Spread Function Method Research Articles

P‐49: Angular Dependent Point Spread Function Analysis for Virtual Reality Head Mounted Displays

We demonstrate a point spread function method for measuring the angular dependence of the spatial resolution of a virtual reality head mounted display. The angular dependence of spatial resolution of the imaging detector was characterized to remove the detector's contribution at each angular location measured on the VR HMD. This method allows measuring the twodimensional spatial resolution and modulation transfer function.

Likelihood function modelling of radar targets under high‐speed observation

AbstractThe likelihood ratio function of the target plays a crucial role in applications such as tracking before detection (TBD). In the framework of random finite sets, the performance of radar target TBD based on particle filters is limited by the performance of the likelihood ratio function. Traditional likelihood ratio functions only consider the likelihood ratio between the target and background noise, thus requiring a high signal‐to‐noise (SNR) ratio for the input signal. In scenarios where the observation time interval is extremely short, there exists a strong autocorrelation between the complex amplitudes of the radar target at different time instants. Based on this characteristic, an autoregressive model is utilized to establish the autocorrelation of the target complex amplitudes and update the target's complex amplitudes using a Kalman filter. The likelihood ratio is derived from the model and it is compared with the traditional likelihood ratio under pulse‐Doppler radar. This comparison aims to demonstrate the effectiveness of the proposed likelihood ratio. Due to the fact that this likelihood ratio only requires the extraction of the complex amplitudes of the target scattering centre, without the need to extract the energy around the scattering centre like traditional point spread function methods, the algorithm complexity is greatly reduced, enabling real‐time operation of the proposed method.

Sparse Inversion for the Iterative Marchenko Scheme of Irregularly Sampled Data

The Marchenko method is a data-driven way that makes it possible to calculate Green’s functions from virtual points in the subsurface using the reflection data at the surface and requiring only a macro velocity model. This method requires collocated sources and receivers. However, in practice, irregular sampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green’s functions. To solve this problem, this paper proposes to integrate a sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply the sparse inversion during the iterative process. To reduce the strict requirements on acquisition geometries, our work deals with the situation in which the sources are subsampled where the integrations are carried out over the receivers, while the existing point spread function method solves the situation where the receivers are subsampled. We make a step to handle both situations at the same time by integrating this method with our work because of the same iterative framework. Our new method is applied to a two-dimensional numerical example with irregularly sampled data. The result shows that it can effectively fill gaps in the obtained focusing functions and Green’s functions in the Marchenko method.

Accurate 3D morphological computational model reconstruction of suspended cells imaged through stratified media by the precise depth-varying point spread function method.

Accurate three-dimensional (3D) morphological computational models of cells are important in a number of biological studies. This study proposes a precise depth-varying point spread function (PDV-PSF) method for reconstructing 3D computational models of suspended cells from two-dimensional (2D) confocal image stacks. Our approach deblurs the 2D images in horizontal plane and corrects the deformation in vertical direction to overcome the refractive index mismatch problem caused by suspended cells imaging through stratified media. Standard fluorescent polystyrene spheres and Jurkat T-lymphocytes are selected to evaluate the validity and accuracy of this PDV-PSF method. Qualitative and quantitative results demonstrate that our approach has superior performance in 3D morphological computational models reconstruction of suspended cells.

Implementation of a point spread function method to analyze flash radiography images: Image enhancement, movie generation, and projection detangling

This work investigates how one can postprocess a series of flash-generated X-ray radiographs with known point spread functions and collection geometries to produce radiographs with enhanced image quality and/or to approximate a multiframe X-ray movie by spatially correlating temporally sequenced images. To produce images with enhanced quality, one collects multiple individual projections, simultaneously, and then uses the known point spread function and acquisition geometry to correlate and integrate the numerous projections as if they were acquired from approximately the same perspective. If using sources of similar spectral characteristics, the outcome correlates with that which would be produced from a multiflash integration, where one benefits from an increase in flux of X-ray photons. If using sources of different spectral characteristics, a composite radiograph can be produced where the unique source spectrum can be matched to known material absorption cross-sections to accentuate radiographic features within the target material. To produce multiframe movies, similar mathematics are applied to images collected throughout a timespan over which the object changes. The aforementioned processes' mathematics and examples are demonstrated for the case in which the individual projections are completely separable on the detector with no overlap. Finally, a potential method is discussed for separation of images in the case where multiple radiograph projections are overlapped and entangled on the detector.

Effect of Ultra High-Resolution Computed Tomography and Model-Based Iterative Reconstruction on Detectability of Simulated Submillimeter Artery

To evaluate the effect of ultra high-resolution computed tomography (UHRCT) and model-based iterative reconstruction (MBIR) on the detectability of simulated submillimeter artery. A small vessel phantom ranging from 0.4 to 2.0 mm in diameter and edge phantoms of low to high attenuation values were scanned by UHRCT (super-high-resolution mode and normal-resolution-mode) and conventional CT, and data were reconstructed by MBIR and filtered back projection (FBP). Vessel detectability was assessed subjectively and the effective size at which 50% of response was achieved (ES50 [mm]) was calculated. Modulation transfer function (MTF) was calculated by an edge spread function method. ES50 of super high-resolution mode (0.36 mm for MBIR and 0.50 mm for FBP) was significantly smaller than those of normal-resolution mode (P < 0.01). In the MTF analysis, the MTF of MBIR improved as the edge phantom attenuation increased, whereas that of FBP was stable. Both UHRCT and MBIR are effective for the detectability of simulated submillimeter artery.

Design of a collimated UV-LED exposure unit based on light spread function method.

A collimated and uniform UV-LED exposure unit (EU) applied in a printed circuit board is investigated by the light spread function (LSF) method. To accurately calculate the source-to-source distance of collimated UV-LED sources and achieve uniform irradiance in the exposure area, we propose a regional maximally flat condition for the LSF. This regional maximally flat condition contains irradiance information from multiple positions in two dimensions. To verify the design results, we built this parameter into optical simulation software and used it in our LSF method calculations. The obtained collimated UV-LED EU results show uniformity and average irradiance values of 98.23% and 43.32 mW/cm2, respectively. Thus, we can conclude that the proposed LSF method is effective for achieving a uniform irradiance distribution.

Detection and quantification of regional cortical gray matter damage in multiple sclerosis utilizing gradient echo MRI.

Cortical gray matter (GM) damage is now widely recognized in multiple sclerosis (MS). The standard MRI does not reliably detect cortical GM lesions, although cortical volume loss can be measured. In this study, we demonstrate that the gradient echo MRI can reliably and quantitatively assess cortical GM damage in MS patients using standard clinical scanners. High resolution multi-gradient echo MRI was used for regional mapping of tissue-specific MRI signal transverse relaxation rate values (R2*) in 10 each relapsing–remitting, primary-progressive and secondary-progressive MS subjects. A voxel spread function method was used to correct artifacts induced by background field gradients. R2* values from healthy controls (HCs) of varying ages were obtained to establish baseline data and calculate ΔR2* values – age-adjusted differences between MS patients and HC. Thickness of cortical regions was also measured in all subjects. In cortical regions, ΔR2* values of MS patients were also adjusted for changes in cortical thickness. Symbol digit modalities (SDMT) and paced auditory serial addition (PASAT) neurocognitive tests, as well as Expanded Disability Status Score, 25-foot timed walk and nine-hole peg test results were also obtained on all MS subjects. We found that ΔR2* values were lower in multiple cortical GM and normal appearing white matter (NAWM) regions in MS compared with HC. ΔR2* values of global cortical GM and several specific cortical regions showed significant (p < 0.05) correlations with SDMT and PASAT scores, and showed better correlations than volumetric measures of the same regions. Neurological tests not focused on cognition (Expanded Disability Status Score, 25-foot timed walk and nine-hole peg tests) showed no correlation with cortical GM ΔR2* values. The technique presented here is robust and reproducible. It requires less than 10 min and can be implemented on any MRI scanner. Our results show that quantitative tissue-specific R2* values can serve as biomarkers of tissue injury due to MS in the brain, including the cerebral cortex, an area that has been difficult to evaluate using standard MRI.

POINT SPREAD FUNCTION OF FOUR-WAVE RADIATION CONVERTER ON THE KERR NONLINEARITY UNDER QUASIPERPENDICULAR INTERACTION

Accuracy of conversion of radiation by degenerate four-wave-converter on the Kerr nonlinearity under quasiperpendicular interaction geometry was analyzed with the use of point spread function method. The increasing of accuracy of radiation conversion by such converter compared to the same converter with quasicollinear geometry interaction. Correlation between the half-width module of point spread function and divergence of the pump wave, position of the focusing plane of signal wave, shear wave propagation direction with respect to the pump face of the nonlinear layer were obtained.

Travelling wave magnetic resonance imaging at 3 T

Waveguides have been successfully used to generate magnetic resonance images at 7 T with whole-body systems. The bore diameter limits the magnetic resonance signal transmitted because its specific cut-off frequency is greater than the majority of resonant frequencies in magnetic resonance imaging and spectroscopy. This restriction can be overcome by using a parallel-plate waveguide whose cut-off frequency is zero for the transverse electromagnetic modes and it can propagate any frequency. To study the potential benefits of travelling-wave excitation for whole-body imaging at 3 T, we compare numerical simulations of the principal mode propagation for a parallel-plate waveguide filled with a cylindrical phantom and two surface coils for all simulations at 1.5 T, 3 T, 4.7, 7 T, and 9.4 T. The principal mode shows very little variation of the field magnitude along the propagation direction at 3 T when compared to other higher resonant frequencies. Unlike the standard method for travelling-wave magnetic resonance imaging, a parallel-plate waveguide prototype was built and used together with a whole-body birdcage coil for signal transmission and a pair of circular coils for reception. Experimental B1 mapping was computed to investigate the feasibility of this approach and, the point spread function method was used to measure the imager performance. Human leg images were acquired to experimentally validate this approach. The numerical magnetic field and specific absorption rate of a simulated leg were computed and results are within the safety limits. The B1 mapping and point spread function results showed that it is possible to conduct travelling-wave imaging experiments with good imager performance. Human leg images were also obtained with the whole-body birdcage coil for comparison purposes. The simulated and in vivo travelling-wave results of the human leg correspond very well for the signal received. A similar image signal-to-noise ratio was observed for the travelling-wave approach and the conventional one. We have demonstrated the feasibility of travelling-wave magnetic resonance imaging at 3 T and whole-body magnetic resonance systems, using a parallel-plate waveguide with standard pulse sequences and only one coil array. This extends the use of the waveguide approach to a wider range of resonant frequencies.

Voxel spread function method for correction of magnetic field inhomogeneity effects in quantitative gradient-echo-based MRI.

Macroscopic magnetic field inhomogeneities adversely affect different aspects of MRI images. In quantitative MRI when the goal is to quantify biological tissue parameters, they bias and often corrupt such measurements. The goal of this article is to develop a method for correction of macroscopic field inhomogeneities that can be applied to a variety of quantitative gradient-echo-based MRI techniques. We have reanalyzed a basic theory of gradient echo MRI signal formation in the presence of background field inhomogeneities and derived equations that allow for correction of magnetic field inhomogeneity effects based on the phase and magnitude of gradient echo data. We verified our theory by mapping effective transverse relaxation rate in computer simulated, phantom, and in vivo human data collected with multi-gradient echo sequences. The proposed technique takes into account voxel spread function effects and allowed obtaining virtually free from artifacts effective transverse relaxation rate maps for all simulated, phantom and in vivo data except of the edge areas with very steep field gradients. The voxel spread function method, allowing quantification of tissue specific effective transverse relaxation rate-related tissue properties, has a potential to breed new MRI biomarkers serving as surrogates for tissue biological properties similar to longitudinal and transverse relaxation rate constants widely used in clinical and research MRI.

TH-C-I-611-06: MTF(f), NPS(f) and DQE(f) of An X-Ray Imaging System Based On a Photon Counting MCP Detector

Purpose: To evaluate inherent MTF(f), NPS(f) and DQE(f) of a prototype x-ray imaging system with photon counting microchannel plate (MCP) detector. Method and Materials: The MCP detector was used in edge illumination mode as a linear array x-ray detector in scanning slit image acquisition geometry. The detector FOV was 60 mm. MCPs with 63 mm length, 25 μm channel diameter and 5 μm channel wall thickness were used. The slit width was 0.25 mm. Delay line position encoding electronics was used. Images were acquired using an x-ray tube with 0.4 mm nominal focal spot size at 40 and 90 kVp using an SID of 50 cm and a magnification 1.1. MTF was measured using edge spread function method. NPS was calculated using flat field corrected flood images. DQE was calculated from MTF, NPS and using both measured and Monte Carlo calculated QE. Results: For 25 μm channel MCP, 50% MTF was achieved at 6 lp/mm and 4 lp/mm for 40 and 90 kVp tube voltages, respectively. The highest visualized frequency was 11 lp/mm at 40 kVp. NPS was shown to be frequency independent. QE measured at 90 kVp was 56% and 70% for 25 μm and 5 μm channel MCPs, respectively. Calculated QE was 64%, 86% and 92% for 25, 5 and 2 μm channel MCPs, at 90 kVp. The above QE values represent the DQE(0). The MTF(f) curves normalized by QE represent DQE(f) due to frequency independent nature of the NPS. Conclusion: MCP detector has shown adequate MTF(f) and DQE(f) for potential application in medical imaging. This is in addition to its inherently high count rate and scatter rejection feature of the scanning slit system. Combination of these capabilities in the photon counting system would allow for significant decrease in patient dose.

Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part II. Characteristics as a function of angular range

The numerically implemented angular spectrum approach (ASA) is investigated in terms of the characteristics of the ASA as a function of angular range over which the angular spectrally decomposed plane waves are superimposed to construct an acoustic field radiated by a source. The investigation is based on the evaluation of the 2-D fields radiated by striplike planar sources and 1-D linear phased arrays with different aperture sizes and on the comparison with those obtained by using the analytical solution derived with the point spread function method. The convergence and the spatial aliasing of the ASA’s results are systematically dealt with. A region well converging to the analytical solution as the angular range increases is found to exist before the aliasing comes up. Analytical formulas to determine the boundaries of this region are given. Based on the instantaneous frequency concept, an analytical expression for optimal selection of the angular range used is derived. Hence the sampling frequency can be chosen to be optimal and adaptive to the discretization size of the source plane without worrying that the number of the samples for the discretization size should be chosen to be a power of two that the fast Fourier transform (FFT) usually needs. An excellent agreement of the ASA’s results with the analytical solution is demonstrated when using the optimal selection of the angular range for the specified parameters. The analysis made in this paper can be extended to the case of 3-D fields.

Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part I. Errors due to the discrete Fourier transform and discretization

The numerically implemented angular spectrum approach (ASA) is investigated based on the evaluation of the 2-D fields radiated by striplike planar sources and 1-D focusing linear-phased arrays with different aperture sizes and on the comparison with those obtained by using the analytical solution derived with the point spread function method. Since the discrete Fourier transform (DFT) of a finite-size source produces an angular spectrum with spatial frequency aliasing and discretization of the source in even-numbered samples causes a half-sample length phase shift error in the angular spectrum, the effects of the aliasing and the phase shift on calculation accuracy are dealt with. The results show that the frequency aliasing causes an overestimation of the near field and the phase shift distorts the results. A numerical algorithm for eliminating the aliasing is proposed and correction of the phase shift is confirmed to be necessary. The algorithm proposed can completely remove the errors and obtain exact results. The methods used in this paper can be directly applied to the case of 3-D fields. The investigation of the characteristics of the numerically implemented ASA as a function of angular range is carried out in the companion paper [P. Wu, R. Kazys, and T. Stepinski, ‘‘Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part II. Characteristics as a function of angular range,’’ J. Acoust. Soc. Am. 99, 1349–1359 (1996)].

Evaluation of the modulation transfer function of an infrared focal plane array using the talbot effect

The purpose of this paper is to describe a new procedure for evaluating the modulation transfer function (MTF) of an infrared focal plane array. This technique is based on the generalized line spread function method in which the MTF is derived from the image of a periodic target consisting of thin lines. The self-imaging property of this kind of object is used to project the target on to the tested focal plane array.