Beam Response Functions Research Articles

J-comb: An image fusion algorithm to combine observations covering different spatial frequency ranges

Ground-based, high-resolution bolometric (sub)millimeter continuum mapping observations on spatially extended target sources are often subject to significant missing fluxes. This hampers accurate quantitative analyses. Missing flux can be recovered by fusing high-resolution images with observations that preserve extended structures. However, the commonly adopted image fusion approaches do not maintain the simplicity of the beam response function and do not try to elaborate the details of the yielded beam response functions. These make the comparison of the observations at multiple wavelengths not straightforward. We present a new algorithm, J-comb, which combines the high and low-resolution images linearly. By applying a taper function to the low-pass filtered image and combining it with a high-pass filtered image using proper weights, the beam response functions of our combined images are guaranteed to have near-Gaussian shapes. This makes it easy to convolve the observations at multiple wavelengths to share the same beam response functions. Moreover, we introduce a strategy to tackle the specific problem that the imaging at 850 um from the present-date ground-based bolometric instrument and that taken with the Planck satellite do not overlap in the Fourier domain. We benchmarked our method against two other widely-used image combination algorithms, CASA-feather and MIRIAD-immerge, with mock observations of star-forming molecular clouds. We demonstrate that the performance of the J-comb algorithm is superior to those of the other two algorithms. We applied the J-comb algorithm to real observational data of the Orion A star-forming region. We successfully produced dust temperature and column density maps with ~10" angular resolution, unveiling much greater details than the previous results.

Physical insight into Timoshenko beam theory and its modification with extension

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

Development and Evaluation of a Fast Calculation Method for Gamma Ray Skyshine Dose Using Data Libraries

A fast calculation method for gamma ray skyshine dose was developed. Four data libraries including anisotropy factors and buildup factors in the gamma ray transport calculation in air and the buildup flux energy spectrum and edge correction factor in the calculation of the precise energy spectrum of gamma ray flux penetrating through the upper shields were used. The anisotropy factors were generated on the basis of line beam response functions obtained by Hirayama et al. using the EGS4 code. The other three data libraries were generated by the invariant embedding method. Multilayer shields and angular distributions of gamma rays from sources were assumed to have a rotational symmetry with respect to the center axis of the shields along which the sources were located. Accuracy of the method was evaluated through comparison with the measured dose in the skyshine benchmark experiment and doses calculated by other dependable methods. It was found that the present method could simulate the measured dose with a discrepancy of 50% or less, and that transport of gamma rays in air due to a conical beam could be solved within an error of about 10–20%, except for the cases in which the beam angle lies in the range < 10 deg. The present method has two advantageous features: the skyshine dose can be obtained very quickly and very easily by general users.

Gravitational wave radiometry: Mapping a stochastic gravitational wave background

The problem of the detection and mapping of a stochastic gravitational wave background (SGWB), either cosmological or astrophysical, bears a strong semblance to the analysis of the cosmic microwave background (CMB) anisotropy and polarization, which too is a stochastic field, statistically described in terms of its correlation properties. An astrophysical gravitational wave background (AGWB) will likely arise from an incoherent superposition of unmodelled and/or unresolved sources and cosmological gravitational wave backgrounds (CGWB) are also predicted in certain scenarios. The basic statistic we use is the cross correlation between the data from a pair of detectors. In order to “point” the pair of detectors at different locations one must suitably delay the signal by the amount it takes for the gravitational waves (GW) to travel to both detectors corresponding to a source direction. Then the raw (observed) sky map of the SGWB is the signal convolved with a beam response function that varies with location in the sky. We first present a thorough analytic understanding of the structure of the beam response function using an analytic approach employing the stationary phase approximation. The true sky map is obtained by numerically deconvolving the beam function in the integral (convolution) equation. We adopt the maximum likelihood framework to estimate the true sky map using the conjugate gradient method that has been successfully used in the broadly similar, well-studied CMB map-making problem. We numerically implement and demonstrate the method on signal generated by simulated (unpolarized) SGWB for the GW radiometer consisting of the LIGO pair of detectors at Hanford and Livingston. We include “realistic” additive Gaussian noise in each data stream based on the LIGO-I noise power spectral density. The extension of the method to multiple baselines and polarized GWB is outlined. In the near future the network of GW detectors, including the Advanced LIGO and Virgo detectors that will be sensitive to sources within a thousand times larger spatial volume, could provide promising data sets for GW radiometry.

Validity of the Four-Parameter Empirical Formula in Approximating the Response Functions for Gamma-ray, Neutron, and Secondary Gamma-ray Skyshine Analyses

A four-parameter approximating formula, R=A e a x b f(x), accurately represents the skyshine line beam response function (LBRF) as a function of the distance (x) of the source-to-detector separation. Here, A is a constant for a given source energy and f(x)=e cx x dx is a damping factor. The four parameters are obtained as follows. 1. The value of parameter a corresponds to that of the LBRF at x=1 meter, which is the result of integrating the basic dose spectrum due to a single scattering particle from an emitted beam for a specified angle and a specified source energy. 2. The value of parameter b corresponds to the slope of a straight line of the response function, log R vs. log x, in the range of small distance from a source, where a single scattering particle dominates. 3. The damping factor (f (x)) represents the attenuation trend of the LBRF at distances far from the source; the values of parameters c and d control the quantity of attenuation. The necessary reference LBRF data for point mono-directional photon source energies ranging from 0.1 to 10MeV were generated using the EGS4 Monte Carlo code at 20 emission angles from 0.0 to 180° for 24 source-detector distances up to 2,000 m. The validity of using the four-parameter formula to interpolate the LBRF in the source-to-detector distance, in the emitted angle, and in the energy was also ascertained. Furthermore, this formula was applied to the skyshine conical beam response function (CBRF) for a neutron and an associated secondary gamma-ray with the source energy ranged from thermal to 3 GeV. It was ascertained that the CBRF could be accurately approximated by an interpolation of the fitting parameters at an arbitrary distance and emitted cosine angle.

High resolution beamforming for small aperture arrays

Achieving fine resolution bearing estimates for multiple sources using acoustic arrays with small apertures, in number of wavelengths, is a difficult challenge. It requires both large signal-to-noise ratio (SNR) gains and very narrow beam responses. High resolution beamforming for small aperture arrays is accomplished by exploiting acoustical fluctuations. Acoustical fluctuations in the atmosphere are caused by wind turbulence along the propagation path, air turbulence at the sensor, source/receiver motion, unsteady source level, and fine scale temperature variations. Similar environmental and source dependent phenomena cause fluctuations in other propagation media, e.g., undersea, optics, infrared. Amplitude fluctuations are exploited to deconvolve the beam response functions from the beamformed data of small arrays to achieve high spatial resolution, i.e., fine bearing resolution, and substantial SNR gain. Results are presented for a six microphone low-frequency array with an aperture of less than three wavelengths. [Work supported by U.S. Army Armament Research Development and Engineering Center.]

Validity of the Four-Parameter Empirical Formula in Approximating the Response Functions for Gamma-ray, Neutron, and Secondary Gamma-ray Skyshine Analyses

A four-parameter approximating formula, R=A e a x b f(x), accurately represents the skyshine line beam response function (LBRF) as a function of the distance (x) of the source-to-detector separation. Here, A is a constant for a given source energy and f(x)=e cx x dx is a damping factor. The four parameters are obtained as follows. 1. The value of parameter a corresponds to that of the LBRF at x=1 meter, which is the result of integrating the basic dose spectrum due to a single scattering particle from an emitted beam for a specified angle and a specified source energy.2. The value of parameter b corresponds to the slope of a straight line of the response function, log R vs. log x, in the range of small distance from a source, where a single scattering particle dominates.3. The damping factor (f (x)) represents the attenuation trend of the LBRF at distances far from the source; the values of parameters c and d control the quantity of attenuation. The necessary reference LBRF data for point mono-directional photon source energies ranging from 0.1 to 10MeV were generated using the EGS4 Monte Carlo code at 20 emission angles from 0.0 to 180° for 24 source-detector distances up to 2,000 m. The validity of using the four-parameter formula to interpolate the LBRF in the source-to-detector distance, in the emitted angle, and in the energy was also ascertained. Furthermore, this formula was applied to the skyshine conical beam response function (CBRF) for a neutron and an associated secondary gamma-ray with the source energy ranged from thermal to 3 GeV. It was ascertained that the CBRF could be accurately approximated by an interpolation of the fitting parameters at an arbitrary distance and emitted cosine angle.

SHINE-III : Simple Code for Skyshine Dose Calculation up to 3GeV Neutrons

Skyshine dose at site boundary is considered as one of the most fundamental issues to get approval of constructing nuclear installations. Skyshine conical beam response functions (CBRF) for high energy neutrons up to 3GeV are obtained using NMTC-JAERI and MCNP code. This CBRF is fitted to the four parameters equation. Simple code named SHINE-III using this equation with updated data is developed.

Comparison of Line Beam Response Function for Gamma-ray Skyshine Analysis Based on Single Scattering Method with the Monte Carlo Calculations

A simple calculation method for estimating gamma-ray skyshine dose rates has been developed on the basis of the line beam response function (LBRF). The new data of LBRFs were generated by the single scattering with point kernel technique (single-scattering method). These resulting LBRFs were compared with the EGS4 and MCNP Monte Carlo calculations. The values of the new LBRFs for the large emitted angle become smaller than the LBRFs obtained with the Monte Carlo calculations with an increase of the distance from the source. This discrepancy increases with an increase of the photon energy.

Comparison of Line Beam Response Function for Gamma-ray Skyshine Analysis Based on Single Scattering Method with the Monte Carlo Calculations.

A simple calculation method for estimating gamma-ray skyshine dose rates has been developed on the basis of the line beam response function (LBRF). The new data of LBRFs were generated by the single scattering with point kernel technique (single-scattering method). These resulting LBRFs were compared with the EGS4 and MCNP Monte Carlo calculations. The values of the new LBRFs for the large emitted angle become smaller than the LBRFs obtained with the Monte Carlo calculations with an increase of the distance from the source. This discrepancy increases with an increase of the photon energy.

A high-resolution postbeamforming method based on semiinfinite linear optimization

A method for enhancing the bearing resolution obtained by conventional beamforming is described. Using the beamformer power outputs, the beam response functions, and optionally a background-noise spatial power spectral density (PSD) as input, the method gives a point-mass estimate of the signal PSD as function of bearing. The estimate is defined from the solution of a semiinfinite linear optimization problem and can be computed efficiently by solving a sequence of linear programs obtained by discretization using adaptive mesh refinement. In theory the estimate can achieve arbitrary resolution of the bearings of distinct plane-wave signals in stationary noise. For actual hydroacoustic data, it has been shown to yield a significant improvement of the resolution obtained by traditional beamforming. Some results obtained with simulated data and with actual data from a hydroacoustic application are presented. >

Adaptive cross‐sensor beam forming with sparse and random planar arrays

Let the quadrature field measured at sensor j of a planar array, located at (xj, yj), be Fj. The cross‐sensor field Gl is formed as the product Gl = FjFk*, where k represents sensor k and * denotes complex conjugate. The beam response B̃ of the array in look direction φ̂ is B̃(φ̂) = ΣlwlGφ,l*〈Gl〉, where {w̃l} are cross‐sensor weights, Gφ̂,l is the expected value of Gl for a single incident wave of unit amplitude and bearing φ̂, and 〈〉 denotes a time average. To be specific, Gφ̂,l = expi[h(yj − yk) cosφ̂ + h(xj − xk)sinφ̂], where h is the horizontal wave number. A simple adaptive algorithm can be used to remove the strongest signal in the beam response function. Let φ̂1 represent the bearing of the strongest signal and B̃(φ̂1) = A12 be the maximum value of B̃(φ̂). The values of 〈Gl are modified by subtraction 〈Gl〉 = 〈Gl〉 − A12 expi[h(yj − yk) cosφ̂1 + h(xj − xk) sinφ̂1]. A new beam response can now be calculated and the second largest signal then subtracted, etc. Examples are shown for both sparse and random planar arrays. [Work supported by NAVELEX 320.]