Focal Spot Shape Research Articles

Enhanced slit methodology for characterization of x‐ray focal properties

AbstractThe measurement of focal spot sizes in industrial x‐ray tubes using conventional edge and slit methods typically requires complex slit diaphragms and auxiliary testing equipment. Additionally, stringent spatial‐positioning requirements are imposed on the x‐ray tube, auxiliary testing equipment, and detector, making the machining of auxiliary testing equipment and meeting test conditions challenging. This study optimized and improved the auxiliary testing equipment and computations in the slit method based on the principles of the edge method. An experimental setup capable of self‐calibrating the spatial positions was designed, avoiding measurement errors during focal‐spot‐size measurements. We derived a formula for the focal spot size for this experimental setup, allowing measurements using slits of various sizes. Furthermore, we proposed a method for determining the focal spot size through linear fitting of multiple sets of slit dimensions and projected widths of the focal spot on the detector. This approach filters out random noise and errors during data collection, significantly enhancing measurement precision. By adjusting the slit and detector angles, we could measure the focal spot sizes at various angles and draw contour maps of the focal spot shape. This method was applied to measure the focal spot size and shape of a side‐window x‐ray tube under different voltage conditions. The overall measurement error was less than 6%, reflecting the reliability, accuracy, and consistency of the results obtained using the proposed method. Thus, the proposed method supports the inspection, verification, and maintenance of x‐ray sources.

Multifocal tornado beams carrying chirality

The significance of abruptly autofocusing vortex beams with a unique helical phase structure lies in particle trapping and optical spanner applications. This paper presents a novel modulation of a circular Pearcey beam utilizing a multicyclic helical phase and a chirp factor. Both theoretical analyses and experimental results demonstrate that we have successfully designed a beam with tornado properties and optically chiral structure. This beam has multidimensionally tunable parameters, allowing not only different focusing intensities, focal lengths and focal spot shape distributions, but also controllable rotational propagation directions. Furthermore, it has the ability to produce two dual focusing modes with dissimilar focal spot distributions. We believe that such a beam holds potential applications in the realisation of optical spanners, multi-region trapping of particles and the fabrication of chiral metamaterials.

Comparison of wavefront sensing and ablation imprinting for FEL focus diagnostics at FLASH2

Extreme ultraviolet (EUV) photon beam characterization techniques, Hartmann wavefront sensing and single shot ablation imprinting, were compared along the caustic of a tightly focused free-electron laser (FEL) beam at beamline FL24 of FLASH2, the Free-electron LASer in Hamburg at DESY. The transverse coherence of the EUV FEL was determined by a Young’s double pinhole experiment and used in a back-propagation algorithm which includes partial coherence to calculate the beam intensity profiles along the caustic from the wavefront measurements. A very good agreement of the profile structure and size is observed for different wavelengths between the back-propagated profiles, an indirect technique, and ablation imprints. As a result, the Hartmann wavefront sensor including its software MrBeam is a very useful, single shot pulse resolved and fast tool for non-invasive determination of focal spot size and shape and also for beam profiles along the caustic.

Simulation study of electron beam optics for a distributed X-ray source toward stationary CT architecture

For computed tomography (CT) imaging to be considered “real time”, one set of tomographic projections are to be acquired in less than 30 ms. Current conventional CT systems are limited to approximately 300 ms because of mechanical and material limitations. To bypass the mechanical limitations of a conventional gantry system, there is an open design challenge to develop a distributed X-ray source that is tightly packed and bright. The work presented here reports a design for a distributed X-ray source based on a rotating cylindrical anode. In particular, this work focuses on designing the electron beam optics for said X-ray source and refining these optics via multi-physics simulation studies. We designed these studies to investigate the electron beam behavior for switching, steering, and focusing. We demonstrated that the high-energy electron beam could be turned off and on via the grid-switching technique, could be steered, and could be dynamically focused for distinct positions along the cylindrical anode. We also report the optimal set of parameters that result in the desired electronic focal spot size (1 mm × 7 mm) and shape at each source position for our system.

Effective focal spot measurement method for X-ray source based on the dynamic translation of a light barrier.

The accuracy of measuring the effective focal spot of the X-ray source directly affects the spatial resolution of computed tomography (CT) reconstructed images. This study proposes what we believe to be a novel approach to measure the effective focal spot based on the dynamic translation of light barrier using an accessible measuring device. This method discretizes the effective focal spot of the X-ray source into multiple subfocal spots with varying intensities and establishes a nonlinear model between the effective focal spot and measurement data. Measurement data are obtained by moving the light barrier to different positions using the electric displacement stage. The shape, size, and intensity distribution of the effective focal spot are determined by calculating the normalized weighting coefficients for each subfocal spot from measurement data. The measurement device is simple and easy to operate. Additionally, the obtained effective focal spot exhibits high accuracy, and a higher spatial resolution can be realized by reconstructing the CT images using the measured focal spot information. Numerical and real experiments validate the proposed method.

Effects of aberrations on isoSTED microscopy

Aberrations are inevitable in optical microscopes and affect the image quality. In STED microscopy, the optical resolution is especially dominated by the performance of depletion pattern. To quench fluorescence only in the periphery of the excitation focus, the depletion focus ideally has a zero-intensity point that is surrounded by a high-intensity crest. Otherwise, distortion of the depletion beam causes unwanted fluorescence inhibition. The influence of aberrations on isoSTED microscopy differs from that on STED microscopy because isoSTED microscopy generates a more complicated shape of the depletion focal spot with two opposing objectives which have different focusing properties. We present analysis that elucidates the effects on the shape, the central minimum intensity, and the peak intensity of the isoSTED pattern regarding primary aberrations such as astigmatism, coma, and spherical aberration when those aberrations are added in the shared beam path and each beam path in the 4Pi-cavity. The simulation results demonstrate significant resolution degradation (>160%; defined as the focal volume) for the aberrations with root mean square wavefront errors of 0.5 rad.

Outdoor experimental validation for ultra-high concentrator photovoltaic with serpentine-based cooling system

With demand for renewable energy growing, concentrator photovoltaic thermal hybrids have great potential. Maximising concentration ratios through the deployment of multi-stage optics can yield high power outputs from multi-junction solar cells. To prevent damaging thermal stress and to enable extraction of thermal energy, a capable cooling system is necessary.The primary objective of this study is to maximise the effective concentration ratio over a solar cell and calibrate the system to optimise the energetic and exergetic efficiencies. The capability of the serpentine-based cooling system is investigated for each concentrator optic configuration. Originality is found in the presentation of the 3-stage optic, and the use of outdoor real-world experimental data to validate a computational model. This model uses both ray tracing, heat and mass transfer simulations to enhance the understanding of system operation and enable accurate prediction of performance under various conditions. Results show focal spot shape is more important than raw optical efficiency for electrical output, making the 3-stage optic superior to the other configurations in most regards. An effective concentration of over 1200 × is achieved. Higher exergetic efficiencies are consistently found in the double serpentine configuration, though variation does not exceed ±0.3% when only changing cooling system geometry.

Direct LiF imaging diagnostics on refractive X-ray focusing at the EuXFEL High Energy Density instrument.

The application of fluorescent crystal media in wide-range X-ray detectors provides an opportunity to directly image the spatial distribution of ultra-intense X-ray beams including investigation of the focal spot of free-electron lasers. Here the capabilities of the micro- and nano-focusing X-ray refractive optics available at the High Energy Density instrument of the European XFEL are reported, as measured in situ by means of a LiF fluorescent detector placed into and around the beam caustic. The intensity distribution of the beam focused down to several hundred nanometers was imaged at 9 keV photon energy. A deviation from the parabolic surface in a stack of nanofocusing Be compound refractive lenses (CRLs) was found to affect the resulting intensity distribution within the beam. Comparison of experimental patterns in the far field with patterns calculated for different CRL lens imperfections allowed the overall inhomogeneity in the CRL stack to be estimated. The precise determination of the focal spot size and shape on a sub-micrometer level is essential for a number of high energy density studies requiring either a pin-size backlighting spot or extreme intensities for X-ray heating.

Improved two-photon polymerization through an optical fiber using coherent beam shaping

The state of the art for high resolution three-dimensional light-based additive manufacturing mainly relies on two-photon polymerization. It consists of focusing and scanning a femtosecond laser beam on a photosensitive resin to initiate crosslinking and fabricate a 3D part. This is usually achieved with a bulky objective lens which prevents printing in confined spaces. Recently, it was proposed to replace it with a multimode fiber whose core diameter is 400 μm. Thanks to wavefront shaping it was shown that the refocused beam can be digitally scanned for two-photon 3D printing. This provided a new tool to deliver light in hard-to-reach places without any motion of the fiber distal end, but it requires multiple and fine calibration measurement with a relatively complex optical setup. Here, we go a step further and demonstrate a finer digital scanning method based on a transmission matrix approach. The latter is a faster and much easier method than previously reported techniques to manipulate light at the output of the fiber. In addition, it provides smaller hatching distances (down to 200 nm) which translates into smoother 3D printed structures and it also offers the possibility of engineering the focal spot size and shape. We demonstrate the fabrication of a woodpile structure with a focused beam size of 0.8 μm along x-y and 7 μm along z. The printing time for a layer is reduced from 29 minutes to 6 minutes by engineering the voxel shape which opens up new perspectives for high resolution, fast and smooth printing in confined areas.

Contrast based method for the automated analysis of transfer functions and spatial resolution limits of micro- and nano-focus computed tomography systems: Evaluation with simulated data

Micro- and nano-focus X-ray sources are extensively used in X-ray computed tomography systems to achieve high spatial resolution. This is essential, when scanning small objects, where resolution limitations are mainly connected to the size of the focal spot. Therefore, much effort has been put into reducing the size of the focal spot, where the measurement of the focal spot size is challenging. In this paper, the implementation of a new evaluation method for the quantitative determination of the system’s transfer function and the source’ spot size and shape are presented. The spatial resolution is calculated at different evaluation points to assess which particular threshold should be used to obtain the resolution limit and the focal spot size and shape. The implementation is explained and evaluated with the aid of simulated and real radiographs of the test chart, featuring line and star patterns designed to bridge the gap between existing resolution standards.

Collimation of an anastigmat objective with three off-axis aspherical mirrors

Subject of study. Objectives for a wide variety of wavelengths from the visible to the mid-infrared are currently under development for use in small spacecraft. Because of advantages such as the ability to operate over a broad spectral range, the use of low-weight mirror fabrication technologies, and their smaller size, reflective objectives are preferred for space-based applications. This paper discusses the collimation of reflective objectives with off-axis aspheric mirrors (objectives with an off-axis field of view). Collimation of reflective objectives has traditionally been performed using interferometers operating in autocollimation mode, with collimation being verified using compensatory designs. In the case of compact multimirror objectives, it is not always possible to find space for the collimation equipment (either an interferometer with an auxiliary mirror or a holographic compensator). Method. An alternative technique was developed for sequential element-by-element collimation of a prototype multimirror objective, based on monitoring focal-spot shapes and comparing them against a calculated focal-spot shape. We discuss collimation of a four-mirror anastigmat objective, in which the first mirror is an off-axis concave ellipsoid, the second mirror is an off-axis convex hyperboloid, the third mirror is a flat, and the fourth mirror is an off-axis concave ellipsoid. The objective was collimated using a He-Ne laser (wavelength 0.63 µm), with the distribution of light in the focal spot being recorded with a television camera; collimation was verified using a continuously tunable CO laser (emission wavelength of 5.415 µm) and an HF laser (emission wavelength of 2.8–3.2 µm), and the distribution of light in the focal spots was measured with an InSb photodetector array. The focal spots were inspected using a microscope whose object plane coincided with the focal plane of the element being collimated. The entrance aperture of the objective was illuminated by a collimated laser beam parallel to the collimation axis. The quality of collimation was determined by comparing the shapes of the observed focal spots against those theoretically calculated for an ideally collimated objective. Main results. Our research revealed that a test collimation technique based on the shape of the focal spots is insufficiently sensitive to miscollimation of individual mirrors and scattering within a multiple-mirror system. In addition, the technique fails to provide the required collimation accuracy. Practical significance. The proposed technique will be used to develop specialized optoelectronic instrumentation for continuous, step-by-step verification of all optical elements in a four-mirror anastigmat to sufficient accuracy for collimation.

Traceable x-ray focal spot reconstruction by circular edge analysis: from sub-microfocus to mesofocus

The size and shape of the focal spot, i.e. the area where x-rays are generated in an x-ray tube, is a key figure of merit of a radiographic imaging system, because it governs the achievable resolution and, if the shape is irregular, can introduce anisotropic blur in the radiographs. Size and shape are mainly determined by the diameter of the accelerated electron-beam and electron interactions with the target material. Since focal spot parameters change over time, due to target wear and drift in the electron optics, traceable methods to monitor the focal spot size and shape are required. Here, we present a method to map the 2D intensity distributions of focal spots, ranging from sub-microfocus (0.1 µm) to mesofocus (>50 μm). The method evaluates radial profiles of a circular aperture and applies filtered back projection to reconstruct the focal spot intensity distribution. Special emphasis is placed on traceability and influence factors, such as image noise and aperture geometry. The method was validated over a focal spot range from 0.3 µm to 200 µm. Experimental results were compared to complementary methods, using line pair gauges (JIMA) for microfocus (1 µm–10 µm), e-beam characterisation for sub-microfocus (0.3 µm–1.0 µm), and pinhole camera imaging for mesofocus spots (50 µm–200 µm). Good agreement between the focal spot reconstruction and the complementary methods was achieved. Limitations due to edge penetration, caused by the finite thickness of the circular aperture gauge, were experimentally verified. From these findings, we derived recommendations for an improved gauge geometry, regarding its thickness and the aperture diameters. The method perfectly complements the well-established pinhole imaging, which is limited to focal spots larger than ∼50 µm.

Tomography of a seeded free-electron laser focal spot: qualitative and quantitative comparison of two reconstruction methods for spot size characterization.

Performing experiments at free-electron lasers (FELs) requires an exhaustive knowledge of the pulse temporal and spectral profile, as well as the focal spot shape and size. Operating FELs in the extreme ultraviolet (EUV) and soft X-ray (SXR) spectral regions calls for designing ad-hoc optical layouts to transport and characterize the EUV/SXR beam, as well as tailoring its spatial dimensions at the focal plane down to sizes in the few micrometers range. At the FERMI FEL (Trieste, Italy) this task is carried out by the Photon Analysis Delivery and Reduction System (PADReS). In particular, to meet the different experimental requests on the focal spot shape and size, a proper tuning of the optical systems is required, and this should be monitored by means of dedicated techniques. Here, we present and compare two reconstruction methods for spot characterization: single-shot imprints captured via ablation on a poly(methyl methacrylate) sample (PMMA) and pulse profiles retrieved by means of a Hartmann wavefront sensor (WFS). By recording complementary datasets at and nearby the focal plane, we exploit the tomography of the pulse profile along the beam propagation axis, as well as a qualitative and quantitative comparison between these two reconstruction methods.

Impact of the laser spatio-temporal shape on Breit–Wheeler pair production

The forthcoming generation of multi-petawatt lasers opens the way to abundant pair production by the nonlinear Breit–Wheeler process, i.e. the decay of a photon into an electron–positron pair inside an intense laser field. In this paper we explore the optimal conditions for Breit–Wheeler pair production in the head-on collision of a laser pulse with gamma photons. The role of the laser peak intensity versus the focal spot size and shape is examined keeping a constant laser energy to match experimental constraints. A simple model for the soft-shower case, where most pairs originate from the decay of the initial gamma photons, is derived. This approach provides us with a semi-analytical model for more complex situations involving either Gaussian or Laguerre–Gauss (LG) laser beams. We then explore the influence of the order of the LG beams on pair creation. Finally we obtain the result that, above a given threshold, a larger spot size (or a higher order in the case of LG laser beams) is more favorable than a higher peak intensity. Our results match very well with three-dimensional particle-in-cell simulations and can be used to guide upcoming experimental campaigns.

Single-pass cutting of glass with a curved edge using ultrafast curving bessel beams and oblong airy beams

Single-pass cutting of glass substrates with a curved edge is demonstrated using ultrafast curving Bessel and Airy beams, and the advantages of each beam are considered. To achieve successful cutting using the curving Bessel beam, crack directionality is controlled to be perpendicular to the cut by modifying the beam’s spectrum, and a flat-top intensity profile is used to increase consistency. When cutting using Airy beams, a modified beam called an oblong Airy beam is used, which has an oblong focal-spot shape, flat-top intensity profile, and increased contrast between the focal spot and sidelobes as compared to a Gaussian Airy beam. In both cases, the beams’ phase profiles are chosen to maximize edge curvature for a specific sample thickness. Cutting of 500 μm thick glasses in a single laser pass with a high (>10 μm) pitch between laser shots is demonstrated.

Investigation of pixel scale calibration on the Elekta iView electronic portal imager.

This study investigated the variation in electronic portal imager pixel scale at the isocenter plane for Elekta Agility linear accelerators. An in‐house MATLAB script was written to process and calculate the pixel scale based on a metal calibration plate supplied by Elekta. Eight pixel plates were compared and found to have manufacturing tolerances within 0.1 mm of nominal dimensions. The impact of these variations on pixel scale factor was negligible, and plates could be used interchangeably. Uncertainties from other parameters such as source‐to‐surface distance and user variability summed to a combined uncertainty of 0.0003 mm/pixel, compared to a pixel scale range of 0.003 mm/pixel measured across 10 machines. Most of the inter‐machine variation was shown to be attributable to differences in source‐to‐panel distance. Other factors such as focal spot size and shape, electronic portal imager manufacturing consistency, panel sag, and setup errors may account for the residual variation. Individual characterization of machine and imaging panel pixel scale factors is important to ensure accurate geometric information is derived from electronic portal images, which is critical where the portal imager is used for multi‐leaf collimator calibration or other clinical tasks.

Proposing a novel graphical method to determine effective bremsstrahlung focal spot size and shape of the therapeutic beam from a linear accelerator in radiation therapy

The purpose of this study is to introduce and demonstrate a novel graphical method to determine effective bremsstrahlung focal spot size and shape of the therapeutic beam from a linear accelerator. The energy distribution within the beam spot allows in determining effective bremsstrahlung size and shape of beam spot. The transverse and radial dose profiles were measured for a range of field sizes in an isocentric setup. The Length of direct focal region (LDFR) on either side of profiles were determined through the de-convolution of dose profile. The graph plotted for LDFR versus field size helps in determining properties of beam spot. The dimensions of FWHM of effective bremsstrahlung focal spot were found elliptical in nature close to the order of 1 mm. This method allows determination of FWHM of the effective bremsstrahlung focal spot that fairly falls within the range of dimension of FWHM of beamspot published in literature.

Characterization of x-ray focal spots using a rotating edge.

Purpose: The focal spot size and shape of an x-ray system are critical factors to the spatial resolution. Conventional approaches to characterizing the focal spot use specialized tools that usually require careful calibration. We propose an alternative to characterize the x-ray source's focal spot, simply using a rotating edge and flat-panel detector. Methods: An edge is moved to the beam axis, and an edge spread function (ESF) is obtained at a specific angle. Taking the derivative of the ESF provides the line spread function, which is the Radon transform of the focal spot in the direction parallel to the edge. By rotating the edge about the beam axis for 360deg, we obtain a complete Radon transform, which is used for reconstructing the focal spot. We conducted a study on a clinical C-arm system with three focal spot sizes (0.3, 0.6, and 1.0mm nominal size), then compared the focal spot imaged using the proposed method against the conventional pinhole approach. The full width at half maximum (FWHM) of the focal spots along the width and height of the focal spot were used for quantitative comparisons. Results: Using the pinhole method as ground truth, the proposed method accurately characterized the focal spot shapes and sizes. Quantitatively, the FWHM widths were 0.37, 0.65, and 1.14mm for the pinhole method and 0.33, 0.60, and 1.15mm for the proposed method for the 0.3, 0.6, and 1.0mm nominal focal spots, respectively. Similar levels of agreement were found for the FWHM heights. Conclusions: The method uses a rotating edge to characterize the focal spot and could be automated in the future using a system's built-in collimator. The method could be included as part of quality assurance tests of image quality and tube health.

Evaluation of carbon nanotube x-ray source array for stationary head computed tomography.

Stationary computed tomography (s-CT) conceptually offers several advantages over existing rotating gantry-based CT. Over the last 40yr, s-CT has been investigated using different technological approaches. We are developing a s-CT system specifically for head/brain imaging using carbon nanotube (CNT)-based field emission x-ray source array technology. The noncircular geometry requires different assessment approaches as compared to circular geometries. The purpose of the present study is to investigate whether the CNT source array meets the requirements for stationary head CT (s-HCT). Multiple prototype CNT x-ray source arrays were manufactured based on the system requirements obtained from simulation. Source characterization was performed using a benchtop setup consisting of an x-ray source array with 45 distributed focal spots, each operating at 120kVp, and an electronic control system (ECS) for high speed control of the x-ray output from individual focal spots. Due to the forward-angled geometry of the linear anode, the projected focal spot shape is expected to vary at wide angle views. A pinhole method was implemented to determine the effective focal spot size (FSS) in the imaging plane at a range of angular viewpoints with a flat panel detector. The output spectrum and half value layer (HVL) were also evaluated for a range of viewing angles to characterize the beam quality across the fan-beam. Dosimetry was performed on a simulated scan to evaluate total exposure. The prototype CNT x-ray source array demonstrated adequate specifications for a s-HCT imaging machine. The source array was operated at 120kVp with long-term stability over a full year of regular laboratory use. Multiple cathode current measurements were used to confirm submicrosecond accuracy with regards to exposure time and subsequently dose control. All 45 focal spots were measured with an average value of 1.26 (±0.04) mm×1.21 (±0.03)mm (equivalent to IEC 1,0). The x-ray spectrum was found to be appropriately filtered based on sources used in existing rotary CT systems. A stable and reliable output of 0.04mAs per emitter and a resulting dose of 0.015mGy per projection were observed over several months of rigorous phantom imaging. Dose per projection was regulated by the ECS and measured with ±0.5% tolerance. The CNT x-ray source array was found to meet the requirements for the proposed stationary head CT scanner, with regard to FSS, beam quality, and dose precision. The remaining challenges are related to the overall system design of a nonrotating CT scanner with distributed sources. The next phase of the project will incorporate multiple CNT source arrays with multirow detectors in a proof-of-concept study and analysis of a fully functional s-HCT system.

X-ray image quality and system exposure parameters for a hybrid Angio-MR system

This study investigates the exposure parameters and required x-ray tube output when performing neurological procedures on a hybrid Angio-MR concept system proposed by Siemens Healthineers. The x-ray part of this system uses a longer source to detector distance than conventional (C-arm) systems and will have a fixed amount of filtration. Additionally, as the x-ray source is situated inside a magnetic field, the focal spot size and shape may be slightly distorted. In order to compare the Angio-MR system to a typical C-arm system, the exposure parameters of 60 thrombectomy procedures, performed in our hospital over the course of one year, were investigated in detail and a set of median values was determined. An analytical simulation platform was then developed to calculate the required tube voltage, tube current and pulse length to reach similar spatial frequency dependent signal difference to noise ratio (SDNR(u)) values as a conventional C-arm angiography system. These simulations were performed for a variety of focal spot sizes for the Angio-MR system. Results show that a standard current x-ray tube has sufficient power to reach similar SDNR(u) values as obtained in a conventional system if the focal spot size between both systems is comparable.