Beam Diameter Measurements Research Articles

Energy dependence of x‐ray beam size produced by polycapillary x‐ray optics

AbstractIn this work, we studied the x‐ray energy dependence of x‐ray beam diameter focused by polycapillary optics. A quantitative beam diameter–energy relation enables more accurate estimation of the element‐specific interrogation area of a sample using the compositional maps produced by a micro‐XRF system. This improves upon our ability to visualize individual beam‐diameter sized mineral grains and in turn directly benefits Planetary Instrument for X‐ray Lithochemistry (PIXL) analyses of martian soil in addition to benefitting other micro‐focused x‐ray fluorescence (XRF) systems. The spatial distribution of an array of characteristic XRF emission lines was measured by sampling via a knife‐edge approach with small motor stepping of the beam across target edges. Data taken as part of this effort, from the Planetary Flight Model (PFM), were limited to only seven beam energies corresponding to the elements Ni, Cu, Se, Ta, Au, Ti and Ba. Hence, we conducted additional analysis using JPL's lab‐based breadboard (LBB) micro‐XRF system, a system that emulates PIXL's functionality where we measured beam diameter corresponding to 18 elements: Na, Mg, Al, Si, Cl, Ca, Ti, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, Se, Sr and Mo. The experimental results were also compared with Monte Carlo simulations. The beam diameter (y)–energy (x) relation that we obtained for LBB was y = 185.79 exp(−0.078x) whose exponential component was then used to get a more accurate relation for the PFM even with the limited data set: y = 227.53 exp(−0.078x). The difference in the two coefficients for the PFM and LBB stems mainly from the difference in the polycapillary optic design, and this work establishes x‐ray beam diameter versus energy relation quantitatively for both the systems.

Electron beam broadening in electron-transparent samples at low electron energies.

Scanning transmission electron microscopy (STEM) at low primary electron energies has received increasing attention in recent years because knock-on damage can be avoided and high contrast for weakly scattering materials is obtained. However, the broadening of the electron beam in the sample is pronounced at low electron energies, which degrades resolution and limits the maximum specimen thickness. In this work, we have studied electron beam broadening in materials with atomic numbers Z between 10 and 32 (MgO, Si, SrTiO3 , Ge) and thicknesses up to 900 nm. Beam broadening is directly measured using a multisegmented STEM detector installed in a scanning electron microscope at electron energies between 15 and 30 keV. For experimental reasons, the electron beam diameter is defined to contain only 68% of the total intensity instead of the commonly used 90% of the total beam intensity. The measured beam diameters can be well described with calculated ones based on a recently published model by Gauvin and Rudinsky. Using the concept of anomalous diffusion the Hurst exponent H is introduced that varies between 0.5 and 1 for different scattering regimes depending on t/Λel with the specimen thickness t and the elastic mean free path length Λel . The calculations also depend on the fraction of the beam intensity that defines the electron beam diameter. A Hurst exponent H of 1 is characteristic for the ballistic scattering regime with t/Λel → 0 and can be excluded for the experimental conditions of our study with 6 ≦ t/Λel ≦ 30. We deduced H = 0.75 from measured beam diameters which is larger than H = 0.5 that is expected under diffusion conditions. The deviation towards larger H values can be rationalised by our definition of electron diameter that contains only 68% of the total beam intensity and requires therefore larger sample thicknesses before the diffusion regime is reached. Our results clearly deviate from previous analytical approaches to describe beam broadening (Goldstein etal., Reed, Williams etal., Kohl and Reimer). Measured beam diameters are compared with simulated ones, which are obtained by solving the electron transport equation. This approach is advantageous compared to the commonly used Monte Carlo simulations because it is an exact solution of the electron transport equation and requires less computer time. Simulated beam diameter agree well with the experimental data and yield H = 0.80. LAY DESCRIPTION: In scanning transmission electron microscopy (STEM), a focused electron beam is scanned over an electron-transparent sample and an image is formed by detecting the intensity of the transmitted electrons by a STEM detector. STEM resolution is ultimately limited by the electron beam diameter and can be better than 0.1nm for the best microscopes. However, the electron-beam diameter increases with increasing specimen thickness because electrons are scattered by the interaction of the specimen material and electrons. Electron scattering leads to a change of the electron propagation direction and reduces focusing of the electron beam. The associated electron-beam broadening degrades the lateral resolution of STEM and generally limits the maximum specimen thickness that can be imaged with good resolution. STEM is up to now mainly performed at high electron energies of 80 keV and above. Lower electron energies are beneficial for the study of weakly scattering and radiation-sensitive materials but electron beam broadening becomes more pronounced with decreasing electron energies. Knowledge of beam broadening is therefore particularly important for the interpretation of STEM images that are taken with low-energy electrons. In this work we have studied electron-beam broadening in different materials with thicknesses up to 900nm at low electron energies between 15 and 30keV. Beam broadening is directly measured with a newly developed technique. We compare measured beam diameters with different models on beam broadening from literature and find that only a recently published model is well suited to describe the experimental results under our experimental conditions. In addition, beam broadening is simulated by modelling electron propagation in the specimen. The simulation results agree well with the measured beam diameters.

The effect of electron transport on the characterization of x-ray free-electron laser pulses via ablation

The spatial intensity distribution of x-ray free-electron laser (XFEL) pulses in-focus is commonly characterized by performing ablative imprints in thin gold films on silica substrates. In many cases, the range of the electrons generated in the gold by x-ray absorption far exceeds the beam size, and so, it is not clear if the results of imprint studies are compromised by electron transport. Thermal conduction could further modify the energy density profile in the material. We used a combination of Monte-Carlo transport and continuum models to quantify the accuracy of the imprint method for characterizing XFEL beam profiles. We found that for x-ray energies in the range of 1 to 10 keV, the actual and the measured beam diameters agree within 12% or better for beam diameters between 0.1 and 1 μm.

Beam Diameter Reduction by Optimization of an Extraction Condition in a Compact Ion Microbeam System

A several hundred keV class compact proton microbeam system was developed as a prototype of a 1 MeV compact microbeam system to be used in micro-fabrication and micro-analyses. Optimization of an extraction condition was performed to increase demagnification and to achieve a beam diameter of approximately 1μm. The beam diameter measurement showed that a diameter of 1.8μm was obtained. This indicates that the compact microbeam system is a feasible alternative to a MeV class conventional large accelerator system.

Thermal lensing in Nd:YVO4 laser with in-band pumping at 914 nm

Thermal lensing in an Nd:YVO4 laser system operating at 1064 nm with in-band pumping at 914 nm was characterized. The focal length of the thermal lens in the crystal was calculated using ABCD matrix formalism from the experimental data of the output beam diameter measurements made at different output power levels. The determined focal lengths of thermal lens were as strong as 4.4 diopters at 3.5 W of output power. The experimental results agree well with the finite element analysis of the developed laser system. A numerical comparison of the thermal lensing effect with 914-, 888-, 880-nm pumping, and with a standard 808-nm pumping was also made, demonstrating effective reduction of thermal lensing up to 2.1 times.

Fluorescence-based knife-edge beam diameter measurement to characterize X-ray beam profiles in reflection geometry

The diameter of an X-ray beam was determined, using the knife-edge technique, widely applied for beam profiling, by taking advantage of the fluorescence emission generated by the X-ray beam. The knife-edge has to be appropriate to the configuration of the device, in our case a double-material target made of plastic and cardboard was scanned in a transversal plane compared to the beam propagation direction. Along the scanning axis, for each position, the intensity of the Kα line of chlorine was recorded. The first derivative of the intensity evolution as a function of the edge position, fitted by a Gaussian function, makes it possible to obtain the beam diameter along the scan direction. We measured a slightly elliptic diameter close to 3mm. In this note we underline the significance of the knife-edge technique which represents a useful tool, easy to be set up, to control X-ray beam dimensions in portable devices often routinely used by non-specialists.

Energy scaling of a tunable terahertz parametric oscillator with a surface emitted configuration

A high-energy THz-wave output has been experimentally demonstrated with a terahertz-wave parametric oscillator based on a surface-emitted configuration. Through optimizing the cavity length and pump beam size, the maximum THz-wave output energy of 854 nJ pulse−1 was obtained at 1.62 THz. The conversion efficiency was 0.57 × 10–5, corresponding to the photon conversion efficiency of 0.099%. The THz beam profile was measured with a THz imager, which had a Gaussian profile. The measured beam diameter sizes were 423 μm and 258 μm in the horizontal and vertical directions, respectively. A wide tunable range from 0.75 to 2.81 THz was realized.

Improving the quantification at high spatial resolution using a field emission electron microprobe

The capabilities of field emitter electron microprobes to perform quantitative measurements at high spatial resolution are discussed. Using Fe-Cr-C particles in a bearing steel (SAE 52100) as example, a generic procedure was established to find the optimal analytical conditions (beam energy, beam current and acquisition time). The influence of these parameters on the accuracy, precision and spatial resolution was evaluated using experimental measurements and Monte Carlo simulations. A quantification procedure was developed for soft X-ray lines, taking into account the overlap of high order X-ray lines and background anomalies. The accuracy of Ka- and La-lines was verified using reference materials. A relationship between experimental and simulated X-ray intensities was determined to evaluate the measurement precision. The spatial resolution of each X-ray line was calculated from the simulated lateral and depth X-ray intensity distribution using simulations integrating experimentally measured beam diameters. The optimal analytical conditions for the studied sample were found to be 5 keV, 10 nA and 10 s acquisition time. Further specialized techniques to improve the spatial resolution are presented: focused ion beam preparation of thin lamella and wedge, and Monte Carlo based reconstruction. The feasibility of the latter to quantify features smaller than the X-ray emission volume was demonstrated.

Electron beam density study using a portable slit imaging system at the Shanghai Electron Beam Ion Trap

In this work, a portable slit imaging system is developed to study both the electron beam diameter and the profile of the newly developed Shanghai Electron Beam Ion Trap (Shanghai EBIT). Images are detected by a charge coupled device (CCD) sensitive to both X rays and longer wavelength photons (up to visible). Large scale ray tracings were conducted for correcting the image broadening effects caused by the finite slit width and the finite width of the CCD pixels. A numerical de-convolution method was developed to analyse and reconstruct the electron beam density distribution in the EBIT. As an example of the measured beam diameter and current density, the FWHM (full width at half maximum) diameter of the electron beam at 81 keV and 120 mA is found to be 76.2 μm and the density 2.00 × 103 A·cm−2, under a magnetic field of 3 T, including all corrections.

Correction to BrainSCAN central axis dose calculations for 6-MV photon beams to lung with lateral electron disequilibrium

Purpose: To develop and evaluate a correction method for lateral electron disequilibrium and tissue inhomogeneities in lung tissues applicable to the BrainSCAN treatment planning system. Methods and Materials: Four noncoplanar 6-MV photon beams with different beam diameters were applied to the right lung of a thorax phantom. The measured/calculated dose value ratio was evaluated as a function of a parameter that describes the degree of the lateral electron disequilibrium based on the primary dose. Results: The dose ratio showed a clearcut linear dependency on the disequilibrium parameter. Applying the proposed correction method, only minor differences between the measured and calculated doses were found for lesions >1 cm. However, for lesions Conclusion: The data have indicated a relevant magnitude of the correction factor only for lung lesions

Small Gaussian laser beam diameter measurement using a quadrant photodiode

A method that uses the quadrant photodiode has been shown to be relatively inexpensive and robust in measuring Gaussian laser beam diameters in two axes. This approach requires neither component rotation nor precision alignment, and it facilitates integration of Gaussian laser beam diameter measurement with laser beam tracking in instruments. The physical gap between sensors in the quadrant photodiode, however, limits laser beam diameter measurements to those in the millimeter range. Here, we describe a modified approach to measure Gaussian laser beam diameters that are significantly smaller.

In situ measurement of absorption in high-power interferometers by using beam diameter measurements

We present a simple technique to make in situ measurements of the absorption in the optics of high-power laser interferometers. The measurement is particularly useful to those commissioning large-scale high power optical systems.

Gaussian laser beam diameter measurement using a quadrant photodiode

Gaussian laser beam diameters are typically measured using knife-edges or gratings. Both require precise alignment with the photodiode placed after them from the laser source. In addition, beam diameter measurement in two orthogonal axes is only possible via rotation of the knife-edge or grating. Here, we report a novel measurement method that uses a relatively inexpensive and robust quadrant photodiode to circumvent the alignment requirement as well as allow two axes laser beam diameter measurement without rotation of any component. The theoretical basis of this approach is described and experimental results using it are presented. This method portends possibilities in the design of instrumentation that integrates Gaussian laser beam diameter measurement with laser beam tracking in a compact manner using fewer components.

Measurement of a broad range of Gaussian laser beam diameters using various periodic and aperiodic rulings

A novel analytical approach is proposed for an accurate estimation of a broad range of Gaussian laser beam diameters. The new approach, based on the Fourier transform and the convolution operations, is used to study the performance of most recently proposed periodic and aperiodic rulings. Further, for applications that require extremely small beam diameter measurements, a new Ronchi-like ruling is proposed; while for applications requiring large beam diameters measurements, various aperiodic non-Ronchi rulings are proposed. Furthermore, for spot-size measurement applications, which range from very small to very large beam diameters, a new single aperiodic exponential ruling is proposed. This new ruling eliminates the necessity of using a large number of rulings for measuring a broad range of beam diameters.

Accurate measurement of small Gaussian laser beam diameters using various rulings

A new analytical approach based on Fourier transform and convolution operations for measuring very small Gaussian laser beam diameters is proposed. In addition, a comparative study of various recently reported rulings is presented. A general rule of thumb approach to select a ruling for measuring small beam diameters is demonstrated. Finally, a new Ronchi ruling capable of measuring extremely small beam radius is proposed.

High-efficiency optical compression of Ti:sapphire laser pulses at 800 nm using a silver-coated hollow fiber

A 50 cm silver coated hollow fiber with inner diameter of 250 μm and filled with argon has been used to compress optical pulses from a Ti:sapphire laser at 800 nm. Input pulses with energy of 250 μJ and duration of 110 fs were used and compressed pulses with energy of 220 μJ and duration of 20 fs were generated by using a prism compressor. Numerical and experimental results are compared. There is good agreement between the measured beam diameters of the hollow-fiber output pulse and the calculated values obtained from propagation of the HE11 mode into free space. For comparison, a similar uncoated fused-silica hollow fiber was also used to obtain 20 fs compressed pulses with an energy of 190 μJ.

The influence of sunshape on the DLR Solar Furnace beam

The circumsolar ratio CSR is often used as a simple description of the relevant solar energy feature of the solar brightness distribution, known as sunshape. The variation of the CSR can affect the performance of solar concentrators. DLR has conducted sunshape studies since the beginning of the design phase of the DLR Solar Furnace in 1992. In addition, in 1996 a mobile sunshape measurement system was developed with which many CSR measurements have been performed since then. These investigations are still going on for statistical purposes in parallel with the operation of the solar furnace. This work shows new and unique data of simultaneous sunshape records and solar furnace beam diameter measurements. For narrow sun conditions with a CSR <1% the solar furnace beam has a diameter of less than 13 cm. Atmospheric conditions with a higher forward scattering can cause the CSR to exceed 10%, sometimes even above 40%. In the latter case the focal beam measurement showed a beam diameter of more than 16 cm. The increase of the focal diameter turned out to be linear with respect to CSR variation. The measured sunshapes were introduced into the ray-tracing model OPTEC, built for solar furnace and heliostat field simulation. The model results for the DLR Solar Furnace flux maps were compared to the measurements. The model does not show the same linear trend for increasing CSR, but the deviation is not too pronounced. The influence of CSR on the focal spot size leads to a nonlinear decrease with direct normal irradiance of the power collected by a predesigned receiver aperture. Depending on the aperture size, an additional decrease of the order of 10–15% will be encountered under higher CSR conditions.

Beam propagation (M^2) measurement made as easy as it gets: the four-cuts method

Tolerance analysis shows that an efficient M(2) measurement plan is a first cut (beam diameter measurement) at 0.5-2.0 Rayleigh ranges to one side of the waist, which is matched by interpolation between second and third cuts to the opposite side. The waist is measured by a fourth cut halfway between the matched diameters, yielding an easy two-parameter curve fit for M(2).

Optimization of the electron-beam transport in the Israeli tandem FEL

Optimization of electron-beam transport in FEL devices is very important for efficient operation. A new simulation code for electron-beam transport in FELs was developed recently at Tel-Aviv University (TAU) in order to optimize the electron-beam transport. Equations of motion of an electron in the presence of magnetic and electric fields are solved numerically for various magnetic elements. The results of the simulation provided guidelines for setting appropriate currents on quadrupole magnets along the beam line. A comparison between calculated and measured beam diameters is provided.

Increasing the accuracy of laser beam diameter measurement

A procedure for determining the diameter of a focused laser beam based on the measurement of laser damage to a thin film is described. This method has several advantages over the spatial methods of using calibrated diaphragms and the measurement of relative power density distribution with subapertures.