Finite Focal Spot Research Articles

Simplifying tailored generation of complex structured femtosecond pulses with easily fabricated phase plates.

This article presents a novel approach to targeted 4f pulse shaping using phase plates fabricated by single-point diamond turning (SPDT) machining. The manufacturing of the phase plates using SPDT is versatile, cost-effective, fast, robust, and applicable across a wide range of optical materials, spanning from visible to far-infrared spectra (e.g., PMMA, ZnSe). Manufactured profiles can be used for phase manipulation and pulse structuring, analogously to programable spatial light modulators (SLM). We demonstrate that the pulse waveforms can be reproduced with high fidelity by simple simulations based on calculating optical path differences induced by the phase plate for each wavelength and taking into account the finite focal spot. The simulated and reconstructed frequency-resolved optical gating spectrograms featured G errors between 1-2% and intensity errors between 0.02-0.06. Even for complex structured pulses with the rms value of the time-bandwidth product reaching 12, our method maintains high precision, in some cases even reaching lower G error compared to simpler waveforms. Finally, we also show that the phase plate can be used to attain a set of uncorrelated pulse waveforms by moving the plate relatively to the dispersed laser spectrum. Overall, this approach bypasses common limitations associated with pulse shaping using SLMs, such as pixelation, pixel cross-talk, and spectral or laser fluences constraints.

Reducing penumbral blur in computed tomography by learning the inverse finite focal spot model.

Penumbral blur is one of the major limitations of the high spatial resolution micro-CT, due to a nonideal large focal spot. Penumbral blur hinders the ability to resolve small features that may only be a few pixels in size. Reducing the focal spot size by decreasing the x-ray tube power is a straightforward solution, but it leads to prolonged scan durations. In this paper, we propose to mitigate the penumbral blur by learning the inverse finite focal spot model. First, we derived the finite focal spot model that builds a relationship from the ideal point source projection to the finite focal spot projection. Based on the derived model, we numerically compute a paired projection dataset. Second, we utilized two neural networks-U-net, and convolution modulation-based U-net (CMU-net) -to learn the inverse finite focal spot model. The goal is to estimate the ideal point source projection from the actual finite focal spot projection. CMU-net, which introduces convolution modulation blocks into the contracting path of the U-net, is proposed to boost the robustness of the U-net. Finally, the standard filtered back-projection (FBP) is employed for reconstruction using the estimated ideal point projection. The experiments show that both U-net and CMU-net can effectively reduce the penumbral blur, whereas CMU-net demonstrates better performance on the real data. Experiments on real measured data demonstrate that CMU-net is more robust than U-net and can effectively resolve fine details. This method has great potential in improving the efficiency of micro-CT acquisition. It allows increasing the tube power since our method can computationally compensate for the blur caused by an increased focal spot size.

CAD-ASTRA: a versatile and efficient mesh projector for X-ray tomography with the ASTRA-toolbox.

Accurate and fast simulation of X-ray projection data from mesh models has many applications in academia and industry, ranging from 3D X-ray computed tomography (XCT) reconstruction algorithms to radiograph-based object inspection and quality control. While software tools for the simulation of X-ray projection data from mesh models are available, they lack either performance, public availability, flexibility to implement non-standard scanning geometries, or easy integration with existing 3D XCT software. In this paper, we propose CAD-ASTRA, a highly versatile toolbox for fast simulation of X-ray projection data from mesh models. While fully functional as standalone software, it is also compatible with the ASTRA toolbox, an open-source toolbox for flexible tomographic reconstruction. CAD-ASTRA provides three specialized GPU projectors based on state-of-the-art algorithms for 3D rendering, implemented using the NVIDIA CUDA Toolkit and the OptiX engine. First, it enables X-ray phase contrast simulations by modeling refraction through ray tracing. Second, it allows the back-propagation of projective errors to mesh vertices, enabling immediate application in mesh reconstruction, deep learning, and other optimization routines. Finally, CAD-ASTRA allows simulation of polychromatic X-ray projections from heterogeneous objects with a source of finite focal spot size. Use cases on a CAD-based inspection task, a phase contrast experiment, a combined mesh-volumetric data projection, and a mesh reconstruction demonstrate the wide applicability of CAD-ASTRA.

Development, validation, and simplification of a scanner-specific CT simulator.

Simulated computed tomography (CT) images allow for knowledge of the underlying ground truth and for easy variation of imaging conditions, making them ideal for testing and optimization of new applications or algorithms. However, simulating all processes that affect CT images can result in simulations that are demanding in terms of processing time and computer memory. Therefore, it is of interest to determine how much the simulation can be simplified while still achieving realistic results. To develop a scanner-specific CT simulation using physics-based simulations for the position-dependent effects and shift-invariant image corruption methods for the detector effects. And to investigate the impact on image realism of introducing simplifications in the simulation process that lead to faster and less memory-demanding simulations. To make the simulator realistic and scanner-specific, the spatial resolution and noise characteristics, and the exposure-to-detector output relationship of a clinical CT system were determined. The simulator includes a finite focal spot size, raytracing of the digital phantom, gantry rotation during projection acquisition, and finite detector element size. Previously published spectral models were used to model the spectrum for the given tube voltage. The integrated energy at each element of the detector was calculated using the Beer-Lambert law. The resulting angular projections were subsequently corrupted by the detector modulation transfer function (MTF), and by addition of noise according to the noise power spectrum (NPS) and signal mean-variance relationship, which were measured for different scanner settings. The simulated sinograms were reconstructed on the clinical CT system and compared to real CT images in terms of CT numbers, noise magnitude using the standard deviation, noise frequency content using the NPS, and spatial resolution using the MTF throughout the field of view (FOV). The CT numbers were validated using a multi-energy CT phantom, the noise magnitude and frequency were validated with a water phantom, and the spatial resolution was validated with a tungsten wire. These metrics were compared at multiple scanner settings, and locations in the FOV. Once validated, the simulation was simplified by reducing the level of subsampling of the focal spot area, rotation and of detector pixel size, and the changes in MTFs were analyzed. The average relative errors for spatial resolution within and across image slices, noise magnitude, and noise frequency content within and across slices were 3.4%, 3.3%, 4.9%, 3.9%, and 6.2%, respectively. The average absolute difference in CT numbers was 10.2HU and the maximum was 22.5HU. The simulation simplification showed that all subsampling can be avoided, except for angular, while the error in frequency at 10% MTF would be maximum 16.3%. The simulation of a scanner-specific CT allows for the generation of realistic CT images by combining physics-based simulations for the position-dependent effects and image-corruption methods for the shift-invariant ones. Together with the available ground truth of the digital phantom, it results in a useful tool to perform quantitative analysis of reconstruction or post-processing algorithms. Some simulation simplifications allow for reduced time and computer power requirements with minimal loss of realism.

Targeted generation of complex temporal pulse profiles

A targeted shaping of complex femtosecond pulse waveforms and their characterization is essential for many spectroscopic applications. A 4f pulse shaper combined with an advanced pulse characterization technique should, in the idealized case, serve this purpose for an arbitrary pulse shape. This is, however, violated in the real experiment by many imperfections and limitations. Although the complex waveform generation has been studied in-depth, the comparison of the effects of various experimental factors on the actual pulse shape has stayed out of focus so far. In this paper, we present an experimental study on the targeted generation and retrieval of complex pulses by using two commonly-used techniques: spatial-light-modulator (SLM)-based 4f pulse shaper and second-harmonic generation frequency-resolved optical gating (FROG) and cross-correlation FROG (XFROG). By combining FROG and XFROG traces, we analyze the pulses with SLM-adjusted complex random phases ranging from simple to very complex waveforms. We demonstrate that the combination of FROG and XFROG ensures highly consistent pulse retrieval, irrespective of the used retrieval algorithm. This enabled us to evaluate the role of various experimental factors on the agreement between the simulated and actual pulse shape. The factors included the SLM pixelation, SLM pixel crosstalk, finite laser focal spot in the pulse shaper, or interference fringes induced by the SLM. In particular, we observe that including the SLM pixelation and crosstalk effect significantly improved the pulse shaping simulation. We demonstrate that the complete simulation can faithfully reproduce the pulse shape. Nevertheless, even in this case, the intensity of individual peaks differs between the retrieved and simulated pulses, typically by 10–20% of the peak value, with the mean standard deviation of 5–9% of the maximum pulse intensity. We discuss the potential sources of remaining discrepancies between the theoretically expected and experimentally retrieved pulse.

Characterization of a Laboratory-Based X-Ray Computed Nanotomography System for Propagation-Based Method of Phase Contrast Imaging

Phase contrast imaging (PCI) is used to extend X-ray computed nanotomography (nCT) technique for analyzing samples with a low X-ray contrast, such as polymeric structures or soft tissues. Although this technique is used in many variations at synchrotrons, along with the development of X-ray tubes and X-ray detectors, a PCI becomes available also for laboratory systems. This paper is focused on determining the conditions for propagation-based PCI in laboratory nCT systems based on three criteria. It is mostly employed in near-field imaging regime, which is quantified via the Fresnel number. X-rays must reach a certain degree of coherence to form edge enhancement. Finally, the setup of every computed tomography (CT) measurement has to avoid geometrical unsharpness due to the finite focal spot size. These conditions are evaluated and discussed in terms of different properties and settings of the CT machine. Propagation-based PCI is tested on a sample of carbon fibers reinforced polyethylene and the implementation of the Paganin phase retrieval algorithm on the CT data is shown.

A blind-deblurring method based on a compressed-sensing scheme in digital breast tomosynthesis

Background and objectiveDigital breast tomosynthesis (DBT) is a well-established multiplanar imaging modality in breast examinations designed to overcome the limitations of conventional mammography. However, reconstructed DBT images from the acquired projection data are often limited in image performance due mainly to blur artifacts resulting from inherent aspects of imaging systems, including detector resolution and the finite focal spot of the x-ray tube. MethodsWe investigated an effective blind-deblurring method based on a compressed-sensing scheme in an attempt to solve the blurring problem in DBT. We implemented the proposed algorithm and performed a systematic simulation and an experiment to demonstrate its viability. In both simulation and experiment, all of the projection data were taken with a tomographic angle of θ = 32° and an angle step of Δθ = 2°. The proposed deblurring algorithm was then applied to the projection data before performing the common filtered-backprojection-based DBT reconstruction process. ResultsThe deblurred projection images showed much better image performance compared with the blurred projection images, demonstrating the viability of the proposed blind-deblurring scheme in conventional radiography. The PSNR and RMSE characteristics of the deblurred DBT image improved by factors of approximately 1.63 and 0.37, respectively, compared with those of the blurred DBT image. ConclusionsOur results indicate that the proposed blind-deblurring method was effective in reducing the blurring problem in both DBT and in conventional radiography, excluding additional measurement of the system response function.

Synchrotron emission from nanowire array targets irradiated by ultraintense laser pulses

We present a numerical study, based on two-dimensional particle-in-cell simulations, of the synchrotron emission induced during the interaction of femtosecond laser pulses of intensities I = 1021–1023 W cm−2 with nanowire arrays. Through an extensive parametric scan on the target parameters, we identify and characterize several dominant radiation mechanisms, mainly depending on the transparency or opacity of the plasma produced by the wire expansion. At I = 1022 W m−2, the emission of high-energy (>10 keV) photons attains a maximum conversion efficiency of ∼10% for 36–50 nm wire widths and 1 μm interspacing. This maximum radiation yield is found to be similar to that achieved in a uniform plasma of same average (sub-solid) density, but nanowire arrays provide efficient radiation sources over a broader parameter range. Moreover, we examine the variations of the photon spectra with the laser intensity and the wire material, and we demonstrate that the radiation efficiency can be further enhanced by adding a plasma mirror at the backside of the nanowire array. Finally, we briefly consider the influence of a finite laser focal spot and oblique incidence angle.

Feasibility Study for Improving the Image Characteristics in Digital Tomosynthesis (DTS) Using a Compressed-Sensing (Cs)-Based Pre-Deblurring Scheme

ABSTRACTDigital tomosynthesis (DTS) has been widely used in both industrial nondestructive testing and medical x-ray imaging as a popular multiplanar imaging modality. However, although it provides some of the tomographic benefits of computed tomography (CT) at reduced dose and imaging time, the image characteristics are relatively poor due to blur artifacts originated from incomplete data sampling for a limited angular range and also aspects inherent to imaging system, including finite focal spot size of the x-ray source, detector resolution, etc. In this work, in order to overcome these difficulties, we propose an intuitive method in which a compressed-sensing (CS)-based deblurring scheme is applied to the projection images before common DTS reconstruction. We implemented the proposed deblurring algorithm and performed a systematic experiment to demonstrate its viability for improving the image characteristics in DTS. According to our results, the proposed method appears to be effective for the blurring problems in DTS and seems to be promising to our ongoing application to x-ray nondestructive testing.

Spatial and temporal plasma evolutions of magnetic reconnection in laser produced plasmas

Magnetic reconnection is experimentally investigated in laser produced plasmas. By irradiating a solid target with a high-power laser beam, a magnetic bubble is generated due to the Biermann effect. When two laser beams with finite focal spot displacements are utilized, two magnetic bubbles are generated, and the magnetic reconnection can take place. We measure the spatial and temporal plasma evolutions with optical diagnostics using framing camera. We observed the plasma jets, which are considered to be reconnection out flows. Spatial and temporal scales of the plasma jets are much larger than those of laser. The magnetic reconnection time has been estimated from the expansion velocity, which is consistent with the Sweet-Parker model.

Improvement of image characteristics in high-voltage computed tomography (CT) by applying a compressed-sensing (CS)-based image deblurring scheme

We have established a high-voltage computed tomography (CT) system with a 1–3MV LINAC x-ray generator for industrial nondestructive testing. However, reconstructed CT images are typically blurred, limiting its image performance, mainly due to the finite focal spot size of the x-ray source, aspects inherent to detector such as the detector pixel size and the detector resolution, and the reconstruction procedure as well. Thus the recovery of the reconstructed CT images from their degraded version is essential for improving the image characteristics. In this work, we investigated the compressed-sensing (CS)-based deconvolution scheme for more accurate image deblurring in CT. We implemented the proposed image deblurring algorithm for CT and performed a systematic simulation and experiment to demonstrate its viability. Our results indicate that the proposed deblurring scheme appears to be effective for the blurring problems in CT and is applicable to improve its present image characteristics.

TH-AB-207A-09: Tailoring TCM Schemes to a Task: Evaluating the Impact of Customized TCM Profiles On Detection of Lung Nodules in Simulated CT Lung Cancer Screening

Purpose: Recent work has shown that current TCM profile designs boost detection of low-contrast lung lesions in the lung apices, but yield reduced detection performance in the mid and lower lung regions relative to fixed tube current cases. This observed imbalance suggests that the TCM scheme might be tailored in new ways to maximize nodule detection throughout the entire lung. In this work, we begin a preliminary investigation into custom TCM profiles in an attempt to achieve uniform lesion detection throughout the extent of the lung. Methods: Low-contrast (25HU), 6mm nodules representing ground glass opacities were simulated at 1mm intervals over the length the lungs in a voxelized model of the XCAT phantom, one nodule per lung, per simulated scan. Voxel values represented attenuation values at 80keV. CT projection data was created by simulating a finite focal spot and using Joseph's method for forward projection; scanner geometry was that of the Siemens Sensation 64 and the X-ray source was simulated as an 80keV monochromatic beam. Noise realizations were created using Poisson statistics, a realistic bowtie filter and varying tube current. 500 noise realizations were created for the custom TCM designs. All reconstruction was done with FreeCT_wFBP. An SKE/BKE task was used in conjunction with a 2D Hotelling Observer to calculate area-under-the-curve (AUC) as a proxy for “detectability.” AUC was plotted as a function of nodule Z-location to create a “detectability map.” The detectability map for the custom TCM curve was qualitatively assessed relative to previous results for the fixed TC and clinical TCM cases for uniformity. Results: Detection uniformity was improved throughout the mid and lower lungs, however detection remained disproportionately high in the upper lung region. Conclusion: Detection uniformity was improved with a custom TC profile. Future work will incorporate an analytic, task-specific approach to optimize the TC scheme for nodule detection. J. Hoffman: Part-time intern, Toshiba Medical Research Institute; M. McNitt-Gray: Institutional research agreement, Siemens Healthcare; Past recipient, research grant support, Siemens Healthcare; Consultant, Toshiba America Medical Systems; Consultant, Samsung Electronics; F. Noo: Institutional research agreement, Siemens Healthcare; Receives research funding from Siemens Healthcare

Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise

While model-based reconstruction methods have been successfully applied to flat-panel cone-beam CT (FP-CBCT) systems, typical implementations ignore both spatial correlations in the projection data as well as system blurs due to the detector and focal spot in the x-ray source. In this work, we develop a forward model for flat-panel-based systems that includes blur and noise correlation associated with finite focal spot size and an indirect detector (e.g. scintillator). This forward model is used to develop a staged reconstruction framework where projection data are deconvolved and log-transformed, followed by a generalized least-squares reconstruction that utilizes a non-diagonal statistical weighting to account for the correlation that arises from the acquisition and data processing chain. We investigate the performance of this novel reconstruction approach in both simulated data and in CBCT test-bench data. In comparison to traditional filtered backprojection and model-based methods that ignore noise correlation, the proposed approach yields a superior noise-resolution tradeoff. For example, for a system with 0.34 mm FWHM scintillator blur and 0.70 FWHM focal spot blur, using the correlated noise model instead of an uncorrelated noise model increased resolution by 42% (with variance matched at 6.9 × 10−8 mm−2). While this advantage holds across a wide range of systems with differing blur characteristics, the improvements are greatest for systems where source blur is larger than detector blur.

Investigation of spatial resolution characteristics of an in vivo microcomputed tomography system

The spatial resolution characteristics of an in vivo microcomputed tomography (CT) system was investigated in the in-plane (x–y), cross plane (z) and projection imaging modes. The microCT system utilized in this study employs a flat panel detector with a 127µm pixel pitch, a microfocus x-ray tube with a focal spot size ranging from 5–30µm, and accommodates three geometric magnifications (M) of 1.72, 2.54 and 5.10. The in-plane modulation transfer function (MTF) curves were measured as a function of the number of projections, geometric magnification (M), detector binning and reconstruction magnification (MRecon). The in plane cutoff frequency (10% MTF) ranged from 2.31lp/mm (M=1.72, 2×2 binning) to 12.56lp/mm (M=5.10, 1×1 binning) and a bar pattern phantom validated those measurements. A slight degradation in the spatial resolution was observed when comparing the image reconstruction with 511 and 918 projections, whose effect was visible at the lower frequencies. Small value of MRecon has little or no impact on the in-plane spatial resolution owning to a stable system. Large value of MRecon has implications on the spatial resolution and it was evident when comparing the bar pattern images reconstructed with MRecon=1.25 and 2.5. The cross plane MTF curves showed that the spatial resolution increased as the slice thickness decreased. The cutoff frequencies in the projection imaging mode yielded slightly higher values as compared to the in-plane and cross plane modes at all the geometric magnifications (M). At M=5.10, the cutoff resolution of the projection and cross plane on an ultra-high contrast resolution bar chip phantom were 14.9lp/mm and 13–13.5lp/mm. Due to the finite focal spot size of the x-ray tube, the detector blur and the reconstruction kernel functions, the system׳s spatial resolution does not reach the limiting spatial resolution as defined by the Nyquist׳s detector criteria with an ideal point source. The geometric magnification employed in the microCTs provide a tradeoff between field of view and spatial resolution for a wide range of applications.

SU‐E‐I‐08: Investigation of Deconvolution Methods for Blocker‐Based CBCT Scatter Estimation

Purpose:To investigate whether deconvolution methods can improve the scatter estimation under different blurring and noise conditions for blocker‐based scatter correction methods for cone‐beam X‐ray computed tomography (CBCT).Methods:An “ideal” projection image with scatter was first simulated for blocker‐based CBCT data acquisition by assuming no blurring effect and no noise. The ideal image was then convolved with long‐tail point spread functions (PSF) with different widths to mimic the blurring effect from the finite focal spot and detector response. Different levels of noise were also added. Three deconvolutionMethods:1) inverse filtering; 2) Wiener; and 3) Richardson‐Lucy, were used to recover the scatter signal in the blocked region. The root mean square error (RMSE) of estimated scatter serves as a quantitative measure for the performance of different methods under different blurring and noise conditions.Results:Due to the blurring effect, the scatter signal in the blocked region is contaminated by the primary signal in the unblocked region. The direct use of the signal in the blocked region to estimate scatter (“direct method”) leads to large RMSE values, which increase with the increased width of PSF and increased noise. The inverse filtering is very sensitive to noise and practically useless. The Wiener and Richardson‐Lucy deconvolution methods significantly improve scatter estimation compared to the direct method. For a typical medium PSF and medium noise condition, both methods (∼20 RMSE) can achieve 4‐fold improvement over the direct method (∼80 RMSE). The Wiener method deals better with large noise and Richardson‐Lucy works better on wide PSF.Conclusion:We investigated several deconvolution methods to recover the scatter signal in the blocked region for blocker‐based scatter correction for CBCT. Our simulation results demonstrate that Wiener and Richardson‐Lucy deconvolution can significantly improve the scatter estimation compared to the direct method.

Improve spatial resolution by Modeling Finite Focal Spot (MFFS) for industrial CT reconstruction.

The finite focal spot is one of the major limitations of the high spatial resolution CT, especially to the high-energy industrial CT system with a macro-focus x-ray source. In this paper, we propose an efficient reconstruction framework through finite focal spot size based projection modeling to improve the spatial resolution of current industrial CT system, and demonstrate the superior performance of this method. First of all, the blurred projection produced by a finite size source is modeled as the integral ideal projection of a given point source over the finite focal spot support. Under the model discretization, the approximate linear equivalence relation between the actual finite focus model and the ideal point source model is established. Then a projection recovery method with this relationship is presented to recover the projection of the finer focal spot from the blurred projection. Finally, a high-spatial resolution image can be reconstructed from the recovered projections using the standard Filtered Back-Projection (FBP) algorithm. Furthermore the noise in the reconstructed image with different model parameters is studied and a difference image based fusion method is presented for the further suppression of the noise caused by the projection analysis processing. Both numerical simulations and real experiments have shown that the proposed reconstruction framework with the outstanding performance and efficiency characteristics can significantly enhance the spatial resolutions of current high-energy industrial CT systems.

Effects of ray profile modeling on resolution recovery in clinical CT

Iterative image reconstruction gains more and more interest in clinical routine, as it promises to reduce image noise (and thereby patient dose), to reduce artifacts, or to improve spatial resolution. However, among vendors and researchers, there is no consensus of how to best achieve these goals. The authors are focusing on the aspect of geometric ray profile modeling, which is realized by some algorithms, while others model the ray as a straight line. The authors incorporate ray-modeling (RM) in nonregularized iterative reconstruction. That means, instead of using one simple single needle beam to represent the x-ray, the authors evaluate the double integral of attenuation path length over the finite source distribution and the finite detector element size in the numerical forward projection. Our investigations aim at analyzing the resolution recovery (RR) effects of RM. Resolution recovery means that frequencies can be recovered beyond the resolution limit of the imaging system. In order to evaluate, whether clinical CT images can benefit from modeling the geometrical properties of each x-ray, the authors performed a 2D simulation study of a clinical CT fan-beam geometry that includes the precise modeling of these geometrical properties. All simulations and reconstructions are performed in native fan-beam geometry. A water phantom with resolution bar patterns and a Forbild thorax phantom with circular resolution patterns representing calcifications in the heart region are simulated. An FBP reconstruction with a Ram-Lak kernel is used as a reference reconstruction. The FBP is compared to iterative reconstruction techniques with and without RM: An ordered subsets convex (OSC) algorithm without any RM (OSC), an OSC where the forward projection is modeled concerning the finite focal spot and detector size (OSC-RM) and an OSC with RM and with a matched forward and backprojection pair (OSC-T-RM, T for transpose). In all cases, noise was matched to be able to focus on comparing spatial resolution. The authors use two different simulation settings. Both are based on the geometry of a typical clinical CT system (0.7 mm detector element size at isocenter, 1024 projections per rotation). Setting one has an exaggerated source width of 5.0 mm. Setting two has a realistically small source width of 0.5 mm. The authors also investigate the transition from setting one to two. To quantify image quality, the authors analyze line profiles through the resolution patterns to define a contrast factor (CF) for contrast-resolution plots, and the authors compare the normalized cross-correlation (NCC) with respect to the ground truth of the circular resolution patterns. To independently analyze whether RM is of advantage, the authors implemented several iterative reconstruction algorithms: The statistical iterative reconstruction algorithm OSC, the ordered subsets simultaneous algebraic reconstruction technique (OSSART) and another statistical iterative reconstruction algorithm, denoted with ordered subsets maximum likelihood (OSML) algorithm. All algorithms were implemented both without RM (denoted as OSC, OSSART, and OSML) and with RM (denoted as OSC-RM, OSSART-RM, and OSML-RM). For the unrealistic case of a 5.0 mm focal spot the CF can be improved by a factor of two due to RM: the 4.2 LP/cm bar pattern, which is the first bar pattern that cannot be resolved without RM, can be easily resolved with RM. For the realistic case of a 0.5 mm focus, all results show approximately the same CF. The NCC shows no significant dependency on RM when the source width is smaller than 2.0 mm (as in clinical CT). From 2.0 mm to 5.0 mm focal spot size increasing improvements can be observed with RM. Geometric RM in iterative reconstruction helps improving spatial resolution, if the ray cross-section is significantly larger than the ray sampling distance. In clinical CT, however, the ray is not much thicker than the distance between neighboring ray centers, as the focal spot size is small and detector crosstalk is negligible, due to reflective coatings between detector elements. Therefore,RM appears not to be necessary in clinical CT to achieve resolution recovery.

Interesting detector shapes for third generation CT scanners

To discuss options in designing detector shapes in third generation CT and to quantify potential cost savings for compact third generation CT systems, and to extend the work from two-dimensional fan-beam CT to three-dimensional cone-beam CT for circular, sequential, and spiral scan trajectories. Third generation CT scanners typically comprise detectors which are flat or whose shape is the segment of a cylinder or a sphere that is focused onto the focal spot of the x-ray source. There appear to be two design criteria that favor this choice of detector shape. One is the possibility of performing fan-beam and cone-beam filtered backprojection in the native geometry (without rebinning) and the other criterion could be to enable the early use of focused antiscatter grids. It is less known, however, that other detector shapes may also have these properties. While these designs have been evaluated for 2D CT from a theoretical standpoint more than one decade ago the authors revisit and generalize these considerations, extend them to 3D circular, sequential, and spiral cone-beam CT and propose an optimal design in terms of detector costs while keeping image quality constant. Their considerations and conclusions are based on considering the sampling density of the x-rays, including the effects of finite focal spot and finite detector element size. Proposing image reconstruction algorithms or numerically evaluating the results by reconstructing simulated projection data is not within the scope of this work. If the detector arc is curved to be nearly concentric with the circle describing the edge of the field of measurement significantly less detector area and detector pixels are required compared to today's third generation CT systems where the detector arc is centered about the focal spot. Combined with a detector that just covers the spiral Tam window cost savings of 60% or more are possible in compact CT systems. In terms of practicability the new designs appear to be nearly as easy to realize as today's third generation systems. Compact CT systems, which require the focal spot to be mounted close to the edge of the field of measurement, may significantly benefit from using detector shapes other than the typical equiangular detector that is focused onto the focal spot.

Finite detector based projection model for high spatial resolution

For finite detector and focal spot sizes, here we propose a projection model for high spatial resolution. First, for a given x-ray source point, a projection datum is modeled as an area integral over a narrow fan-beam connecting the detector elemental borders and the x-ray source point. Then, the final projection value is expressed as the integral obtained in the first step over the whole focal spot support. An ordered-subset simultaneous algebraic reconstruction technique (OS-SART) is developed using the proposed projection model. In the numerical simulation, our method produces improved spatial resolution and suppresses high-frequency artifacts.

Evaluation of X-ray phase-contrast imaging with the Medipix

In the recent decade phase-contrast imaging in the X-ray regime has been developed as a competitive alternative to conventional absorption radiography and computed tomography Wilkins et al. (1996) [1]. As phase-contrast is an energy dependent phenomenon, the use of a spectroscopic detector like the Medipix is a key tool to characterize and optimize imaging methods such as in-line or interferometric phase-contrast imaging. In the following the energy dependency of interference patterns caused by phase shifts in a coherent wavefront will be shown. Moreover, the spatial coherence of X-rays, considered as wavefronts, is crucial for the formation of detectable interference effects. The newest generations of X-ray sources produce small but finite focal spot sizes, so that partial spatial coherence of the wave-field has to be taken into account. The contribution of partial coherence to the image recorded in the detector plane has been investigated and the outcome will be presented. For a fuller understanding of a complete phase-contrast imaging setup the incoherent scattering effects were additionally simulated with Monte-Carlo methods. Furthermore, to develop a realistic simulation-tool for X-ray phase-contrast imaging, a good comprehension of the detection system is needed. This was also achieved by Monte-Carlo simulations. The comparison with measurements of the simulations of a complete setup shows a very good agreement.