [010] Ω and the truncation of this prism section by a second pinacoid normal to this 2-fold axis. The six facets thus defined are equivalent geometrically and may be associated with the hexagonal lattice on which the orthorhombic structure of the precipitate phase is based. Energy dispersive X-ray microanalysis indicates that the Ag in quaternary alloys partitions to the Ω phase during ageing and there is evidence that it may segregate at the interface with the matrix. On the other hand, Ag does not partition to the phase θ′ when it coexists with Ω in these alloys or is present alone in the ternary alloy Al-Cu-Ag. There is also evidence to suggest that Mg associates itself with the Ω phase, but the observations are not conclusive.

The use of the Prism Scale to Neutralize and Center Spectacle Lenses

This paper describes the prism scale and method of using it. Practical demonstration of its readings and a table of resultant and equivalent prisms produced by various oblique positions are also given.