Radon transform and pattern functions in quantum tomography

Abstract

The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the latter is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and non-normalizable eigenfunctions to the number operator is considered from the point of view of this new representation.     

Survey of practice in paediatric computed tomography

The purpose of this study was to explore the frequency of paediatric computed tomography (CT) examinations in several hospitals in Bulgaria and to assess the current practice. The standard forms provided by the International Atomic Emergency Agency for survey of the paediatric CT practice were used. Six hospitals provided data on frequency of paediatric CT examinations performed in 2009. Large variations in dose, up to a factor of 4, were found among the centres within the same age group for a given procedure, and in one of the hospitals the paediatric dose was twice higher than the adult dose. Seven departments use dedicated CT protocols for children. Only 4 in 12 departments keep records of patient dose. Dose information for previous examinations is not required by the radiologists. The collected detailed data provided preliminary information how the patient doses in paediatric CT can be reduced. Recommendations were given based on the findings.     

Interferometric measurement of the refractive-index distribution in plastic lenses by use of computed tomography

A nondestructive measurement method that makes possible the measurement of a three-dimensional refractive-index distribution of any shape plastic lens is presented. In this method, a Mach-Zehnder interferometer and shearing interferometer are combined into a single optical system and are used selectively. Interference fringes of a test object that is immersed in matching liquid are detected at various rotation angles. And transmitted wave fronts are calculated with these interference fringes. Finally, the refractive-index distribution is obtained by computed tomography analysis. In addition, accurate control of the matching liquid temperature makes it possible to measure the absolute refractive index of the test object. This system has good performance with a measurement accuracy of 10(-4) or better peak to valley.     

Evaluation of the homogeneity of the metal of welded joints by ultrasonic computed tomography

We consider the possibilities of a new (in the field of the ultrasonic testing of present-day structural materials) information technology of ultrasonic computed tomography for the diagnostics of the quality of welded joints and control of the parameters of welding technological processes, including the technology of electron-beam welding of present-day aluminum alloys. This kind of diagnostics is based on the obtained information on the volume homogeneity of mechanical properties of the metal under consideration in the heat-affected zone of a weld. Analysis of the information aspects of the method of transmission ultrasonic computed tomography shows that the technologies of ultrasonic testing based on it are the most efficient for thick-walled plane-sheet articles with welded joints because high-quality reconstruction of the space distribution of the parameter under study over the article thickness is possible if this parameter changes in the plane parallel to the article surface. We describe the results of tomographic experiments with the use of a UST-04M ultrasonic computer tomograph, developed at the Physicomechanical Institute, on the reconstruction of the space distribution of acoustic and mechanical characteristics of the metal in specimens of the mentioned articles, made of steel and AMG-6v aluminum alloy by the technology of electron-beam welding, as well as the data of verification of the reconstructed tomographic images by means of their comparison with the results of metallographic investigations. The data obtained corroborate the efficiency of the technology of ultrasonic computed tomography for evaluating the quality of welded joints and optimizing welding technologies on the basis of experimental determination of the volume homogeneity of properties of the metal in the zone of a welded joint. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 4, pp. 71–84, July–August, 2007.     

Scan region and organ doses in computed tomography

The purpose of this study was to investigate how the choice of the scanned region affects organ doses in CT. ImPACT CT Patient Dosimetry Calculator (version 1.0) was used to compute absorbed doses to eight organs of interest in medical radiation dosimetry. For 13 dosimetry data sets, the authors calculated the maximum organ dose (D(max)) as well as the corresponding organ dose for a scan with selected length D(L). These data permitted the relative dose (D(r) = D(L)/D(max)) to be determined for varying scan lengths. Computations were performed for a nominal X-ray tube current of 100 mA, a rotation time of 1 s and a CT pitch of 1. The authors also determined values of D(max)/CTDI(vol), where CTDI(vol) is obtained in a 32-cm diameter CT dosimetry phantom using the same radiographic techniques. For each organ, D(r) was independent of the type of scanner, and increased monotonically to unity with increasing scan length. Relative doses for a scan restricted to the organ length ranged from 0.65 D(max) for the bladder to 0.86 D(max) for the lungs. There was good correlation (r = 0.64) between relative organ dose and the corresponding organ length. At 120 kV, the lowest value of D(max)/CTDI(vol) was 1.23 for the breast and the highest was 2.22 for the thyroid. Varying the X-ray tube voltage between 100 and 130 kV results in changes in D(max)/CTDI(vol) of no more than 4 %. CT scans limited to the direct irradiation of an average-sized organ results in an absorbed dose of ~0.75 D(max).     

The construction and use of convex hulls in limited-angle computerized tomography

A method is developed to construct the convex hull of an object and make use of it in limited-angle x-ray computerized tomography (CT). The convex hull of an object is the smallest convex region containing the object, and therefore it can serve as boundary information in the reconstruction of the object from limited-angle data. Two methods, the intersection version and the superimposition version, of constructing the convex hull of an object from x-ray data are presented. It is shown that the intersection version is very efficient when the noise is very low, whereas the superimposition version is more stable with respect to noise. The usefulness and the construction of the convex hulls of embedded flaws in industrial x-ray CT are also studied. It is demonstrated with simulated data that the use of convex hulls makes it possible to reconstruct high-quality images from limited-angle data.     

Patient doses using multidetector computed tomography scanners in Kenya

Assessment of patient dose attributed to multislice computed tomography (CT) examination. A questionnaire method was developed and used in recording the patient dose and scanning parameters for the head, chest, abdomen and lumbar spine examinations. The patient doses due to brain, chest and abdomen examination were above the international diagnostic reference levels (DRLs) by factors of between one and four. The study demonstrated that the use of multislice CT elevates patient radiation dose, justifying the need for local optimised scanning protocols and the use of institutional DRL for dose management without affecting diagnostic image quality.     

Quality control and patient doses in X-ray computed tomography

Results of quality control (QC) tests for a period of over a year and patient doses were analysed for several computed tomography units in our centre. The results of the QC tests were generally within limits for all of the examined scanners, proving good and stable performance of the systems. The tests were not helpful in predicting breakdowns of the systems such as tube failure. The doses for the same anatomical areas differed between scanners and in some cases exceeded the diagnostic reference levels (DRLs). DRLs are defined for typical diagnostic examinations performed in general hospitals and are not directly applicable to the examinations performed in the oncological centre.     

X-ray computed tomography proof of bacterial-based self-healing in concrete

Self-healing strategies are regarded as a promising solution to reduce the high maintenance and repair cost of concrete infrastructures. In the present work, a bacterial-based self-healing by use of hydrogel encapsulated bacterial spores (bio-hydrogels) was investigated. The crack closure behavior of the specimens with/without bio-hydrogels was studied quantitatively by light microscopy. To have a view of the self-healing inside the specimens, a high resolution X-ray computed microtomography (X-ray μCT) was used. The total amount and the distribution of the healing products in the whole matrix were investigated. This study indicates that the specimens incorporated with bio-hydrogels had distinct improved healing efficiency compared to the reference ones with pure hydrogel only. The healing ratios in the specimens with bio-hydrogels were in the range from 70% to 100% for the cracks smaller than 0.3 mm, which is more than 50% higher than for the ones with pure hydrogel; and the maximum crack bridging was about 0.5 mm (in 7 d), while pure hydrogels only allowed healing of cracks of about 0.18 mm. The total volume ratio of the healing product in the specimens with bio-hydrogels amounted to 2.2%, which was about 60% higher than for the ones with pure hydrogel (1.37%).     

Resolution,artifacts and the design of computed tomography systems

The factors that limit the fidelity of a computed tomography image have been demonstrated by a series of imaging experiments. The observed spatial resolution, contrast resolution and artifacts are, for the most part, consistent with existing theories.     

Density gradients in aluminium foams: characterisation by computed tomography and measurements of the effective thermal conductivity

The density gradients present in several aluminium foams, produced by the powder metallurgical route, have been analysed by using computed tomography and by measuring the effective thermal conductivity (λ). The method used to measure λ, Transient Plane Source (TPS) technique, allows obtaining values of the local thermal conductivity, i.e. conductivity of a localised zone within the sample. These values have been related to the density of the measured zone, which was obtained from the computed tomography experiments. A power law relationship between local effective thermal conductivity and local density has been obtained.     

Evaluation of cortical bone by peripheral quantitative computed tomography in continuous ambulatory peritoneal dialysis patients

Several studies have suggested an increased prevalence of osteopenia in dialysis. Peripheral quantitative computed tomography (pQCT) is a new technique that allows the noninvasive evaluation of trabecular and cortical bone separately. The aim of the study was: (1) to evaluate cortical bone by pQCT in continuous ambulatory peritoneal dialysis (CAPD) patients and compare the data with that obtained in healthy controls; and (2) to correlate cortical bone parameters with bone mineral density (BMD) of the lumbar spine and femoral neck and total bone mineral content (TBMC). Cortical bone parameters were obtained in 22 CAPD patients and 27 healthy individuals at the distal radius using a Stratec XCT 960 pQCT machine. In the dialysis patients, we also determined BMD and TBMC by bone densitometry. Dialysis patients, compared with controls, showed a significant reduction in volumetric cortical BMD (VcBMD) (p = 0.04) and cortical thickness (cThk) (p < 0.0001) with a significant increase in radial total cross-sectional area (TA) (p = 0.006), endosteal circumference (p < 0.0001), and buckling ratio (p < 0.0001). In CAPD patients, total time on dialysis correlated negatively with radial total BMD (p < 0.01) and VcBMD (p < 0.01). Age correlated positively with TA (p < 0.01), endosteal (p < 0.01), and periosteal circumferences (p < 0.01). Serum intact parathyroid hormone (PTH) levels correlated positively with endosteal (p = 0.04) and periosteal perimeter (p = 0.01). Total alkaline phosphatase correlated negatively with VcBMD (p < 0.01), and positively with endosteal perimeter (p = 0.02). Total bone mineral content correlated significantly with radial cortical content (p < 0.001), cross-sectional cortical area (cA; p < 0.001), and cThk (p < 0.01) but not with total radial BMD, VcBMD, or buckling ratio. No correlations were found between radial cortical parameters and BMD measured at the lumbar spine or femoral neck. We conclude that dialysis patients show cortical osteopenia with marked cortical thinning partially mediated by PTH action on bone. Total bone mineral content correlated with various radial cortical parameters (content, area, and thickness) but not with others. No correlations were found between cortical bone parameters measured at the peripheral skeleton with areal bone density measured at the axial skeleton. These findings suggest that pQCT may be a new tool in the assessment of bone fragility in dialysis patients.     

基于微观尺度X射线断层扫描技术的短切碳纤维SMC复合材料失效分析

短切碳纤维片状模塑料(SMC)复合材料内部复杂的纤维三维分布及其造成的多样微裂纹演化过程加剧了其失效分析的难度。针对短切碳纤维SMC复合材料的失效行为进行研究, 提出采用微观尺度X射线断层扫描技术实时表征材料内部的微观结构, 捕捉碳纤维和微裂纹的几何信息, 结合先进的图像采集和图像处理技术, 进而准确重构出短切碳纤维SMC复合材料在受力过程中的三维结构变化以及微裂纹的完整演变过程, 定量测量微裂纹的几何尺寸, 实现损伤的精准诊断, 并利用Tsai-Wu失效判据和界面开裂后的基体应力场理论等失效方法探究短切碳纤维SMC复合材料的失效机制。该方法的提出对于研究短切碳纤维SMC复合材料的失效过程以及分析相应的失效行为提供了重要依据。     

Inherent homogenous media dispersion compensation in frequency domain optical coherence tomography by accurate k-sampling

Depth dependent broadening of the axial point spread function due to dispersion in the imaged media, and algorithms for postprocess correction, have been previously described for both time domain and frequency domain optical coherence tomography. We show that homogeneous media dispersion artifacts disappear when frequency domain samples are acquired with uniform spacing in circular wavenumber, as opposed to uniform sampling in optical frequency. We further explicate the source of this point spread broadening and simulate its magnitude in aqueous media. We experimentally demonstrate media dispersion compensation in high dispersion glass by choosing sample frequencies at equal intervals of media index of refraction divided by vacuum wavelength, and we recover unbroadened reflections without an additional postprocessing step.     

Comparison of different methods for shielding design in computed tomography

The purpose of this work is to compare different methods for shielding calculation in computed tomography (CT). The BIR-IPEM (British Institute of Radiology and Institute of Physics in Engineering in Medicine) and NCRP (National Council on Radiation Protection) method were used for shielding thickness calculation. Scattered dose levels and calculated barrier thickness were also compared with those obtained by scatter dose measurements in the vicinity of a dedicated CT unit. Minimal requirement for protective barriers based on BIR-IPEM method ranged between 1.1 and 1.4 mm of lead demonstrating underestimation of up to 20 % and overestimation of up to 30 % when compared with thicknesses based on measured dose levels. For NCRP method, calculated thicknesses were 33 % higher (27-42 %). BIR-IPEM methodology-based results were comparable with values based on scattered dose measurements, while results obtained using NCRP methodology demonstrated an overestimation of the minimal required barrier thickness.     

Image quality and patient dose in computed tomography examinations in Greece

The purpose of this study is to evaluate image quality of various computed tomography (CT) scanners installed in Greece, as well as to investigate patient doses from common CT examinations. An image quality survey was performed in 44 CT scanners countrywide. The imaging performance of the systems was evaluated by measurements of certain parameters, such as image noise, spatial uniformity, high- and low-contrast resolution and slice thickness accuracy. Moreover, preliminary results of patient dose survey are presented. Concerning image quality, 80 % of the scanners were found to be in compliance with the national legislation and relative international guidelines for all the examined parameters. Weighted CT dose index and dose-length product values for chest and abdomen routine examinations were generally below the dose reference levels (DRLs) suggested by the European Commission. However, some scanners were found to deliver significantly higher doses than the suggested DRL for head routine examinations. Finally, differences in the performance among scanners of the same type and similar age were observed, pointing out the importance of frequent calibration, routine quality control and proper maintenance.