Point Response Function Research Articles

Simulation of High-contrast Polarimetric Observations of Debris Disks with the Roman Coronagraph Instrument

The Nancy Grace Roman Space Telescope Coronagraph Instrument will enable the polarimetric imaging of debris disks and inner dust belts in the optical and near-infrared wavelengths, in addition to the high-contrast polarimetric imaging and spectroscopy of exoplanets. The Coronagraph uses two Wollaston prisms to produce four orthogonally polarized images and is expected to measure the polarization fraction with measurement errors <3% per spatial resolution element. To simulate the polarization observations through the Hybrid Lyot Coronagraph (HLC) and Shaped Pupil Coronagraph (SPC), we model disk scattering, the coronagraphic point-response function, detector noise, speckles, jitter, and instrumental polarization and calculate the Stokes parameters. To illustrate the potential for discovery and a better understanding of known systems with both the HLC and SPC modes, we model the debris disks around Epsilon Eridani and HR 4796A, respectively. For Epsilon Eridani, using astrosilicates with 0.37 ± 0.01 as the peak input polarization fraction in one resolution element, we recover the peak disk polarization fraction of 0.33 ± 0.01. Similarly, for HR 4796A, for a peak input polarization fraction of 0.92 ± 0.01, we obtain the peak output polarization fraction as 0.80 ± 0.03. The Coronagraph design meets the required precision, and forward modeling is needed to accurately estimate the polarization fraction.

Long-term 4.6 μm Variability in Brown Dwarfs and a New Technique for Identifying Brown Dwarf Binary Candidates

Using a sample of 361 nearby brown dwarfs, we have searched for 4.6 μm variability, indicative of large-scale rotational modulations or large-scale, long-term changes on timescales of over 10 yr. Our findings show no statistically significant variability in Spitzer’s Infrared Array Camera (IRAC) channel 2 (ch2) or Wide-field Infrared Survey Explorer W2 photometry. For Spitzer the ch2 1σ limits are ∼8 mmag for objects at 11.5 mag and ∼22 mmag for objects at 16 mag. This corresponds to no variability above 4.5% at 11.5 mag and 12.5% at 16 mag. We conclude that highly variable brown dwarfs, at least two previously published examples of which have been shown to have 4.6 μm variability above 80 mmag, are very rare. While analyzing the data, we also developed a new technique for identifying brown dwarf binary candidates in Spitzer data. We find that known binaries have IRAC ch2 point response function (PRF) flux measurements that are consistently dimmer than aperture flux measurements. We have identified 59 objects that exhibit such PRF versus aperture flux differences and are thus excellent binary brown dwarf candidates.

A novel methodological study for monitoring proton beam spot using back-streaming secondary neutrons from the high-power target

The power of the proton beam of a high-power spallation neutron source generally ranges from 100 kW to several MW. The distribution of the power density of the beam on the target is critical for the stable operation of the high-power spallation target. This study proposes a beam monitoring method that involves restoring the image of a high-power proton beam spot on a target based on the principle of pinhole imaging by using the back-streaming of secondary neutrons from the spallation target. Fast and indirect imaging of the beam spot can be achieved at a distance of tens of meters from the target. The proposed method of beam monitoring can flexibly adjust the size of the pinhole and the measurement distance to control the intensity of flux of the secondary neutrons according to the demands of the detection system, which is far from the high-radiation target area. The results of simulations showed that the proposed method can be used to restore the beam spot of the incident proton by using the point response function and images of the secondary neutrons. Based on the target and the Back-n beamline in the CSNS, the effectiveness of this method has also been confirmed by means of Monte Carlo simulation.

Imaging and reconstruction of high-energy proton beam spot before target based on secondary gamma rays.

The distribution and stability of the incident proton beam spot are critical for the stable operation of a high-power spallation target. This study proposes a method to capture images of the incident proton beam spot based on secondary gamma rays. The distribution of the backward secondary gamma rays irradiated by the primary proton beam on the incident surface of the target is close to the distribution of the protons and can be measured at a low-radiation position far from the target area. A relation of distributions between the incident protons and the secondary gammas is constructed by using the point response function of this pinhole imaging system. The proposed method of imaging is suitable for monitoring the distribution of the proton beam on the target in facilities that use a beam power of several megawatts or tens of megawatts, such as spallation neutron sources or accelerator-driven subcritical systems.

A backprojection kernel (KRNL3D) for very-wide-aperture 3D tomography applied to PET with Multigrid for precise use of time-of-flight data

In ‘KRNL3D’ we derive a kernel function K(y 1, y 2, φ) whose backprojections from all directions (θ, φ) in the spherical band on the celestial sphere, when integrated with respect to solid angle, yield ρ, the 3D Gaussian point response function (PRF) of radius 1. This K, when convolved against line integral data from an unknown density function f, yields an integral formula for the ‘mollification’ ff = ρ ∗ f, which is a slightly blurred version of f, and which stabilizes the mild ill-posedness. Applied to positron emission tomography that backprojection reconstruction occurs stochastically and one emission event at a time, after needed data corrections. We describe Octave (≈Matlab) codes to tabulate K and to test its use with a large aperture or π/6. ‘KRNL3D- TOF’ truncates backprojection to a cylindrical patch about the TOF approximate location of each event. These ‘backplacements’ decrease the computational cost and limit noise and streaking in one region from contaminating the reconstruction in more distant regions. They also retain the ability to count emission events in an isolated blob despite very low event counts, a valuable feature for dynamic studies of metabolic processes. ‘Multigrid’ allows further reduction in the radius and lengths of the cylinders, thereby enabling even more precise use of the TOF information. This precision should be especially important as researchers decrease the TOF uncertainty in newer generation scanners. Finally, we discuss ‘further work’ that needs to be done. Our codes are being made freely available at https://github.com/keithmillerberkeley/PET-codes.

Determination of Rotation Periods for a Large Sample of Asteroids from the K2 Campaign 9

Abstract The Kepler mission is a powerful tool for the study of different types of astrophysical objects or events in the distant universe. However, the spacecraft also provides an opportunity to study solar system objects passing in the telescope’s field of view. The aim of this paper is to determine, for the first time, the rotation periods of a number of asteroids observed by the K2 satellite during the K2 Campaign 9. Using publicly available data from the Kepler mission, we have used the Modified Causal Pixel Model code to perform the aperture-like and point-response function–like photometry of 1026 asteroids. The results allowed us to determine the rotation periods for 188 asteroids. For asteroids with rotation periods that were previously measured, we compared the results and found very good agreement. There are an additional 20 asteroids for which we obtained lower limits on rotation periods and in all cases these limits are at least 100 hr.

Identification and Mitigation of a Vibrational Telescope Systematic with Application to Spitzer

Abstract We observed Proxima Centauri with the Spitzer Space Telescope Infrared Array Camera five times in 2016 and 2017 to search for transits of Proxima Centauri b. Following standard analysis procedures, we found three asymmetric, transit-like events that are now understood to be vibrational systematics. This systematic is correlated with the width of the point-response function (PRF), which we measure with rotated and nonrotated-Gaussian fits with respect to the detector array. We show that the systematic can be removed with a novel application of an adaptive elliptical-aperture photometry technique, and compare the performance of this technique with fixed and variable circular-aperture photometry, using both BiLinearly Interpolated Subpixel Sensitivity (BLISS) maps and nonbinned Pixel-Level Decorrelation (PLD). With BLISS maps, elliptical photometry results in a lower standard deviation of normalized residuals, and reduced or similar correlated noise when compared to circular apertures. PLD prefers variable, circular apertures, but generally results in more correlated noise than BLISS. This vibrational effect is likely present in other telescopes and Spitzer observations, where correction could improve results. Our elliptical apertures can be applied to any photometry observations, and may be even more effective when applied to more circular PRFs than Spitzer’s.

Design, Performance Evaluation, and Modeling of an Ultrahigh Resolution Detector Dedicated for Simultaneous SPECT/MRI

In this paper, we report design and preliminary performance evaluation of a CdTe detector module for use in an MR-compatible preclinical SPECT system. The detector module consists of four CdTe detectors. Each of them has a CdTe crystal with a dimension of 1.125 cm × 2.25 cm × 2 mm (thickness). The crystal anode side is divided into 32 × 64 square pixels with a width of 350 μm and attached to a custom-designed energy-resolved photon-counting (ERPC) ASIC. The ERPC CdTe detector module has a median energy resolution of 7.0 keV across 8192 (4 × 32 × 64 ) pixels and 95% of the pixels have energy resolution better than 9 keV inside a Siemens clinical 3-T MR scanner; it has a median detection efficiency of 0.47 and 95% of the pixels have detection efficiency between 0.44 and 0.49; the detector spatial resolution enables one to observe the point response function (PRF) distortion caused by a 3T magnetic field. An analytical method has been developed to model this distortion and the corresponding modeled PRF has a root of mean square error within 5%, compared to the experimental PRF.

Introducing a New Spitzer Master BLISS Map to Remove the Instrument Systematic Phase-curve-parameter Degeneracy, as Demonstrated by a Reanalysis of the 4.5 μm WASP-43b Phase Curve

Abstract While Spitzer Infrared Array Camera (IRAC) systematics are generally well understood, each data set can provide its own challenges that continue to teach us about the underlying functional form of these systematics. Multiple groups have analyzed the phase curves of WASP-43b with varying detrending techniques, each obtaining different results. In this work, we take another look at WASP-43b while exploring the degenerate relation between Bilinearly Interpolated Subpixel Sensitivity (BLISS) mapping, point response function (PRF)–FWHM detrending, and phase curve parameters. We find that there is a strong correlation between the detrending parameters in the two models, and best-fit phase curve amplitudes vary strongly when the data are temporally binned. To remove this degeneracy, we present a new Gaussian centroided intrapixel sensitivity map (hereafter fixed sensitivity map), generated using 3,712,830 exposures spanning 5 yr, for a variety of aperture sizes at 4.5 μm. We find evidence for time variability in the sensitivity at 3.6 μm and do not generate a visit-independent map for this channel. With the fixed 4.5 μm intrapixel sensitivity map, the best fits for WASP-43b no longer vary strongly with bin size and PRF–FWHM detrending is no longer required to remove correlated noise. For data sets that do not fall completely within the sweet spot, temporal binning should not be used in the analysis of Spitzer phase curves. We confirm nightside emission for WASP-43b with a disk-integrated nightside temperature of 806 ± 48 K at 4.5 μm. The 4.5 μm maps are available at github.com/kevin218/POET.

Assessment of the impact of modeling axial compression on PET image reconstruction.

To comprehensively evaluate both the acceleration and image-quality impacts of axial compression and its degree of modeling in fully 3D PET image reconstruction. Despite being used since the very dawn of 3D PET reconstruction, there are still no extensive studies on the impact of axial compression and its degree of modeling during reconstruction on the end-point reconstructed image quality. In this work, an evaluation of the impact of axial compression on the image quality is performed by extensively simulating data with span values from 1 to 121. In addition, two methods for modeling the axial compression in the reconstruction were evaluated. The first method models the axial compression in the system matrix, while the second method uses an unmatched projector/backprojector, where the axial compression is modeled only in the forward projector. The different system matrices were analyzed by computing their singular values and the point response functions for small subregions of the FOV. The two methods were evaluated with simulated and real data for the Biograph mMR scanner. For the simulated data, the axial compression with span values lower than 7 did not show a decrease in the contrast of the reconstructed images. For span 11, the standard sinogram size of the mMR scanner, losses of contrast in the range of 5-10 percentage points were observed when measured for a hot lesion. For higher span values, the spatial resolution was degraded considerably. However, impressively, for all span values of 21 and lower, modeling the axial compression in the system matrix compensated for the spatial resolution degradation and obtained similar contrast values as the span 1 reconstructions. Such approaches have the same processing times as span 1 reconstructions, but they permit significant reduction in storage requirements for the fully 3D sinograms. For higher span values, the system has a large condition number and it is therefore difficult to recover accurately the higher frequencies. Modeling the axial compression also achieved a lower coefficient of variation but with an increase of intervoxel correlations. The unmatched projector/backprojector achieved similar contrast values to the matched version at considerably lower reconstruction times, but at the cost of noisier images. For a line source scan, the reconstructions with modeling of the axial compression achieved similar resolution to the span 1 reconstructions. Axial compression applied to PET sinograms was found to have a negligible impact for span values lower than 7. For span values up to 21, the spatial resolution degradation due to the axial compression can be almost completely compensated for by modeling this effect in the system matrix at the expense of considerably larger processing times and higher intervoxel correlations, while retaining the storage benefit of compressed data. For even higher span values, the resolution loss cannot be completely compensated possibly due to an effective null space in the system. The use of an unmatched projector/backprojector proved to be a practical solution to compensate for the spatial resolution degradation at a reasonable computational cost but can lead to noisier images.

Modeling and analysis for the image mapping spectrometer**Project supported by the National Natural Science Foundation of China (Grant Nos. 61635002 and 61307020) and the Changjiang Scholars and Innovative Research Team in University (PCSIRT) Program, China.

The snapshot image mapping spectrometer (IMS) has advantages such as high temporal resolution, high throughput, compact structure and simple reconstructed algorithm. In recent years, it has been utilized in biomedicine, remote sensing, etc. However, the system errors and various factors can cause cross talk, image degradation and spectral distortion in the system. In this research, a theoretical model is presented along with the point response function (PRF) for the IMS, and the influence of the mirror tilt angle error of the image mapper and the prism apex angle error are analyzed based on the model. The results indicate that the tilt angle error causes loss of light throughput and the prism apex angle error causes spectral mixing between adjacent sub-images. The light intensity on the image plane is reduced to 95% when the mirror tilt angle error is increased to (). The prism apex error should be controlled within the range of 0–36 (0.01 ) to ensure the designed number of spectral bands, and avoid spectral mixing between adjacent images.

Modified Gaussian Interpolations with Geometric Calibrations for Rapid Constructions of Circular-Orbit Pinhole SPECT System Matrices

For high-spatial-resolution reconstructions in SPECT imaging, an accurate and fine system matrix (H matrix) should be constructed. In this study, the modified Gaussian interpolation method (GIM) and the modified GIM combined with geometric parameter estimations (GIMGPE) are developed to rapidly construct the complete H matrices of circular-orbit 1-pinhole/4-pinhole SPECT systems. The multi-module multi-resolution (M3R) pinhole SPECT system (in the Center for Gamma-Ray Imaging, University of Arizona) is utilized to verify the usefulness of the proposed interpolation methods. The modified GIM and GIMGPE apply a geometric calibration, a rough grid-scan experiment, and point response parameterization based on Gaussian fitting to construct the full H matrices with a 0.5-mm voxel size and 60 projection angles. The geometric calibration uses a 3-point calibration phantom projected at 60 projection angles to construct the geometric projection model. In the rough grid-scan experiment, a point source is stepped on a regular grid pattern with a 1-mm grid spacing to measure the point response functions (PRFs) at the 0° projection angle. Sequentially, the measured PRFs are parameterized into two-dimensional Gaussians. The PRFs of full H matrices are interpolated by the relations between the Gaussian coefficients and the geometric parameters. The processing time of constructing the complete H matrices with the modified GIM and GIMGPE are respectively reduced by about 347× and 336×, compared to that of the full three-dimensional grid-scan experiment. According to the results of geometric calibration, the magnification of M3R with 1- and 4-pinhole patterns are 1.9× and 2.6×, respectively. The reconstructions of a hot-rod phantom show that the spatial resolutions of M3R with 1- and 4-pinhole patterns are 1.4 mm and 1.0 mm, respectively.

TU‐H‐CAMPUS‐IeP1‐01: Bias and Computational Efficiency of Variance Reduction Methods for the Monte Carlo Simulation of Imaging Detectors

Purpose:Variance reduction techniques (VRTs) are employed in Monte Carlo simulations to obtain estimates with reduced statistical uncertainty for a given simulation time. In this work, we study the bias and efficiency of a VRT for estimating the response of imaging detectors.Methods:We implemented Directed Sampling (DS), preferentially directing a fraction of emitted optical photons directly towards the detector by altering the isotropic model. The weight of each optical photon is appropriately modified to maintain simulation estimates unbiased. We use a Monte Carlo tool called fastDETECT2 (part of the hybridMANTIS open‐source package) for optical transport, modified for VRT. The weight of each photon is calculated as the ratio of original probability (no VRT) and the new probability for a particular direction. For our analysis of bias and efficiency, we use pulse height spectra, point response functions, and Swank factors. We obtain results for a variety of cases including analog (no VRT, isotropic distribution), and DS with 0.2 and 0.8 optical photons directed towards the sensor plane. We used 10,000, 25‐keV primaries.Results:The Swank factor for all cases in our simplified model converged fast (within the first 100 primaries) to a stable value of 0.9. The root mean square error per pixel for DS VRT for the point response function between analog and VRT cases was approximately 5e‐4.Conclusion:Our preliminary results suggest that DS VRT does not affect the estimate of the mean for the Swank factor. Our findings indicate that it may be possible to design VRTs for imaging detector simulations to increase computational efficiency without introducing bias.

Measurement of the Point Response Functions of CERES Scanning Radiometers

Some applications of data from the Clouds and the Earth's Radiant Energy System (CERES) scanning radiometer require the use of the point response function (PRF), which describes the influence of radiance from each point on the measurement. A radiance source for the measurement of the PRF of the CERES instruments was built and installed into the Radiometric Calibration Facility, in which the CERES instruments have been calibrated. The design and application of the PRF source and the computation of the PRF from these measurements are described. In order to compare the PRF based on measurements with the theoretical PRF, it is necessary to account for the finite size of the beam from the source. The use of the PRF source and the analysis of the data are demonstrated by application to the FM-5 instrument. The measured results compare well with theory for the CERES instruments and are presented for FM-5.

MEASURING HIGH-PRECISION ASTROMETRY WITH THE INFRARED ARRAY CAMERA ON THE SPITZER SPACE TELESCOPE*

ABSTRACT The Infrared Array Camera (IRAC) on the Spitzer Space Telescope currently offers the greatest potential for high-precision astrometry of faint mid-IR sources across arcminute-scale fields, which would be especially valuable for measuring parallaxes of cold brown dwarfs in the solar neighborhood and proper motions of obscured members of nearby star-forming regions. To more fully realize IRAC's astrometric capabilities, we have sought to minimize the largest sources of uncertainty in astrometry with its 3.6 and 4.5 μm bands. By comparing different routines that estimate stellar positions, we have found that Point Response Function (PRF) fitting with the Spitzer Science Center's Astronomical Point Source Extractor produces both the smallest systematic errors from varying intra-pixel sensitivity and the greatest precision in measurements of positions. In addition, self-calibration has been used to derive new 7th and 8th order distortion corrections for the 3.6 and 4.5 μm arrays of IRAC, respectively. These corrections are suitable for data throughout the mission of Spitzer when a time-dependent scale factor is applied to the corrections. To illustrate the astrometric accuracy that can be achieved by combining PRF fitting with our new distortion corrections, we have applied them to archival data for a nearby star-forming region, arriving at total astrometric errors of ∼20 and 70 mas at signal to noise ratios of 100 and 10, respectively.

Experimental procedures for testing the performance of rail dampers

Rail dampers work by increasing the attenuation with distance of vibration transmitted along the rail, a quantity known as the track decay rate. Currently, there are no standardized procedures to measure their effectiveness in reducing rolling noise without the need for in-track installation and time-consuming tests. This paper describes and evaluates experimental procedures for assessing rail dampers. Instead of field measurements it is proposed to use laboratory measurements of vertical and lateral decay rates on a free rail equipped with dampers. These are combined with in-situ measurements on an undamped track. The decay rates of a damped track can be approximated by adding the results of the damped free rail to those of the undamped track.Three different methods are studied to measure the decay rates of damped free rails: (i) using a long rail, in the present work 32m long, from frequency response functions measured at intervals along the rail; (ii) using a short rail, in the present work 6m long, from the modal properties of the rail; and (iii) directly from the point and transfer frequency response functions at both ends of the short rail. The latter two are complementary: the modal method is more suited to low frequencies while the direct method is more suited to high frequencies. These methods are evaluated theoretically and by comparison with experimental results.Good agreement is found between the various methods, for vibration in both vertical and lateral directions, between 300Hz and 5kHz. In practice, the direct short-rail method is likely to be sufficient for most applications. The limitations of the methods are identified and corrections are proposed for the effect of near-field waves in the rail.

Application of electromechanical impedance-based SHM for damage detection in bolted pipeline connection

The work discusses the effectiveness of the electromechanical impedance-based Structural Health Monitoring system for damage detection in a laboratory test stand – a bolted pipeline section. The impedance-based system developed by the authors and equipped with 12 piezoelectric transducers was used to acquire the data. Different damage scenarios related to loosened bolts and measurement configurations are analysed. Both point and transfer frequency response functions are applied to deterministic and stochastic damage metrics, which are used to assess the condition of the monitored structure. The thresholds levels are proposed for different measurement configurations. Moreover, the authors discuss the perspective to determine the size and localisation of a damage. As confirmed in the work, the stochastic damage metric, preferably applied with a transfer frequency response, is found as of the most practical significance for the tested structure. The carried out analyses consider an outlier removal technique, which becomes necessary to prevent from errors due to temporary variation of the acquired characteristics after initialisation of the measurements.

Least Asymmetry Centering Method and Comparisons

The interpretation of astronomical photometry, astrometry, and orbit determination data depends on accurately and consistently identifying the center of the target object’s photometric point spread function in the presence of noise. We introduce a new technique, called least asymmetry, which is designed to find the point about which the distribution is most symmetric. This technique, in addition to the commonly used techniques Gaussian fitting and center of light, was tested against synthetic datasets under realistic ranges of noise and photometric gain. With subpixel accuracy, we compare the determined centers to the known centers and evaluate each method against the simulated conditions. We find that in most cases center of light performs the worst, while Gaussian fitting and least asymmetry are alternately better under different circumstances. Using a real point response function with “reasonable signal-to-noise,” we find that least asymmetry provides the most accurate center estimates, and Gaussian centering is the most precise. The least asymmetry routine implemented in the Python Programming Language can be found at https://github.com/natelust/least_asymmetry.

Reducing multiplexing artifacts in multi-pinhole SPECT with a stacked silicon-germanium system: a simulation study.

In pinhole single photon emission computed tomography (SPECT), multi-pinhole collimators can increase sensitivity but may lead to projection overlap, or multiplexing, which can cause image artifacts. In this work, we explore whether a stacked-detector configuration with a germanium and a silicon detector, used with 123I (27-32, 159 keV), where little multiplexing occurs in the Si projections, can reduce image artifacts caused by highly-multiplexed Ge projections. Simulations are first used to determine a reconstruction method that combines the Si and Ge projections to maximize image quality. Next, simulations of different pinhole configurations (varying projection multiplexing) in conjunction with digital phantoms are used to examine whether additional Si projections mitigate artifacts from the multiplexing in the Ge projections. Reconstructed images using both Si and Ge data are compared to those using Ge data alone. Normalized mean-square error and normalized standard deviation provide a quantitative evaluation of reconstructed images' error and noise, respectively, and are used to evaluate the impact of the additional nonmultiplexed data on image quality. For a qualitative comparison, the differential point response function is used to examine multiplexing artifacts. Results show that in cases of highly-multiplexed Ge projections, the addition of low-multiplexed Si projections helps to reduce image artifacts both quantitatively and qualitatively.

Point response function of the Clouds and Earth Radiant Energy System scanning radiometer

An overview of work related to the point response function (PRF) of the Clouds and Earth Radiant Energy System (CERES) scanning radiometer is presented. The aspects of the CERES design that affect the PRF are described, and then the design of the PRF is explained. The PRF was designed by shaping the field of view so as to minimize the blur plus alias errors of the radiance field reconstructed from the CERES measurements. The design is conducted in the Fourier domain. The PRF can then be computed by transforming the resulting transfer function to the physical domain. Alternatively, the PRF can be computed in the physical plane. The PRF of each model of the CERES instrument has been tested in the Radiation Calibration Facility by use of a PRF source and compared well with prediction. CERES instruments are aboard the Terra, Aqua, and Suomi-NPP spacecraft. In orbit, lunar observations are used to validate the PRF. These results showed nominal performance except for the longwave window channel of flight model 2, for which a region of anomalously high sensitivity was found.