Lateral Intensity Distribution Research Articles

Spinal deformity measurement using a low-density flexible array ultrasound transducer: A feasibility study with phantoms

Spinal deformities assessment using 3D ultrasound scanning has limitations in fitting onto different back surface contour as well as fitting within the gaps between subject and their spinal brace during bracing assessments. The study proposed a flexible array ultrasound transducer to overcome these limitations.The results demonstrated the feasibility of spinal deformity assessments with a flexible ultrasound array when arranged in four shapes, namely Linear, Concave, Convex, and S-shaped. For comparisons of imaging performance on spinous process using the four shapes, Convex and S-shaped transducer showed a depth dependence and lateral location dependence of the lateral intensity distribution of spinous process, respectively. S-shaped transducer had the least accurate prediction of the location of spinous process, with measurement error of 4.8 ​± ​3.2 ​mm, it also showed poorer prediction on spinal curvature measurements. This is suggested to be due to the asymmetrical distortion to the spinous process due to the lateral location dependence of the image. However, the coronal curve prediction of spine phantom performed well with R-squared values of >0.97 in all transducer shapes.The results of this study paved the way for further investigation on the improvement of image quality and measurement accuracy under different shapes for the flexible array, mechanism of dynamic shape change during the scanning to fit different body contour, as well as extension from 1D to 2D flexible array.

Identification and visualisation of microplastics/ nanoplastics by Raman imaging (ii): Smaller than the diffraction limit of laser?

We recently reported (Sobhani et al., 2020) that when a confocal Raman microscope imaged a nanoplastic with the diameter of 100 nm, the imaging lateral size was 300–400 nm, due to the diffraction limit of the laser spot. In this study, we examine the lateral intensity distribution of the Raman signal emitted by nanoplastics (diameters ranging ∼30–600 nm) within the excitation laser spot. We find that the Raman emission intensity, similar to the excitation power density distributed within a laser spot, also follows a lateral Gaussian distribution. To image and visualise individual nanoplastics, we (i) decrease the mapping pixel size, in a hope to generate an image with high-resolution and simultaneously to pick up items from the “blind point”. We can then either (ii) offset the colour to intentionally image only the high-intensity portion of the Raman signal (emitted from the centre of the laser spot), to localise the exact position of the nanoplastic; or (iii) categorise the imaged nanoplastics to different groups via their Raman intensity, to simultaneously and separately visualise large nanoplastics/strong Raman signals, medium nanoplastics and small nanoplastics, in an effort to avoid the shielding and overlooking of weak signals. We (iv) also cross-check multi-images simultaneously mapped at two or three characteristic peaks via either a logic-OR or a logic-AND algorithm. Thus the imaging uncertainty can be significantly reduced from a statistical point of view.

Non-ring perfect optical vortices with p-th order symmetry generated using composite diffractive optical elements

A “perfect” optical vortex (POV), a ring-shaped singular beam whose diameter does not scale with its topological charge, is now being extensively studied owing to its important practical applications ranging from optical trapping and manipulation of microscale objects to laser material processing with structured beams. At the same time, the ability to shape the intensity distribution of the POV in a controlled manner is of crucial importance for the mentioned applications; however, only circular- or elliptical-shaped POVs were demonstrated so far. Here, we propose and design pure phase diffractive optical elements (DOEs) with an optimized composite transmission function allowing high-efficient generation of non-ring-shaped POVs with p-th order symmetry. We demonstrate the generation of POVs with the desired topological charge, transverse size, and variable “polygon-like” lateral intensity distribution. Our experimental results are in good agreement with theoretical and simulation predictions. The proposed DOEs can be characterized by high conversion efficiency (more than 60%), thus substantiating their applicability for high-performing optical manipulation and advanced laser nanopatterning.

Focal-space intensity distribution of an incoherent light source beam behind a focusing lens

Based on ray-tracing technique and vectorial diffraction theory, focal-space intensity distribution of an incoherent light source (ILS) beam after a focusing lens is theoretically described. We investigated the influence of different parameters (the source size, wavelength, focusing lens type, etc.) on the focal-space intensity distribution. For a point source beam, a hyperbolic lens provides 50-fold better axial intensity concentration than a spherical lens of the same focal length (10 mm). Under a chromatic hyperbolic lens, broadening of the spectral bandwidth induces an elongation of the axial intensity distribution, which however is not obvious for spherical lens focusing since the spectral broadening-induced elongation is partly overlapped with that induced by the spherical aberration. Increasing the source size will broaden the lateral intensity distribution, which first looks like a Gaussian and then evolves into a hat top. The axial and/or lateral extension of focal-space intensity would be beneficial to applications where volume heating rather than point heating is required. For example, in an ILS-excited thermal lens microscopy, extension of the intensity distribution brings a quadratic increase of photothermal signal of an ensemble sample but a linear increase of the signal for a point-like target.

Intensity distribution of diffractive axicon with the optical angular spectrum theory

Diffractive axicon is lightweight and easy to be manufactured, it is also efficiently used to produce diffraction-free Bessel beam. But, deducing its expression of the field distribution of light is difficult in theory and the theoretical equation expression has approximation by using the Huygen-Fresnel diffraction integral. Here, the rigorous optical angular spectrum theory that follows the Helmholtz equation is used. The propagation theory of angular-spectrum with fewer approximation, will result in more accurate results. A mathematical model to analyze the field distribution of light of the diffractive axicon is set up. The diffraction intensity distribution of the diffractive axicon with the monochromatic Gaussian beam illumination and multicolor illumination is numerically calculated and discussed. The results of numerical calculation with a monochromatic laser source show that not all the intensity distribution in the focal depth of field has the characteristics of the diffraction-free Bessel beam, and the on-axis diffraction intensity shows direct correlation of the lateral intensity distribution of the incident waves and the period of the diffractive axicon. The extended depth of field of the diffractive axicon with multicolor illumination is increasing as the wavelength reducing. It is expected that our study can provide very useful information for analyzing the diffractive axicon which exists in the optical trapping systems and laser-processing applications and imaging systems.

Imaging properties of a nonlinear multilayered superlens

Imaging properties of a metal/nonlinear dielectric structure with nonequal thickness layers as a superlens have been investigated by using the optical transfer function (OTF) and the lateral intensity distributions at the imaging plane for a given object. It has been shown that even when permittivity of the metal and nonlinear dielectric are mismatched, both modulation transfer function (MTF) and phase transfer function (PTF) show high cutoff frequency at optical wavelength. This is the case of a superlens and also shows a good improvement rather than a metal/linear dielectric superlens.

Holographic fluorescence mapping using space-division matching method

Three-dimensional mapping of fluorescence light sources was performed by using self-interference digital holography. The positions of the sources were quantitatively determined by using Gaussian fitting of the axial and lateral intensity distributions obtained from diffraction calculations through position calibration from the observation space to the sample space. A space-division matching method was developed to perform the mapping of many fluorescence light sources, in this experiment, 500 nm fluorescent nanoparticles fixed in gelatin. A fluorescence digital holographic microscope having a 60× objective lens with a numerical aperture of 1.25 detected 13 fluorescence light sources in a measurable region with a radius of ∼20μm and a height of ∼5μm. It was found that the measurable region had a conical shape resulting from the overlap between two beams.

The influence of the atmospheric refractive index on radioXmaxmeasurements of air showers

The refractive index of the atmosphere, which is n ≈ 1:0003 at sea level, varies with altitude and with local temperature, pressure and humidity. When performing radio measurements of air showers, natural variations in n will change the radio lateral intensity distribution, by changing the Cherenkov angle. Using CoREAS simulations, we have evaluated the systematic error on measurements of the shower maximum X max due to variations in n . It was found that a 10% increase in refractivity ( n – 1) leads to an underestimation of X max between 8 and 22 g/cm 2 for proton-induced showers at zenith angles from 15 to 45 degrees, respectively.

A micro-pattern gaseous detector for beam monitoring in ion-therapy

A micro-pattern gaseous detector based on gas electron multiplier technology (GEM detector) was developed as a new transmission beam monitor for charged-particle therapy to obtain real-time information about the parameters of a therapeutic beam. Feasibility tests for the GEM detector were performed using an 80-MeV proton beam to evaluate the lateral intensity distributions of a pencil beam and the dose delivered to a target. The beam intensity distributions measured with the GEM detector were in good agreement with those measured with an imaging plate while the charge output from the GEM detector was in proportion to that of a reference dose monitor of an ionization chamber design. These experimental results showed that the GEM detector can be used not only as a beam monitor for the position and two-dimensional intensity distribution but also as a dose monitor. Thus, it is possible to simultaneously measure these beam parameters for beam control in charged-particle therapy using a single GEM-based transmission monitor.

Line-field parallel swept source MHz OCT for structural and functional retinal imaging.

We demonstrate three-dimensional structural and functional retinal imaging with line-field parallel swept source imaging (LPSI) at acquisition speeds of up to 1 MHz equivalent A-scan rate with sensitivity better than 93.5 dB at a central wavelength of 840 nm. The results demonstrate competitive sensitivity, speed, image contrast and penetration depth when compared to conventional point scanning OCT. LPSI allows high-speed retinal imaging of function and morphology with commercially available components. We further demonstrate a method that mitigates the effect of the lateral Gaussian intensity distribution across the line focus and demonstrate and discuss the feasibility of high-speed optical angiography for visualization of the retinal microcirculation.

Development of spot size and lateral intensity distribution generated by exponential, logarithmic, and linear axicons.

Axicons are known to produce a nearly Bessel beam transverse intensity distribution. It has been previously recognized that linear axicons and logarithmic axicons with a predefined distant depth of field (DOF) and no blocking present a development region characterized by an enlarged central spot size. In this paper, we aim to obtain a better insight on the formation of lateral light distribution in this development region. We also examine the spot size and transverse intensity distribution of the recently developed exponential axicon. We present experiments and detailed nonparaxial numerical simulations for a plane wave passing through these optical elements and show that the lateral intensity distribution they generate differs from that of a Bessel beam for a significant part of their DOF. This anomaly/irregularity in the formation of nondiffracting Bessel beams has to be taken into account in applications of these axicons, such as imaging or optical trapping.

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.

Characterization of the primary X-ray source of an XPS microprobe Quantum 2000

The outstanding design feature of an XPS microprobe Quantum 2000 is the double focussing ellipsoidally shaped quartz monochromator of the X-ray source. This device monochromatizes the Alkα radiation and refocuses the X-rays from the Al anode to the sample surface. This way, on one hand a variation of the diameter of the X-ray generating electron beam allows to vary the X-ray beam diameter on the sample surface. On the other hand a scanning of the electron beam across the Al anode scans the X-ray beam across the sample surface.The X-ray source was characterized in detail. The lateral dependency of the primary X-ray intensity and the peaks FWHM were measured as function of the position within the electrostatically rasterable scan area. Additionally, the focussing quality of the monochromator was determined. Therefore the lateral intensity distribution within the primary X-ray beam was estimated far below the 1% intensity level.

Binary diffractive mask as a beam-shaping element for direct application in large-angle gray scale element fabrication

The capability of binary gray scale masks in generating beams with a desired lateral intensity profile is extensively studied in order to fabricate large-angle microprisms. Using a recently introduced technique, some samples based on pulsewidth modulation are designed, so that the pulsewidth is changed with different linear rates from a completely clear to a fully dark slit, which results in a different number of gray steps. Then, the influence of the rate on turning an incident plane wave into beams with different specially linear lateral intensity distributions was studied by simulation, experiment, and fabrication of a large-angle microprism. Further, it was shown that the width of the first slit and the increment of gray level have an effective impact on the slope and smoothness of the generated linear intensity profile across the beam. Simulation results are completely verified by experimental data and the fabricated linear gray scale element.

Generating of quadratic gray scale beam profile using binary gray scale masks

Generating beams with a desired quadratic lateral intensity distribution using 1D binary masks was analyzed, in detail. Effect of width of the first bar as well as the gray scale increment rate on the generated shaped beam was examined. It is shown that increasing the gray scale rate produces smoother and broaden profile. Besides, it was demonstrated that width of the first bar has great impact on the generated profile, so by increasing the width, the generated profile becomes sharper. Theoretical results are confirmed by experiment, as well.

Electromagnetic Analysis of Apodized Annular-Aperture Logarithmic Axicons in Wave Imaging Systems

An apodized annular-aperture logarithmic axicon (3ALA) can be applied potentially to improve imaging resolution in quasi-optical and/or millimeter wave imaging systems, due to its property of long depth of field (DOF). Electromagnetic analyses of forward and backward 3ALAs are conducted respectively at mm- and submm-wavebands. Their lateral and axial intensity distributions are evaluated by rigorous electromagnetic analysis method. And the comparative conclusions are drawn at last in our present work

Turbulence characteristics of flow in a spiral corrugated culvert fitted with baffles and implications for fish passage

Baffles are often used to retrofit culverts to aid in fish passage. The objective of this experimental investigation was to compare the turbulent flow structure inside a full-scale spiral corrugated culvert fitted with sloped- and slotted-weir baffles to available turbulence descriptions for non-baffled culverts. In addition, the turbulent flow structure inside a full-scale culvert was compared to fish passage preferences. Velocity measurements were taken in a 1.83 m-diameter, 12.2 m-long corrugated metal culvert fitted with sloped- and slotted-weir baffles using a Sontek Micro-Acoustic Doppler Velocimeter for flow rates of 0.043, 0.085, 0.113, and 0.198 m 3/s and a culvert slope of 1.14%. Results showed there were only minor differences in the turbulent flow structure created by each baffle type. The most significant differences included higher lateral turbulent intensities on the edges of the jet created by the slotted-weir baffles, and higher turbulent kinetic energies on the left side of the culvert (looking downstream) caused by the sloped-weir baffles. Downstream from a slotted-weir baffle, a reduced velocity and streamwise turbulent intensity zone was found near the left edge of the flow that was similar to that found in the bare culvert. The sloped-weir baffles produced a less pronounced zone near the right edge of the flow. No significant relationships could be found between the turbulence results of this study and biological fish passage tests performed at the same experimental site due to the lack of substantial differences in streamwise and lateral turbulence intensity distributions downstream from the tested baffles.

(Al,In)GaN laser diodes in spectral, spatial, and time domain: near-field measurements and basic simulations

The near-field lateral intensity distribution of 405 nm (Al,In)GaN laser diodes is measured in time and wavelength domain. Spectral properties, relaxation oscillations, and filaments are observed. A thermally induced change of the refractive index profile is found to be the driving force behind changes in the dynamic mode configuration. With rate equations those effects can be described in first approximation.

High quality quasi-Bessel beam generated by round-tip axicon

We study theoretically and experimentally the spatial intensity distribution of the zero-order Bessel beam formed by the axicon which possess a rounded tip. Such a tip generates a refracted beam that interferes with the quasi-Bessel beam created behind the axicon. In turn an undesired intensity modulation occurs that significantly disturbs the unique properties of the quasi-Bessel beam--namely the constant shape of the lateral intensity distribution and the slow variation of the on-axis beam intensity along the beam propagation. We show how the spatial filtration of the beam in the Fourier plane improves this spatial beam distribution and removes the undesired modulation. We use an efficient numerical method based on Hankel transformations to simulate the propagation of the beam behind the axicon and filter. We experimentally measure the intensity distribution of the beam in many lateral planes and subsequently reconstruct the spatial intensity distribution of the beam. Computed and measured beam distributions are compared and the obtained agreement is very good.

Determination of positron beam parameters by various diagnostic techniques

Various diagnostic techniques have been applied at the neutron-induced positron source Munich NEPOMUC in order to determine the positron beam parameters such as intensity, beam shape and energy distribution. The positron beam intensity is determined by the detection of the annihilation radiation of positrons, which annihilate in a movable target. The use of a micro-channel plate (MCP) detector with a CCD-camera allows a direct measurement of the positron beam shape and the lateral resolved intensity distribution. At NEPOMUC a movable MCP-assembly inside the evacuated beam line enables a quick examination of the beam shape during operation. A retarding grid was mounted inside the homogeneous magnetic guiding field in order to determine the distribution of the longitudinal positron momentum, and hence estimate the energy distribution of the positrons.