Spherical Filter Research Articles

Another preprocessing algorithm for generalized one-dimensional fast multipole method

The fast multipole method (FMM), which is originally an algorithm for fast evaluation of particle interactions, is also effective for accelerating several numerical computations. Yarvin and Rokhlin proposed “generalized” FMM using the singular value decomposition (SVD), which gives the optimum low-rank approximation. Their algorithm reduces the computational costs of the FMM evaluation and frees the FMM from analytical approximation formulae. However, the computational complexity of the preprocessing for an N× N matrix is O( N 3) because of the SVD, and it requires orthogonal matrices of the low-rank approximations. In this paper we propose another preprocessing algorithm for the generalized FMM. Our algorithm runs in time O( N 2) even with the SVD and releases the low-rank approximations from orthogonal matrices. The triangularization by the QR decomposition with sparsification, which reduces the costs of the FMM more than the diagonalization, is enabled. Although the algorithm by Yarvin and Rokhlin can be accelerated to O( N 2) using the QR decomposition, our preprocessing algorithm outperforms it in fast spherical filter, fast polynomial interpolation and fast Legendre transform.

Color correction of metal halide arc lamp sources

Metal halide arc lamps have a number of advantages over state-of-the-art xenon arc lamp sources, including higher watts-to-lumens conversion efficiency, longer lifetime, and lower cost. However, metal halide source white color, in terms of CIE xy color coordinates and color rendering index (CRI), is generally inferior to that of xenon arc lamp sources. We describe an approach that corrects the color of the characteristic spectral spikes in the metal halide lamp spectrum using a dual notch dielectric thin film filter, producing xenon arc equivalent performance in terms of both color temperature and CRI. Several novel design techniques are implemented, including high index ion-assisted deposition (IAD) dielectric materials and curved spherical filter substrates, to minimize angular spectral shifts in the fiber optically coupled light output. Results show the practical trade-offs that exist between color correction and filter notch depth.

A Fast Spherical Filter with Uniform Resolution

This paper introduces a fast algorithm for obtaining a uniform resolution representation of a function known at a latitude–longitude grid on the surface of a sphere, equivalent to a triangular, isotropic truncation of the spherical harmonic coefficients for the function. The proposedspectral truncation method,which is based on the fast multipole method and the fast Fourier transform, projects the function to a space with uniform resolution while avoiding surface harmonic transformations. The method requiresO(N2logN) operations forO(N2) grid points, as opposed toO(N3) operations for the standard spectral transform method, providing a reduced-complexity spectral method obviating the pole problem in the integration of time-dependent partial differential equations on the sphere. The filter's performance is demonstrated with numerical examples.

Spherical harmonic analysis, aliasing, and filtering

Spherical harmonic analysis, aliasing, and filtering

In-Flight Calibration of theNimbus-7Earth Radiation Budget (ERB) Sensors. Part I: A Thermal Model for the Shortwave Channels

Abstract Much of the early record of spectrally broadband earth radiation budget (ERB) measurements was taken by the ERB instrument launched on the Nimbus-7 spacecraft in October 1978. The wide-field-of-view (WFOV) sensors measured the emitted and reflected radiation from November 1978 through January 1993, and the first nine years have been processed into a stable, long-term dataset. However, heating and cooling of the ERB experiment introduced thermal perturbations in the original measurements that were only significant in the shortwave (SW) channels. These sensors were covered by spherical filter domes to absorb incident longwave (LW) radiation. In this paper, a thermal regression model—the thermal calibration adjustment table (CAT)—is developed to track and remove these thermal signals from the SW data. The model relies on instrument temperatures within and near the surface of the ERB instrument, and the observed nonzero nighttime sensor readings represent the thermal signals. Confidence that the mode...

Link design for nondirected wireless infrared communications

We optimize the design of a short-range communication system using nondirected line-of-sight IR radiation. We propose a receiver structure comprising a spherical thin-film optical filter and a truncated spherical lens that can significantly outperform an optimized planar-filter system. We can make the passband of the spherical filter arbitrarily narrow without constraining the field of view by using an arbitrarily large filter radius. We argue that a truncation angle of 90° maximizes the receiver field of view when a spherical filter is used. We jointly optimize the transmitter radiation pattern and receiver optical components. Numerical results show that 269 mW of transmitted signal power is sufficient to achieve 100 Mbit/s throughout a 4-m-radius cell with high background irradiance.

The habitat and behaviour of Cephalodiscus gracilis (Pterobranchia, Hemichordata) from Bermuda

Cephalodiscus gracilis lives in shallow water around Bermuda. The zooids secrete a transparent coenecium. Several zooids can be attached to a common point. The zooids may be of differing maturity, having from none to five pairs of arms. The mature zooids feed by extending their arms like meridians around a globe with the tentacles of adjacent arms interdigitating to make a spherical filter net. Feeding currents are induced by cilia. The mucus flows along the external surfaces of the arms, around the collar and into the mouth. The rejection current runs on the inside surface of the arms. The rejected material is stored in pellets near the arm tips. It is‘flicked’away at intervals.The larvae are found in densely pigmented stalks attached to the common sucker. The zooids also reproduce by budding.

Diffusional filtration of dust in a fluidized bed

This work provides a mathematical model for calculating filtration efficiencies in a fluidized bed filter comprised of spherical particles. A numerical solution of the diffusion equation was obtained for one spherical filter element, by using the “unit cell model of Kuwabara” for the flow field. The diffusional capture factor for a single spherical filter element was obtained for Peclet numbers in the range 10 4–10 7, bed porosities, ϵ., from 0.4 to 0.999 and interception parameters from 0 to 1/20. The present theoretical results agree quite well with previous experiments for packed bed filters. The present calculations coupled with the inertial capture factors for spheres provide a plot of the deposition efficiencies on spherical filter elements situated in a fluidized bed filter. Total bed filtration efficiencies are computed from the single sphere deposition efficiencies. The high total filtration efficiencies predicted by the present work are in accordance with existing experimental evidence.

RBE and Quality of Electromagnetic Radiation at Depths in a Water Phantom

The biological effectiveness of electromagnetic radiation in the Xand y-ray regions has been investigated quite extensively along with that of many other types of radiation (1, 2). These studies have resulted in the determination of an RBE for these radiations compared to a standard X-radiation. Although the RBE is known to depend on a great number of factors, it is strongly dependent on the linear energy transfer (LET); LET, in turn, varies with the type and quality of radiation being considered. The biological indicators used in most RBE investigations have been small animals or organisms or the surfaces of larger animals. As a result of thris, little o no attenuation and subsequent energy degradation of the radiation has taken place prior to the production of the biological effect. It is of great interest to know whether the biological effectiveness of a given primary type of radiation is affected by the degradation that takes place when this beam of radiation passes through material that overlies the site of biological interest. Very little information is available at the present time regarding the RBE of radiation in depth (3-5). There has, however, been an interest in the change in radiation quality which takes place when Xor -y-rays pass through tissue or tissue-equivalent material, and several papers have been written on this subject. In 1932 Quimby and McNattin (6) measured changes in radiation quality by measuring absorption within tissue-equivalent phantom material, using spherical ionization chambers with surrounding spherical copper filters. This absorption method of studying radiation quality was further pursued by Greening (7) in 1951. Another physical line of attack was initiated by Clarkson and Mayneord in 1939 (8). They used a pair of coaxial ionization chambers which were identical except for inner wall material, one chamber having a