Sagittal Focusing Research Articles

Variable-sagittal-radii elliptical x-ray crystal spectrometers for high-neutron-yield plasma diagnostics.

Sagittally focusing x-ray crystal spectrometers with elliptical profiles in the meridional (x-ray dispersion) plane are proposed for plasma diagnostics in experiments accompanied by high neutron yields. The spectrometers feature a variable sagittal radius of curvature to ensure the sagittal focusing of rays for each photon energy in a chosen detection plane. The detector is placed after the ray crossing point at the second ellipse focus, and the source-to-detector distance is maximized to reduce the neutron-induced background. The elliptical shape imposes a limitation on the spectrometer geometry such that the influence of the source size on the spectral resolution can be avoided only for a demagnifying spectrometer (the source-to-crystal distance is larger than that of crystal-to-detector). Hence, two designs are proposed. The first design, featuring high magnification and limited spectral resolution can be suitable for x-ray continuum spectroscopy. The second design of high demagnification is optimized for spectral resolution, and can be used for time-resolved spectroscopy of plasma's characteristic emission lines using streak cameras. The key performance characteristics of the two designs are verified using ray tracing.

Investigation of Focusing Properties on Astigmatic Gaussian Beams in Nonlinear Medium.

Ultra-short laser filamentation has been intensively studied due to its unique optical properties for applications in the field of remote sensing and detection. Although significant progress has been made, the quality of the laser beam still suffers from various optical aberrations during long-range transmission. Astigmatism is a typical off-axis aberration that is often encountered in the off-axis optical systems. An effective method needs to be proposed to suppress the astigmatism of the beam during filamentation. Herein, we numerically investigated the impact of the nonlinear effects on the focusing properties of the astigmatic Gaussian beams in air and obtained similar results in the experiment. As the single pulse energy increases, the maximum on-axis intensity gradually shifted from the sagittal focus to the tangential focus and the foci moved forward simultaneously. Moreover, the astigmatism could be suppressed effectively with the enhancement of the nonlinear effects, that is, the astigmatic difference and the degree of beam distortion were both reduced. Through this approach, the acoustic intensity of the filament (located at the tangential focal point) increased by a factor of 22.8. Our work paves a solid step toward the practical applications of the astigmatism beam as the nonlinear lidar.

Sagittal Balance Using Position and Orientation of Each Vertebra in an Asymptomatic Population.

A monocentric, retrospective radiographic study with 99 asymptomatic volunteers. The authors performed the postural analysis commonly scheduled when evaluating sagittal balance in a vertebra-by-vertebra manner by enrolling an asymptomatic population. They measured the position and angulation of each vertebra to reveal those for which the spatial positioning could be relevant during spinal surgeries. Several recent publications detailed the sagittal alignment parameters and focus on global analysis parameters. Some patients with identical commonly evaluated spinal parameters have exhibited very different profiles, with notable differences in vertebral positions and orientations. Therefore, a fine segmental analysis of position of each vertebra could be interest to gain understanding of spine alignment. The authors obtained full-spine EOS x-rays of 99 volunteers in the standard free-standing position. We used a validated three-dimensional reconstruction technique to extract current spinal parameters and the positions and angulations of all vertebrae and lumbar discs. Particular attention was paid to the positions and angulations of the apical and transitional vertebrae in the general population and in subgroups according to pelvic incidence (PI). T1 was the most common transitional cervicothoracic vertebra (in 89.9% of subjects) and was oriented downwards by an average of 22.0° (SD=7.3°, minimum=2.3°, maximum=40.1°). The thoracic apex trio of T5 (22.2%), T6 (28.3%), and T7 (36.4%) were equally found. The transitional thoracolumbar vertebrae were L1 (39.4%) and T12 (33.3%). The lumbar apex was usually the L3-L4 disc (36.4%). T1 seemed to be the transitional vertebra (90%) irrespective of the PI. For the other relevant vertebrae, the greater the PI, the more cranial the vertebra. We performed a detailed three-dimensional assessment of overall spinal balance using positional and rotational parameters. The positions and orientations of all vertebrae were specified, particularly the apical and transitional vertebrae. Level 3.

Analytic function for heliostat flux mapping with astigmatism and defocus

Off-axis incidence is inherent to sun tracking mirrors, named heliostats. Moreover, heliostat defocus takes place, provided that the focal length of the mirrors usually differs from their distance to the target. Defocus, along with high incidence angles, lead to astigmatic aberrations, that are overlooked by analytic functions based on convolution. This paper presents an analytic function on the image plane that reproduces these aberrations. As the reflection of the heliostat axes is non-orthogonal with defocus, the identification of the reflected axes plays a key role in the resulting model. In comparison with Monte Carlo Ray-Tracing, the model shows correlation coefficients above 90%, except at the tangential and sagittal foci, where the analytic function is indeterminate. An astigmatic parameter is provided to assess the model validity, which is complementary to UNIZAR at high incidence angles.

Oblique astigmatism and field curvature measured with light-field imaging.

The testing of astigmatism and field curvature of an optical system with light-field imaging is proposed. The method consists in measuring the depth map, obtained with a plenoptic camera, of the image of a test pattern formed by the optical system. To demonstrate the accuracy of the method, the virtual image formed by a plano-convex lens was tested. The resulting depth map was compared with the sagittal and tangential foci distances calculated with the Coddington theory. The proposed method could be applied to the quality testing of ocular optics, including eyeglasses, eyepieces, virtual reality goggles, and augmented reality devices.

Far-field vector-diffraction of off-axis parabolic mirror under oblique incidence**Project supported by the Science Foundation for Youth Scholars of Minjiang University, China (Grant No. Mj9n201602) and the National Science and Technology Major Project of the Ministry of Science and Technology of China.

Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-diffraction properties of an off-axis parabolic mirror in the presence of misalignments of the incoming beam. The physical origin of these effects is also explored. The results show that the far-field intensity profile is altered by the distortion-, coma-, and astigmatism-like aberrations, which are caused by oblique incidence rather than inherent aberrations for the off-axis configuration. The radius of 90% encircled energy also increases but does not change monotonically with incident beam size increasing, or rather, it first decreases and then increases. The focal shift strongly depends on the effective focal length and oblique incidence angle, but it is almost independent of the beam size, which affects the focusing spot patterns. The intensity distribution produces a higher astigmatic image with off-axis angle increasing. Coma-like aberration starts to become dominant with beam size increasing and results in larger curved propagation trajectory. The incident polarization also affects the intensity distribution. The variation in the Strehl ratio with oblique incidence angle strongly depends on the misalignment direction and beam size as well. In addition, we find that the difference in locus between the catacaustic and the diffraction focus in the meridian is small. But the locus of the sagittal foci is obviously different from the locus of the meridian foci and the catacaustic focus. Moreover, the peak intensity of the sagittal focus is maximum, and the ratio of the peak intensity to that in the meridian plane is approximately 1.5. Understanding these effects is valuable for assessing a practical focused intensity and describing the motion of charged particles under a strong electric field in ultraintense laser–matter interaction.

Sagittal and tangential foci produced by tilted plane wavefronts refracted through simple lenses.

We study the formation of caustic and wavefront surfaces produced by a tilted plane wavefront propagating through spherical positive lenses. The shape of the caustic surface is a function of the indices of refraction, the geometrical parameters of the lens involved in the process of refraction, and the obliquity angle with respect to the optical axis, as we expect. We provide exact and approximate analytic equations for tangential and sagittal focal surfaces and also for Petzval field curvature considering arbitrary lenses.

一种新型keV波段超高分辨光栅光谱仪设计

This paper presents a novel grating spectrometer design that combines a convexly cylindrical mirror with a concavely cylindrical varied line spacing grating to achieve an extreme resolving power of 33000-70000 in the photon energy range of 0.6-1.5 keV for a Gaussian light source with effective meridional size of 30 μm (root mean square) at an upstream initial object distance of 10 m. This type of spectrometer can be used to diagnose the radiation spectrum of a soft X-ray free electron laser and properly measure the spectral distribution and the detailed structure of the self-amplified spontaneous emission mode due to its extremely high resolving power. The overall optical aberrations of the system are well analyzed and compensated, providing an excellent flat field at the detector domain throughout the entire spectral range. A machine learning support vector machine algorithm is introduced into explore the optimal system to deliver the desired resolving performance. In addition, to enhance the spectral intensity and detection efficiency simultaneously, a sagittal confinement focusing mirror is introduced into the optical path of the spectrometer to reduce the astigmatism in spectral imaging. © 2019, Chinese Lasers Press. All right reserved.

Strategic Considerations for Effective Sagittal Resection of the Mandible to Achieve a Slim and Attractive Jawline.

Sagittal resection of the mandible has been widely used to reduce the width of the lower face and is usually carried out in combination with a mandibular contouring procedure. However, the surgical outcomes of this procedure are unclear because sagittal resection is rarely performed as a single procedure. The authors clarify misunderstandings regarding this procedure and introduce an improved strategic approach for sagittal resection of the mandible. Under general anesthesia, mandible contouring was performed first with a curved osteotomy, followed by sagittal resection of the outer cortex of mandible. The amount and extent of each procedure was determined in accordance with preoperative analysis. From 2012 to 2014, a consecutive series of 212 patients who underwent mandible contouring surgery without concomitant chin surgery were included in the study. A total of 189 patients underwent both mandibular contouring surgery and sagittal resection, whereas 13 underwent only sagittal resection and 10 underwent only mandibular contouring surgery. All operations were carried out successfully without any severe complications, and most patients had satisfactory aesthetic outcomes. The authors found that the sagittal resection of the mandible should be performed in accordance with the shape of the mandible to effectively reduce facial width and achieve better aesthetic outcomes for both profile and frontal views. In an outcurved-type mandible, conventional mandibular contouring may be effective alone, whereas sagittal resection focusing on removing the mandible body region is essential for incurved-type mandibles. In straight line-type mandibles, both procedures are necessary. Therapeutic, IV.

Changes in Peripheral Refraction, Higher-Order Aberrations, and Accommodative Lag With a Radial Refractive Gradient Contact Lens in Young Myopes.

To evaluate changes in the peripheral refraction (PR), visual quality, and accommodative lag with a novel soft radial refractive gradient (SRRG) experimental contact lens that produces peripheral myopic defocus. 59 myopic right eyes were fitted with the lens. The PR was measured up to 30° in the nasal and temporal horizontal visual fields and compared with values obtained without the lens. The accommodative lag was measured monocularly using the distance-induced condition method at 40 cm, and the higher-order aberrations (HOAs) of the entire eye were obtained for 3- and 5-mm pupils by aberrometry. Visual performance was assessed through contrast sensitivity function (CSF). With the lens, the relative PR became significantly less hyperopic from 30° to 15° temporally and 30° nasally in the M and J0 refractive components (P<0.05). Cylinder foci showed significant myopization from 30° to 15° temporally and 30° to 25° nasally (P<0.05). The HOAs increased significantly, the CSF decreased slightly but reached statistical significance for 6 and 12 cycles per degree (P<0.05), and the accommodative lag decreased significantly with the SRRG lens (P=0.0001). There was a moderate correlation between HOAs and CSF at medium and high spatial frequencies. The SRRG lens induced a significant change in PR, particularly in the temporal retina. Tangential and sagittal foci changed significantly in the peripheral nasal and temporal retina. The decreased accommodative lag and increased HOAs particularly in coma-like aberration may positively affect myopia control. A longitudinal study is needed to confirm this potential.

Generalized design of a zero-geometric-loss, astigmatism-free, modified four-objective multipass matrix system.

During this study we constructed a generalized parametric modified four-objective multipass matrix system (MMS). We used an optical system comprising four asymmetrical spherical mirrors to improve the alignment process. The use of a paraxial equation for the design of the front transfer optics yielded the initial condition for modeling our MMS. We performed a ray tracing simulation to calculate the significant aberration of the system (astigmatism). Based on the calculated meridional and sagittal focus positions, the complementary focusing mirror was easily designed to provide an output beam free of astigmatism. We have presented an example of a 108-transit multipass system (5×7 matrix arrangement) with a relatively larger numerical aperture source (xenon light source). The whole system exhibits zero theoretical geometrical loss when simulated with Zemax software. The MMS construction strategy described in this study provides an anastigmatic output beam and the generalized approach to design a controllable matrix spot pattern on the field mirrors. Asymmetrical reflective mirrors aid in aligning the whole system with high efficiency. With the generalized design strategy in terms of optics configuration and asymmetrical fabrication method in this paper, other kinds of multipass matrix system coupled with different sources and detector systems also can be achieved.

Spherical quartz crystals investigated with synchrotron radiation.

The quality of x-ray spectra and images obtained from plasmas with spherically bent crystals depends in part on the crystal's x-ray diffraction across the entire crystal surface. We employ the energy selectivity and high intensity of synchrotron radiation to examine typical spherical crystals from alpha-quartz for their diffraction quality, in a perpendicular geometry that is particularly convenient to examine sagittal focusing. The crystal's local diffraction is not ideal: the most noticeable problems come from isolated regions that so far have failed to correlate with visible imperfections. Excluding diffraction from such problem spots has little effect on the focus beyond a decrease in background.

Performance of the Compact Visual Beam Imaging System on the GM/CA BM Beamline at the APS

A typical problem encountered on a beamline with a sagittal focusing monochromator is the difficulty of optimizing the crystal alignment because the full width of the monochromatic, unfocused beam cannot be visualized. This problem is particularly acute on beamlines that accept a wide swath of radiation combined with a fixed experimental setup consisting of constrained apertures that only allow the focused beam to pass through to the sample position. To address this problem, an imaging system has been designed and implemented on the GM/CA bending magnet beamline at the Advanced Photon Source, Argonne National Laboratory. This imaging system consists of a 30mm × 50mm flat YAG crystal, right angle prism/mirror and video camera located downstream of the vertical collimating mirror, sagittally focusing monochromator and vertical focusing mirror. The YAG crystal was installed in a 6-way vacuum cross in the beam path, and was mounted on a linear translation feedthrough allowing remote controlled insertion and removal of the crystal from the beam path. The CCD camera was mounted outside the vacuum chamber and views the x-ray induced scintillation from the YAG crystal through a window. This visualizer allows one to optimize the twist, yaw and roll of the second crystal, facilitates proper sagittal focusing and serves as a remote controlled diagnostic tool. An overview of the design and the performance of the imaging system will be presented.

A double crystal X-ray monochromator for the SpLine diffraction and absorption synchrotron bending magnet beamline at the ESRF

The CRG BM25-SpLine Beamline is located at bending magnet 25 of the ESRF. The beamline, which is split in two branches, is devoted to XAS, XRD and HAXPES. The photon energy covered by both branches range between 5 and 45 keV. The beamline double crystal monochromator (DCM) uses two parallel Si(111) crystals in (+, −) configuration to produce a monochromatic exit beam parallel to the incident white X-ray beam. It accepts 2mrad of radiation from the bending magnet. The DCM has been recently upgraded. Several special features concerning the cooling of the first crystal, second crystal positioning and sagittal focusing mechanism has been improved. In this work a detailed description of the performed modifications is presented.

Sagittal focusing of synchrotron radiation X-rays using a winged crystal.

A Si(111) winged crystal has been designed to minimize anticlastic bending and improve sagittal focusing efficiency. The crystal was thin with wide stiffening wings. The length-to-width ratio of the crystal was optimized by finite element analysis, and the optimal value was larger than the `golden value'. The analysis showed that the slope error owing to anticlastic bending is less than the Darwin width. The X-rays were focused two-dimensionally using the crystal and a tangentially bent mirror. The observed profiles of the focal spot agreed well with the results of a ray-tracing calculation in the energy range from 8 to 17.5 keV. X-ray diffraction measurements with a high signal-to-noise ratio using this focusing system were demonstrated for a small protein crystal.

Peripheral Refraction and Retinal Contour in Stable and Progressive Myopia

To compare the patterns of relative peripheral astigmatic refraction (tangential and sagittal power errors) and eccentric eye length between progressing and stable young-adult myopes. Sixty-two right eyes of 62 white patients participated in the study, of which 30 were nonprogressing myopes (NP group) for the last 2 years and 32 were progressing myopes (P group). Groups were matched for mean spherical refraction, axial length, and age. Peripheral refraction and eye length were measured along the horizontal meridian up to 35 and 30 degrees of eccentricity, respectively. There were statistically significant differences between groups (p < 0.001) in the nasal retina for the astigmatic components of peripheral refraction. The P group presented a hyperopic relative sagittal focus at 35 degrees in the nasal retina of +1.00 ± 0.83 diopters, as per comparison with a myopic relative sagittal focus of -0.10 ± 0.98 diopters observed in the NP group (p < 0.001). Retinal contour in the P group had a steeper shape in the nasal region than that in the NP group (t test, p = 0.001). An inverse correlation was found (r = -0.775; p < 0.001) between retinal contour and peripheral refraction. Thus, steeper retinas presented a more hyperopic trend in the periphery. Stable and progressing myopes of matched age, axial length, and central refraction showed significantly different characteristics in their peripheral retinal shape and astigmatic components of tangential and sagittal power errors. The present findings may help explain the mechanisms that regulate ocular growth in humans.

Calculation of the parameters of the X-ray diffraction station with adaptive segmented optics on the side beam from the wiggler of the Sibir’-2 storage ring

The mounting of an X-ray diffraction station on the side beam of a 19-pole superconducting wiggler makes it possible not only to use the central synchrotron radiation beam with a wavelength of 0.5 A, but also to solve problems requiring softer X rays at a synchrotron radiation (SR) intensity exceeding that for the beams from the bending magnet. A numerical simulation of the formation of photon beams from a source and their transmission through the elements of the station (and through the station as a whole) allows one to calculate the parameters of the station, compare it with the existing analogs, determine its potential and actual efficiency of its elements, and estimate the adjustment quality. A numerical simulation of the SR source on the side beam from the wiggler and the focusing channel (segmented condenser mirror, monochromator with sagittal focusing by the segmented second crystal, and segmented focusing mirror) has been performed. The sizes of the focus and the divergence of rays in it are determined with allowance for the finite sizes of segments. The intensity of radiation with a wavelength λ = 1.0 A in the focus is determined taking into account the loss in the SR extraction channel and in the focusing channel. The values of the critical wavelength for the side beam from the wiggler and the wavelength resolution are calculated. The intensities in the X-ray diffraction pattern and its angular resolution are found.

Bifocal miniature toroidal shaped X-ray mirrors

We have fabricated a bifocal miniature toroidal mirror that horizontally and vertically focuses to two different locations to provide a smaller footprint of the beam for grazing-incidence wide-angle scattering (GIWAXS), while at the same time focusing the beam in the horizontal direction on the detector to further enhance the angular resolution. At CHESS we traditionally use glass single-bounce monocapillary optics for a wide range of X-ray experiments to get a fine X-ray beam of 5 to 20 μm. This miniature toroidal mirror was prepared by designing and fabricating an X-ray focusing capillary in which the sagittal and meridional focusing is decoupled and only a quadrant of the accepted annulus is used for focusing the beam. The mirror produced a 120 μm horizontal by 25 μm vertical focus at 50 mm from the tip of the optic and a 44 μm horizontal by 70 μm vertical focus at 150 mm from the tip of the optic.

Optimization of the flat-field holographic concave grating in wide spectral range

Based on the geometric theory of concave grating, we deduce the mathematical expressions of the meridional curve, Sagittal curve and the relational expression for the holographic flat-field image concave grating. We also propose a new optimal method in all used range for correcting the meridional and sagittal aberrations. Different from the design method using CODE V or ZEMAX, we use mathematical expression and adopt grating optimal factor instead. By fitting the meridional focusing curve and Sagittal focusing curve of concave grating, we find an image surface in theory to ensure that the meridional and also the Sagittal aberrations tend to zero, and then design and fabricate the grating based on the fitting parameters. We solve the problem that the meridional curve transcendental equation cannot solve by Matlab, and discuss the influence of two curves for different grating constants and different incidence angles. We find that the aberrations in a wide spectral range can be corrected by diminishing the incidence angle and increasing the grating scribed lines.

In-situ metrology for the optimization of bent crystals used in hard-X-ray monochromators: Comparison between measurement and simulation

Crystal sagittal focusing is known as one of the most efficient way of focusing synchrotron X-ray radiation from bending magnet sources, thus delivering increases photon flux at the sample position. To optimize the performance of a sagittaly bent crystal inside a monochromator, it is necessary to have knowledge of its radius of curvature. However, this measurement is not very easy to obtain. Even though the use of the X-ray beam is the ultimate source for optimizing the system, it is still necessary to have a prior knowledge of the radius of curvature as a function of the motor bender positions to avoid any catastrophic failure. In this paper, we describe a simple, efficient and accurate method of measuring the radius of curvature of sagitally bent monochromator crystals at several bending magnet beamlines at synchrotron SOLEIL. To optimize the crystal bending inside these monochromators, we used a Shack–Hartmann sensor (HP 26) developed by the Imagine Optic Company (Orsay/France). This high accuracy two-dimensional metrology tool was originally designed to be installed on a Long Trace Profiler translation stage to measure the mirrors profiles. During a period where the SOLEIL synchrotron was in shutdown, this instrument was directly mounted inside the monochromator so that the radius of curvature could be measured in-situ. This method allows us to optimize the curvature and eliminate twist before bending strongly the crystal below radii of curvature of less than 2 m. The second step in the optimization process was to use the X-ray beam for the final adjustments of the bending system, where X-ray images are then used to analyse the residual defaults of the system. Using SpotX, a ray-tracing simulation tool, these errors can be fully analysed and a fully optimized system can then be obtained. Overall, five beamlines at synchrotron SOLEIL have used in this method to optimize their monochromators.