Finite Detector Size Research Articles

The inverse problem of a Gaussian convolution and its application to the finite size of the measurement chambers/detectors in photon and proton dosimetry

A Gaussian convolution kernel K is deduced as a Green's function of a Lie operator series. The deconvolution of a Gaussian kernel is developed by the inverse Green's function K−1. A practical application is the deconvolution of measured profiles Dm(x) of photons and protons with finite detector size to determine the profiles Dp(x) of point-detectors or Monte Carlo Bragg curves of protons. The presented algorithms work if Dm(x) is either an analytical function or only given in a numerical form. Some approximation methods of the deconvolution are compared (differential operator expansion to analytical adaptations of 2 × 2 cm2 and 4 × 4 cm2 profiles, Hermite expansions to measured 6 × 6 cm2 and 20 × 20 cm2 profiles and Bragg curves of 80/180 MeV protons, FFT to an analytical 4 × 4 cm2 profile). The inverse problem may imply ill-posed problems, and, in particular, the use of FFT may be susceptible to them.

Incoherent X-radiation produced by relativistic electrons in crystals

Differential and integral features of incoherent X-radiation, induced by relativistic electrons in crystals, are studied for observation angles θγ several times greater than γ-1, where γ is the projectile Lorentz factor. The existence of sharp maxima and a minimum of the five-folded incoherent differential cross-section as a function of the final electron angles, and a dip minimum when the cross-section is taken as a function of the photon energies, is demonstrated. At near backward observation angles the three-folded cross-section shows a maximum in the region of several keV photon energies. The obtained results allow us to optimize the conditions for coincidence experiments, minimizing the incoherent contribution to the total radiation yield, and helping to analyse results of finite-size detector experiments with crystal targets.

Edge and corner effects on spectra of segmented CdZnTe detectors

We present a theoretical and experimental study on the effect of detector edges on the performance of coarsely segmented CdZnTe pad detectors. We performed an analytical calculation of the weighting potential of a finite-size detector and studied the induced charge profile on central, edge, and corner pads. The calculation involves a closed-form solution of the three-dimensional Laplace equation inside a rectangular detector. The edge effects are introduced via the boundary conditions at the detector edges. The results are that the spectra in edge and corner pads are inherently inferior with respect to the central pads. We compare our calculations to experimental results and show that they are both qualitatively and quantitatively consistent. We demonstrate that pad uniformity can be achieved by tuning of electron trapping and also by introducing a novel electrode configuration that generates almost uniform spectra from the entire detector.

Characterization of geometrical detection-system properties for two-dimensional tomography

Quantities that characterize the three-dimensional geometrical properties of detection systems for two-dimensional tomography are reviewed and compared. It is discussed how the quantities can be calculated and how they can be measured, including a measuring technique that uses a parallel laser beam. In many detection systems the finite detector size and the finite sizes of bounding apertures are not negligible, and these result in instrument functions with finite widths. Line-integral measurements are referred to as ideal measurements, whereas measurements by systems with instrument functions with finite width are nonideal. The quantities discussed make it possible to take into account these finite sizes in several tomography algorithms. If the spacing between adjacent lines of sight is much smaller than the widths of the instrument functions, the ideal measurements can be approximately reconstructed from the nonideal measurements. Such a reconstruction has been applied to bolometer measurements in a high plasma-density discharge in the Joint European Torus tokamak by sweeping the plasma in front of the bolometer detectors. The sweeping creates many extra virtual lines of sight and thus increases the resolution of the measurements close to the X point, where in high-density plasmas a peak in the radiation is found.

Extraction of molecular dynamics in intense laser fields from mass-resolved momentum imaging maps: application to Coulomb explosion of NO

The nuclear dynamics of NO in intense laser fields (~1.4 PW cm-2) is studied on the basis of the momentum-scaled time-of-flight spectra and mass-resolved momentum imaging maps of the atomic fragment ions, Np+ and Oq+ (p,q = 1-3), produced from the (p,q) Coulomb explosion pathways of NO, i.e. NO(p+q)+Np++Oq+. A procedure to extract nuclear dynamics from the momentum maps is proposed by taking account of the effect of the finite detector size. The resultant nine (p,q) single-pathway components show that (a) the distributions of the N-O internuclear distance of NOz+ just before the Coulomb explosion exhibit significant broadening (~1 Å); (b) the distance at which the corresponding distribution takes a maximum increases from 1.68 to 2.34 Å as z increases from 2 to 6 with a small amount of suppression at odd z (z = 3,5); and (c) the atomic fragment ions exhibit narrower angular distributions for a larger total charge z ( = p+q) of NOz+.

Choice of Radiation Detector in Dosimetry of Stereotactic Radiosurgery-Radiotherapy

Dosimetry of the small radiation fields used in radiosurgery is often difficult because of finite detector size and loss of lateral electronic equilibrium. However, small-field dosimetry is critical in radiosurgery where a relatively high dose in a single fraction is often delivered. Radiosurgery dosimetry varies significantly in small fields depending upon the choice of detector. Small-volume (0.015 cm3–0.125 cm3) cylindrical ion chambers, parallel-plate ion chamber, films (Kodak and CEA), thermoluminescent dosimeter (TLD), diamond detector, and Monte Carlo simulation were used to study the small-field (≤ 4 cm) dosimetry of a radiosurgery unit, which consists of Radionics hardware with cone sizes of 12.5 mm to 40 mm with a 6-MV linear accelerator. Results indicate that, in general, ion chambers and TLDs are not suitable for beam profiles. The diamond detector provides better resolution when faced parallel, rather than the perpendicular, to the beam axis. The dose profiles measured with laser-film densitometer are found to be moderately sensitive to the aperture sizes (200 μm–470 μm). The profiles generated using film and diamond detectors are nearly identical. The cone factors measured using film, diamond detectors, and TLD varies (+ 5%) depending upon the uncertainty of the measurements; however, the measured cone factors differ significantly (≤ 10%) among various ion chambers. The Pinpoint (0.015 cm3) ion chamber provides reliable data, which differs from other detectors. Monte Carlo data are in between all other measured data. The large variation in SRS dosimetry suggests that there should be a national protocol to review the dosimetry in small fields.

Dosimetry techniques for narrow proton beam radiosurgery

Characterization of narrow beams used in proton stereotactic radiosurgery (PSRS) requires special efforts, since the use of finite size detectors can lead to distortion of the measured dose distributions. Central axis depth doses, lateral profiles and field size dependence factors are the most important beam characteristics to be determined prior to dosimetry calculations and beam modelling for PSRS. In this paper we report recommendations for practical dosimetry techniques which were developed from a comparison of beam characteristics determined with a variety of radiation detectors for 126 and 155 MeV narrow proton beams shaped with 2-30 mm circular brass collimators. These detectors included small-volume ionization chambers, a diamond detector, an Hi-p Si diode, TLD cubes, radiographic and radiochromic films. We found that both types of film are suitable for profile measurements in narrow beams. Good agreement between depth dose distributions measured with ionization chambers, diamond and diode detectors was demonstrated in beams with diameters of 20-30 mm. The diode detector can be used in smaller beams, down to 5 mm diameter. For beams with diameters less than 5 mm, reliable depth dose data may be obtained only with radiochromic film. The tested ionization chambers are appropriate for calibration of beams with diameters of 20-30 mm. TLD cubes and diamond detectors are useful to determine relative dose in beams with diameters of 10-20 mm. Field size factors for smaller beams should be obtained with diode and radiochromic film. We conclude that dosimetry characterization of proton beams down to several millimetres in diameter can be performed using the described procedures.

High-resolution image reconstruction from digital video by exploitation of nonglobal motion

Many imaging systems utilize detector arrays that do not sample the scene according to the Nyquist criterion. As a result, the higher spatial frequencies admitted by the optics are aliased. This creates undesirable artifacts in the imagery. Furthermore, the blurring effects of the optics and the finite detector size also degrade the image quality. Several approaches for increasing the sampling rate of imaging systems have been suggested in the literature. We propose an algorithm for resolution enhancement that exploits object motion in digital video sequences. Unlike previously defined techniques, we use an automated segmentation method to isolate rigid moving objects. These are accurately registered and the multiple observations of the object are used to produce an effectively high sampling rate over the object. The experimental results presented illustrate the breakdown of resolution enhancement algorithms that assume global scene motion when the actual scene motion is nonglobal. The performance of the proposed algorithm is illustrated using images from a forward looking IR imager and a visible range camera.

Projection-space methods to take into account finite beam-width effects in two-dimensional tomography algorithms

The geometrical properties of detection systems used for computerized tomography are often approximated by line integrals, despite the fact that the systems have nonnegligible beam widths as the result of a finite detector size and a finite acceptance angle. Ways to take into account these distance-dependent beam widths in algorithms for two-dimensional straight-line emission tomography are discussed. It is shown that the full three-dimensional imaging properties of the detection system, including filter functions, can be described in projection space. The relationships with the geometric matrix and the étendue (integral of solid angle over area) are discussed. Two methods to compensate for most of the beam-width effects have been developed, which can be combined with many tomography algorithms. The two methods are demonstrated to improve the quality of tomographic reconstructions of measurements by the bolometer tomography system on the Joint European Torus (JET) tokamak. The strengths and limitations of the methods are discussed.

Probability density of the intensity of two partially correlated speckle fields: the influence of finite size detectors

The probability density function of the intensity of the sum of two partially (spatially) correlated speckle patterns, each spatially averaged by being interrogated by a detector of finite size, is determined assuming that the probability density of the aperture-averaged intensity is gamma distributed. The analysis is worked out in detail and numerical calculations performed when the mean and variance of the individual gamma probability density are equal. An “interpolation” gamma probability density function, valid for all values of the intensity correlation, is developed. It is shown to be an excellent approximation to the more exact analysis.

Nondestructive inspection using Compton scatter tomography

A method for non-invasively generating tomographic images of electron density in materials using Compton scattered gamma rays is investigated. Electron density is an indicator of density or composition changes in a material. In Compton scatter tomography, the energy distribution of monoenergetic gamma rays is measured after scattering from a material target. Measuring a scattered gamma ray's energy localizes the scattering position to a definable region of the sample. We develop an analytic computational model to study the image quality of a realistic system. In particular, the deleterious effects of finite source and detector size, Compton broadening, and Poisson noise are investigated. A backprojection algorithm is presented to demonstrate the impact of these effects on image reconstruction and contrast recovery. Detection of corrosion in low-Z materials is an application of interest, and is used to study the Compton scatter tomography technique.

Monte Carlo simulation of underground muon events in a finite size detector

Abstract Two methods of folding a distribution of simulated muon bundle events underground with a finite size detector are compared. A general strategy to fully exploit the statistics produced by the event generator is described. The aim is to minimize the amount of computing time required in the analysis of data taken by large area detectors. The method presented here can also be used for other applications typical of cosmic ray physics.

Three-dimensional Partially-coherent Image Formation in Confocal Microscopes with a Finite-sized Detector

Abstract The concept of the transmission cross-coefficient (TCC) is used to describe three-dimensional (3D) imaging in transmission and reflection confocal scanning microscopes with a finite-sized detector. The effects of the detector size are studied in detail in terms of the 3D weak-object transfer functions (WOTFs) for weakly scattering objects. As is already known, 3D transmission imaging for an infinitely large detector and for a point detector are identical, whereas it is shown that between two limiting cases the behaviour is different, suggesting that axial phase information can be imaged. It is found that 3D reflection imaging for an infinitely large detector can be equivalent to 3D true confocal imaging using one annular and one circular pupil. The 3D WOTF in reflection reveals negative values which may reverse the contrast of an image at some spatial frequencies.

Beyond the conventional information limit: the relevant coherence function

The theory of partial coherence functions as applied to a super-resolution reconstruction algorithm is developed in detail, taking into account the phase gradients across the aperture function, the source and detector sizes, and temporal coherence. Experimental examples demonstrate the main properties of the relevant coherence envelopes, and why they need not limit the total band-pass of the microscope. It is demonstrated that finite detector size in the STEM configuration can facilitate a simpler reconstruction algorithm by creating a virtual objective aperture which obviates the need for a physical objective aperture. These results are also relevant to the question of uniquely deconvolving shadow images.

Calibration of low activity caesium tubes and needles traceable to the therapy level standard

A technique for deriving the reference air kerma rate for low activity brachytherapy sources that is traceable to the therapy level standard at the National Physical Laboratory is presented. Correction factors have been generated to account for the finite source and detector size. The air kerma rate calibration of the secondary standard for caesium quality has been derived by polynomial curve fitting. The reference air kerma rates for several caesium tubes and needles have been determined and the results compared with the manufacturers' source test reports. For all the source types used the agreement between methods was within 2%.

Effects of a Finite-sized Pinhole on 3D Image Formation in Confocal Two-photon Fluorescence Microscopy

Abstract We investigate three-dimensional (3D) imaging properties in confocal two-photon (2-p) fluorescence microscopy with a finite-sized detector. The 3D intensity point spread function, the 3D optical transfer function (OTF), the strength of optical sectioning and the signal levels for point, planar and volume objects are calculated in order to reveal their relationships to the detector size. It is shown that confocal 2-p fluorescence imaging with a point detector gives super-resolution, compared with conventional 2-p imaging without a confocal pinhole. Although optical sectioning can be attained in the latter case, its strength is inferior to that in the confocal case. In particular, a finite-sized detector can result in negative values in the 3D OTF and reduce the effective cut-off spatial frequencies, thus degrading the capability of confocal 2-p fluorescence microscopy for 3D imaging. Unlike the single-photon fluorescence microscope, there is no missing cone of spatial frequencies in the 3D OTF for...

Three-dimensional Transfer Function Analysis of a Confocal Fluorescence Microscope With a Finite-sized Source and Detector

Abstract The influence of a finite source and detector on the three-dimensional imaging of an incident light fluorescent confocal scanning optical microscope is investigated on the basis of its three-dimensional optical-transfer function. It is shown that the optical resolution in such set-ups remains the same as with punctiform pinholes if the source and the detecting pinhole radii are both smaller than the size of the Airy disc.

Automated structure-factor refinement from convergent-beam electron diffraction patterns

An improved algorithm is described for automated structure-factor refinement using convergent-beam electron diffraction patterns. In addition to refinement of structure factors, absorption coefficients and sample thickness, the new algorithm includes beam-direction refinement, the inclusion of weak-beam effects using the Bethe potential and the inclusion of finite-sized detector effects. The use of these new features is illustrated through the refinement of the MgO 200 systematic reflections.

Superresolved tomography by convex projections and detector motion.

If the spatial resolution of an image-acquisition system is limited by the size of its component detector elements, then scanning may be required for the signal to be fully sampled. In such cases interpolation methods are normally applied to reproduce a uniformly sampled signal from the set of observations. Alternatively, however, this step can be treated as a restoration problem, in which case the extra measurements made accessible by detector motion may contain sufficient information to superresolve the signal, i.e., to recover information beyond the limit normally associated with finite detector size. We describe the application of this concept to the problem of constructing the projection matrix from a set of noise-corrupted tomographic measurements made by a moving detector array. In particular we focus on the case encountered in many tomographic applications in which the spatial response functions are approximately stationary with object depth. The method of projections onto convex sets is used in conjunction with an underrelaxation scheme to recover the projection matrix, from which the image is reconstructed by the standard filtered backprojection algorithm. Simulation results demonstrate that this approach applied to data acquired by a wobbling positron emission tomography system can substantially enhance the quality of the reconstructed image, even in the presence of high levels of quantum noise. The projection-matrix recovery step can be performed in a matter of seconds; thus the benefits of signal recovery are gained without a significant sacrifice in computation time.

Effects of Annular Pupils on Confocal Fluorescent Imaging

Abstract For a confocal fluorescent microscope with annular lenses, the effects of varying the radii of central obstruction of the annular lenses on three, two and one-dimensional imaging have been investigated in terms of the optical transfer function. In particular, we consider the effects of the central obstruction on the signal strength for a system with either a point or finite-sized detector. The signal level as a function of the detector and the central obstruction sizes is presented for volume, planar and point objects, respectively.