Axial Range Research Articles

Generation of long-distance stably propagating Bessel beams

We put forward a new optical system, which is composed of an existing axicon doublet and a newly proposed amplitude filter. The axicon doublet consists of a positive axicon and a negative axicon with high and low refractive indices, respectively. The Bessel beam generated by the axicon doublet propagates as far as more than 200 meters, owing to a small refractive index difference between the double axicons. The newly proposed amplitude filter is used to flatten the axial intensity distribution. Numerical results calculated by the complete Rayleigh-Sommerfeld method demonstrate that the generated Bessel beam propagates stably within a very long axial range. The proposed optical system is expected to have practical applications in tracking far-distance moving targets.

Modeling, optimization, and validation of an extended-depth-of-field optical coherence tomography probe based on a mirror tunnel.

The diagnostic capability of high-resolution optical coherence tomography (OCT) may be enhanced by using extended depth-of-field (EDOF) imaging that retains high transverse resolution over long depths. A recently developed mirror-tunnel optical probe design (single-mode fiber to multimode fiber to lens structure) that generates coaxially focused modes has been previously shown to enable EDOF for endoscopic OCT applications. Here, we present ray-tracing optical modeling of this optical configuration, which has the potential to guide performance improvement through optimization. The Huygens wave propagation of the field was traced through probe components with initial lengths. The irradiance along the x-z plane was analyzed, yielding an average full width at half-maximum (FWHM) of 9 µm over a 640 µm DOF (defined as the axial range over which the beam's transverse FWHM is maintained). A custom merit function was then defined, based on the focal region illumination intensity profile that yielded the maximum possible depth having a constrained FWHM size. An orthogonal gradient descent optimization algorithm was then applied using this merit function, using the multimode fiber, spacer, and lens lengths as variables. Optimization resulted in a modeled mean 6 µm FWHM spot diameter over an EDOF of 1 mm. Following optimization, a probe was fabricated, and was validated using a custom-built near-field scanning pinhole beam profiler. The experimental results (6 µm mean FWHM over 800 µm EDOF) showed reasonable correspondence to the simulated predictions, demonstrating the potential utility of optical modeling and optimization for improving EDOF performance in mirror-tunnel endoscopic OCT probes.

Differences in trunk range of motion for various flexibility protocol types, particularly in quarterbacks wearing rib protectors

Summary Background It is unclear how rib protectors may affect trunk mobility in American football players. The purposes of the study were: 1) to determine which flexibility protocol (active-assisted, maximal-speed, self-selected) exhibits the highest range of motion for trunk lateral flexion and axial rotation and 2) to determine the effect of rib protectors (hard-rib and soft-rib protectors and control: compression shirt only) on trunk range of motion. Methods Eleven male participants with competitive quarterback experience were recruited. Participants were instructed to rotate the trunk in the lateral flexion and axial rotation directions during each flexibility protocol and rib protector condition. The lower-thoracic range of motion were measured. Results Two-way repeated measures ANOVA (flexibility protocol by rib protector) demonstrated significant main effect of flexibility protocol for lateral flexion, but not axial rotation. The range of motion during self-selected protocol was significantly greater than maximal-speed protocol by approximately 7° (p = .009). Conclusions Self-selected and maximal-speed protocol produced the highest lateral flexion and axial rotation range of motion, respectively, and can be used to test the influence of rib protectors and potentially other sports equipment on thoraco-lumbar range of motion. Additionally, rib protectors likely do not affect trunk range of motion needed to throw long-distance passes or other movements as performed by football quarterbacks.

3D Particle Localization in Living Cells by Deep Learning

Point spread function engineering techniques have extended the axial range accessible to fluorescence microscopy by simple modifications to the optical path of a microscope. A particularly promising engineered PSF is the double helix PSF (DHPSF), which provides an axial range of over 2 μm. This extended depth allows sub-diffraction localization of point sources in 3D across an axial range approaching the typical thickness of mammalian adherent cells. Thus, DHPSF is not only attractive for PALM-style superresolution experiments but also for tracking small punctate structures in cells. Still, data analysis of DHPSF images presents a challenge because no analytic form of the DHPSF exists. This difficulty has been addressed previously by using heuristic functions for fitting or interpolations of calibration scans of fluorescent beads. However, this approach is limiting for cellular particle tracking applications of DHPSF because of the heterogeneous signal background, high particle densities, and large variation in intensities of the target particles encountered in such experiments. Here, we present a data-driven and fast method based on deep learning (DL) to address these challenges. Specifically, we use the DL approach to analyze DHPSF data without the need to introduce heuristic fitting functions or interpolate calibration scans. We demonstrate the accuracy of the method on localizing simulated data in 3D, and test its efficacy in the presence of noisy, heterogeneous backgrounds. Finally, we localize and track in 3D puncta of human T-cell leukemia virus type 1 (HTLV-1) in live cells and present preliminary data on the mobilities of these particles measured in this noisy environment. This work has been supported by grants from the National Institutes of Health (R01 GM098550 and RO1 GM124279).

Nanometric axial localization of single fluorescent molecules with modulated excitation

Distance measurements are commonly performed by phase detection based on a lock-in strategy. Super-resolution fluorescence microscopy is still striving to perform axial localization but through entirely different strategies. Here we show that an illumination modulation approach can achieve nanometric axial localization precision without compromising the acquisition time, emitter density or lateral localization precision. The excitation pattern is obtained by shifting tilted interference fringes. The molecular localizations are performed by measuring the relative phase between each fluorophore response and the reference modulated excitation pattern. We designed a fast demodulation scheme compatible with the short emission duration of single emitters. This modulated localization microscopy offers a typical axial localization precision of 6.8 nm over the entire field of view and the axial capture range. Furthermore, the interfering pattern being robust to optical aberrations, a nearly uniform axial localization precision enables imaging of biological samples by up to several micrometres in depth. Adapting the amplitude-modulated light detection and ranging approach to super-resolution microscopy offers a typical axial localization precision of 6.8 nm over the entire field of view and the axial capture range, enabling imaging of biological samples by up to several micrometres in depth.

Sensitivity of remote focusing microscopes to magnification mismatch.

Remote focusing (RF) is a technique that greatly extends the aberration-free axial scan range of an optical microscope. To maximise the diffraction limited depth range in an RF system, the magnification of the relay lenses should be such that the pupil planes of the objectives are accurately mapped on to each other. In this paper we study the tolerance of the RF system to magnification mismatch and quantify the amount of residual spherical aberration present at different focusing depths. We observe that small deviations from ideal magnification results in increased amounts of residual spherical aberration terms leading to a reduction in the diffracted limited range. For high-numerical aperture objectives, the simulation predicts a 50% decrease in the diffracted limited range for 1% magnification mismatch. The simulation has been verified against an experimental RF system with ideal and nonideal magnifications. Experimentally confirmed predictions also provide a valuable empirical method of determining when a system is close to the ideal phase matching condition, based on the sign of the spherical aberration on either side of focus.

Age-related gait development in children with autism spectrum disorder

BackgroundA better understanding of gait development and asymmetries in children with autism spectrum disorder (ASD) may improve the development of treatment programs and thus, patient outcomes. Research questionDoes age affect walking kinematics and symmetry in children with ASD? MethodTwenty-nine children (aged 6–14 years old) with mild ASD (level one) were recruited and assigned to one of the three groups based on their ages: 6–8 years (U8), 9–11 years (U11) and 12–14 years (U14). Walking kinematics were captured using an inertia measurement unit system placed bilaterally on participants’ foot, lower leg, upper leg, upper arm, pelvis, and thoracic spine. Joint angles were computed and compared among the age groups. Symmetry angles were used to assess the gait symmetry and were compared among the age groups. ResultsOlder children exhibited less ankle dorsiflexion and knee flexion angles at heel-strike and greater plantarflexion angles at toe-off compared with younger children. In addition, a decreased pelvis and thorax axial rotation range of motion and increased shoulder flexion/extension range of motion were observed for older children. However, no age-related difference in gait symmetry was observed. SignificanceThese findings could suggest that older children with ASD may develop gait kinematics to a more energy-efficient walking pattern.

Flow physics of highly loaded tandem compressor cascade with non-axisymmetric endwall profiling

Tandem configuration is an effective methodology to reduce flow separation on compressor blade suction surface and to improve blade loading. However, in modern highly loaded cases, corner separation remains as its single blade counterpart. In this study, non-axisymmetric endwall profiling (NAEP) was utilized in a highly loaded tandem cascade (diffusion factor D = 0.69), aiming at reducing its severe corner separation and revealing the unique flow mechanism while NAEP is utilized in tandem cascade. NAEP was designed in both forward (F) blade and rare (R) blade separately, and was investigated numerically in tandem environment. Results show that, NAEP in F blade passage can effectively eliminate the corner separation and reduce loss generation, whereas NAEP in R blade passage has no positive effect on corner separation and even promotes loss production. The optimal NAEP approximately removes the corner separation completely, with loss coefficient reducing by as much as 37.8%. The optimal NAEP for the tandem cascade features optimal axial location at the origin of corner separation. There is an optimal NAEP height (0.02 of blade height), under which NAEP can achieve pretty good control effect while the peak of NAEP varies in a large axial location range. In the tandem configuration, it is found that NAEP transfers blade loading from R blade to F blade; the static pressure increases significantly for the entire cascade, but the static pressure distribution of F blade does not exhibit as the design intent of NAEP. In addition, it is interesting to find that the flow turning near endwall reduces after endwall profiling, which is unique in tandem cascade and is contrast to the view on conventional configuration. On the contrary, NAEP in R blade has no influence on the corner separation of the tandem cascade; due to the decrement of cross-passage pressure gradient for R blade, the flow overturning near endwall reduces.

Axially resolved volumetric two-photon microscopy with an extended field of view using depth localization under mirrored Airy beams.

It is a great challenge in two-photon microscopy (2PM) to have a high volumetric imaging speed without sacrificing the spatial and temporal resolution in three dimensions (3D). The structure in 2PM images could be reconstructed with better spatial and temporal resolution by the proper choice of the data processing algorithm. Here, we propose a method to reconstruct 3D volume from 2D projections imaged by mirrored Airy beams. We verified that our approach can achieve high accuracy in 3D localization over a large axial range and is applicable to continuous and dense sample. The effective field of view after reconstruction is expanded. It is a promising technique for rapid volumetric 2PM with axial localization at high resolution.

Adaptive optics enables aberration-free single-objective remote focusing for two-photon fluorescence microscopy.

Two-photon fluorescence microscopy has been widely applied to three-dimensional (3D) imaging of complex samples. Remote focusing by controlling the divergence of excitation light is a common approach to scanning the focus axially. However, microscope objectives induce distortion to the wavefront of non-collimated excitation beams, leading to degraded imaging quality away from the natural focal plane. In this paper, using a liquid-crystal spatial light modulator to control the divergence of the excitation beam through a single objective, we systematically characterized the aberrations introduced by divergence control through microscope objectives of NA 0.45, 0.8, and 1.05. We used adaptive optics to correct the divergence-induced-aberrations and maintain diffraction-limited focal quality over up to 800-µm axial range. We further demonstrated aberration-free remote focusing for in vivo imaging of neurites and synapses in the mouse brain.

High-NA two-photon single cell imaging with remote focusing using a diffractive tunable lens.

Fast, volumetric structural and functional imaging of cellular and sub-cellular dynamics inside the living brain is one of the most desired capabilities in the neurosciences, but still faces serious challenges. Specifically, while few solutions for rapid 3D scanning exist, it is generally much easier to facilitate fast in-plane scanning than it is to scan axially at high speeds. Remote focusing in which the imaging plane is shifted along the optical axis by a tunable lens while maintaining the position of the sample and objective is a promising approach to increase the axial scan speed, but existing techniques often introduce severe optical aberrations in high-NA imaging systems, eliminating the possibility of diffraction-limited single-cell imaging. Here, we demonstrate near diffraction-limited, volumetric two-photon fluorescence microscopy in which we resolve the deep sub-micron structures of single microglia cells with axial scanning performed using a novel high-NA remote focusing method. Image contrast is maintained to within 7% compared to mechanical sample stepping and the focal volume remains nearly diffraction-limited over an axial range greater than 86 µm.

Automated extended depth of focus digital holographic microscopy using electrically tunable lens

A combination of electrically tunable lens with a microscope objective lens (MO) for multifocal plane imaging capability is proposed. The method aims at extending the depth of focus of the MO by changing its axial range and field of view. The combination is implemented in a common path off-axis digital holographic microscopy configuration experimentally and it achieves an axial scanning range of 363.5 μm. It utilizes image plane holography to obtain in-focus images throughout the axial range. The proposed method demonstrates its application in quantitative phase imaging of the USAF 1951 test chart and flowing red blood cells at different axial depths. An axial depth variation of 0.76 μm–0.81 μm is obtained between two consecutive focused planes. The results validate and postulate the advantage of the proposed method over traditional extended depth-of-focus algorithms. The quantitative and qualitative results exploit the possibility of using the proposed method further for localization and tracking of flowing microscopic samples.

Ex-vivo biomechanics of repaired rat intervertebral discs using genipin crosslinked fibrin adhesive hydrogel

Microdiscectomy is the current standard surgical treatment for intervertebral disc (IVD) herniation, however annulus fibrosus (AF) defects remain unrepaired which can alter IVD biomechanical properties and lead to reherniation, IVD degeneration and recurrent back pain. Genipin-crosslinked fibrin (FibGen) hydrogel is an injectable AF sealant previously shown to partially restore IVD motion segment biomechanical properties. A small animal model of herniation and repair is needed to evaluate repair potential for early-stage screening of IVD repair strategies prior to more costly large animal and eventual human studies. This study developed an ex-vivo rat caudal IVD herniation model and characterized torsional, axial tension–compression and stress relaxation biomechanical properties before and after herniation injury with or without repair using FibGen. Injury group involved an annular defect followed by removal of nucleus pulposus tissue to simulate a severe herniation while Repaired group involved FibGen injection. Injury significantly altered axial range of motion, neutral zone, torsional stiffness, torque range and stress-relaxation biomechanical parameters compared to Intact. FibGen repair restored the stress-relaxation parameters including effective hydraulic permeability indicating it effectively sealed the IVD defect, and there was a trend for improved tensile stiffness and axial neutral zone length. This study demonstrated a model for studying IVD herniation injury and repair strategies using rat caudal IVDs ex-vivo and demonstrated FibGen sealed IVDs to restore water retention and IVD pressurization. This ex-vivo small animal model may be modified for future in-vivo studies to screen IVD repair strategies using FibGen and other IVD repair biomaterials as an augment to additional large animal and human IVD testing.

Long-range remote focusing by image-plane aberration correction.

Laser scanning plays an important role in a broad range of applications. Toward 3D aberration-free scanning, a remote focusing technique has been developed for high-speed imaging applications. However, the implementation of remote focusing often suffers from a limited axial scan range as a result of unknown aberration. Through simple analysis, we show that the sample-to-image path length conservation is crucially important to the remote focusing performance. To enhance the axial scan range, we propose and demonstrate an image-plane aberration correction method. Using a static correction, we can effectively improve the focus quality over a large defocusing range. Experimentally, we achieved ∼three times greater defocusing range than that of conventional methods. This technique can broadly benefit the implementations of high-speed large-volume 3D imaging.

Evaluation of axial decay length of plasma pressure in detached plasma

Abstract This study proposes a method for evaluating the axial decay length of the plasma pressure in detached helium plasmas with a fixed-point laser Thomson scattering and spectroscopic measurements in the linear divertor plasma simulator NAGDIS-II. By controlling the neutral gas pressure, the highly volume-recombining region called the “recombination front” was moved along the magnetic field. The differential terms for the electron pressure and the recombination-front position with respect to the neutral pressure were obtained. By using these two terms, the decay length of the plasma pressure was qualitatively calculated. In addition, from the movable Langmuir probe measurement, difference between the locally estimated decay length around the recombination front and the decay lengths over a wide axial range was discussed. The proposed method can be applied even in the huge heat flux condition where direct-contact measurements such as the Langmuir probe are not available.

Characterization of chondroitinase-induced lumbar intervertebral disc degeneration in a sheep model intended for assessing biomaterials.

Intervertebral disc (IVD) degeneration (IVDD) leads to structural and functional changes. Biomaterials for restoring IVD function and promoting regeneration are currently being investigated; however, such approaches require validation using animal models that recapitulate clinical, biochemical, and biomechanical hallmarks of the human pathology. Herein, we comprehensively characterized a sheep model of chondroitinase-ABC (ChABC) induced IVDD. Briefly, ChABC (1 U) was injected into the L1/2 , L2/3 , and L3/4 IVDs. Degeneration was assessed via longitudinal magnetic resonance (MR) and radiographic imaging. Additionally, kinematic, biochemical, and histological analyses were performed on explanted functional spinal units (FSUs). At 17-weeks, ChABC treated IVDs demonstrated significant reductions in MR index (p = 0.030) and disc height (p = 0.009) compared with pre-operative values. Additionally, ChABC treated IVDs exhibited significantly increased creep displacement (p = 0.004) and axial range of motion (p = 0.007) concomitant with significant decreases in tensile (p = 0.034) and torsional (p = 0.021) stiffnesses and long-term viscoelastic properties (p = 0.016). ChABC treated IVDs also exhibited a significant decrease in NP glycosaminoglycan: hydroxyproline ratio (p = 0.002) and changes in microarchitecture, particularly in the NP and endplates, compared with uninjured IVDs. Taken together, this study demonstrated that intradiscal injection of ChABC induces significant degeneration in sheep lumbar IVDs and the potential for using this model in evaluating biomaterials for IVD repair, regeneration, or fusion.

Full-field spectral-domain optical interferometry for snapshot three-dimensional microscopy.

Prevalent techniques in label-free linear optical microscopy are either confined to imaging in two dimensions or rely on scanning, both of which restrict their applications in imaging subtle biological dynamics. In this paper, we present the theoretical basis along with demonstrations supporting that full-field spectral-domain interferometry can be used for imaging samples in 3D with no moving parts in a single shot. Consequently, we propose a novel optical imaging modality that combines low-coherence interferometry with hyperspectral imaging using a light-emitting diode and an image mapping spectrometer, called Snapshot optical coherence microscopy (OCM). Having first proved the feasibility of Snapshot OCM through theoretical modeling and a comprehensive simulation, we demonstrate an implementation of the technique using off-the-shelf components capable of capturing an entire volume in 5 ms. The performance of Snapshot OCM, when imaging optical targets, shows its capability to axially localize and section images over an axial range of ±10 µm, while maintaining a transverse resolution of 0.8µm, an axial resolution of 1.4 µm, and a sensitivity of up to 80 dB. Additionally, its performance in imaging weakly scattering live cells shows its capability to not only localize the cells in a densely populated culture but also to generate detailed phase profiles of the structures at each depth for long durations. Consolidating the advantages of several widespread optical microscopy modalities, Snapshot OCM has the potential to be a versatile imaging technique for a broad range of applications.

Fourier DiffuserScope: single-shot 3D Fourier light field microscopy with a diffuser.

Light field microscopy (LFM) uses a microlens array (MLA) near the sensor plane of a microscope to achieve single-shot 3D imaging of a sample without any moving parts. Unfortunately, the 3D capability of LFM comes with a significant loss of lateral resolution at the focal plane. Placing the MLA near the pupil plane of the microscope, instead of the image plane, can mitigate the artifacts and provide an efficient forward model, at the expense of field-of-view (FOV). Here, we demonstrate improved resolution across a large volume with Fourier DiffuserScope, which uses a diffuser in the pupil plane to encode 3D information, then computationally reconstructs the volume by solving a sparsity-constrained inverse problem. Our diffuser consists of randomly placed microlenses with varying focal lengths; the random positions provide a larger FOV compared to a conventional MLA, and the diverse focal lengths improve the axial depth range. To predict system performance based on diffuser parameters, we, for the first time, establish a theoretical framework and design guidelines, which are verified by numerical simulations, and then build an experimental system that achieves < 3 µm lateral and 4 µm axial resolution over a 1000 × 1000 × 280 µm3 volume. Our diffuser design outperforms the MLA used in LFM, providing more uniform resolution over a larger volume, both laterally and axially.

A Smart Multi-Plane Detector Design for Ultrafast Electron Beam X-ray Computed Tomography.

In this paper, a smart detector design for novel multi-plane ultrafast electron beam X-ray computed tomography is presented. The concept is based on multi-plane electron beam scanning on a transparent X-ray target and elongated cuboid-shape scintillation detectors for radiation detection over an extended axial scanning range. The optical part of the scintillation detector acts as both an X-ray sensitive scintillator with a fast time response and a light guide. With that, we reduce detector complexity, number of detector elements, overall power consumption, and detector costs. We investigated the performance of this new multi-plane detector design with an evaluation detector setup that is made of cerium doped lutetium yttrium oxyorthosilicate (LYSO:Ce) as scintillation material and an avalanche photodiode (APD) array. Thereby, we assessed two design variants: A monolithic LYSO bar detector and a sandwich detector made of multiple LYSO crystals and glass light-guides. Both types reveal excellent linear detector responses, long-term stabilities, and comparable signal qualities.

Extended Dual-Focus Microscopy for Ratiometric-Based 3D Movement Tracking

Imaging the three-dimensional movement of small organelles in living cells can provide key information for the dynamics of drug delivery and virus transmission in biomedical disciplines. To stably monitor such intracellular motion using microscope, long depth of field along optical axis and accurate three-dimensional tracking are simultaneously required. In the present work, we suggest an extended dual-focus optics microscopy system by combining a bifocal plane imaging scheme and objective lens oscillation, which enables accurate localization for a long axial range. The proposed system exploits high-resolution functionality by concatenating partial calibration result acquired each axial imaging level, maintaining the practical advantages of ratiometric method.