Ellipsoidal Mirror Research Articles

Soft X-ray wavefront sensing at an ellipsoidal mirror shell

A reliable `in situ' method for wavefront sensing in the soft X-ray domain is reported, developed for the characterization of rotationally symmetric optical elements, like an ellipsoidal mirror shell. In a laboratory setup, the mirror sample is irradiated by an electron-excited (4.4 keV), micrometre-sized (∼2 µm) fluorescence source (carbon K α, 277 eV). Substantially, the three-dimensional intensity distribution I(r) is recorded by a CCD camera (2048 × 512 pixels of 13.5 µm) at two positions along the optical axis, symmetrically displaced by ±21–25% from the focus. The transport-of-intensity equation is interpreted in a geometrical sense from plane to plane and implemented as a ray tracing code, to retrieve the phase Φ(r) from the radial intensity gradient on a sub-pixel scale. For reasons of statistical reliability, five intra-/extra-focal CCD image pairs are evaluated and averaged to an annular two-dimensional map of the wavefront error {\cal W}. In units of the test wavelength (C K α), an r.m.s. value \sigma_{\cal{W}} = ±10.9λ0 and a peak-to-valley amplitude of ±31.3λ0 are obtained. By means of the wavefront, the focus is first reconstructed with a result for its diameter of 38.4 µm, close to the direct experimental observation of 39.4 µm (FWHM). Secondly, figure and slope errors of the ellipsoid are characterized with an average of ±1.14 µm and ±8.8 arcsec (r.m.s.), respectively, the latter in reasonable agreement with the measured focal intensity distribution. The findings enable, amongst others, the precise alignment of axisymmetric X-ray mirrors or the design of a wavefront corrector for high-resolution X-ray science.

Automatic detection of quartz glass subsurface defects by laser scattering method based on an ellipsoidal mirror.

With the improvement of quality requirements of optical components, the detection of subsurface defects of optical components has become a key technology. The existing detection methods still have some limitations in detection depth and detection efficiency. In this paper, a defect scattering light collection method based on ellipsoidal mirror model is used to analyze the scattering light collection efficiency under different experimental conditions theoretically, and the favorable conditions for improving the scattering light collection are proposed. After simulation verification, the use of ellipsoidal reflectors to collect scattered light can effectively avoid the impact of surface defects compared to lenses. At the same time, an experimental system based on this method is set up to filter the stray light by mean filtering method. The system detected three scratches (2μm in width and 252nm in depth) on the underside of a piece of quartz glass. The results show that the system can clearly detect the subsurface defects of optical components.

Wide-Baseline Light Fields using Ellipsoidal Mirrors.

Traditional hand-held light field cameras only observe a small fraction of the cone of light emitted by a scene point. As a consequence, the study of interesting angular effects like iridescence are beyond the scope of such cameras. This paper envisions a new design for sensing light fields with wide baselines, so as to sense a significantly larger fraction of the cone of light emitted by scene points. Our system achieves this by imaging the scene, indirectly, through an ellipsoidal mirror. We show that an ellipsoidal mirror maps a wide cone of light from locations near one of its foci to a narrower cone at its other focus; thus, by placing a conventional light field camera at a focus, we can observe a wide-baseline light field from the scene near the other focus. We show via simulations and a lab prototype that wide-baseline light fields excel in the traditional applications involving changes in focus and perspective. Additionally, the larger cone of light that they observe allows the study of iridescence and thin-film interference. Perhaps surprisingly, the larger cone of light allows us to estimate surface normals of scene points by reasoning about their visibility.

Design of an image-based BRDF measurement method using a catadioptric multispectral capture and a real-time Lambert calibration.

By utilizing a catadioptric system and a calibration Lambertian sample, a compact measurement method of bidirectional reflectance distribution function (BRDF) has been proposed for rapid and accurate measurement. With the help of an ellipsoidal dome mirror, a hyperboloid mirror, and a high-resolution camera, spatial reflectance distributions from reflected directions with a large field of view (FOV) can be obtained. The built-in Lambertian standard allows for real-time calibration to account for fluctuations in the illumination spectrum, effectively reducing the measurement drift and achieving a high accuracy. Moreover, a multispectral camera captures images at 8 spectral bands for accurate spectral color reconstruction from different directions. To verify the method, a prototype capable of fast, high-resolution measurements with a large FOV has been developed for characterizing the scattering properties of objects. It achieves a measured angular range up to 160°. Multispectral BRDF data for each sample can be obtained within 5 minutes with an angular resolution of less than 0.6°. Eight ceramic samples with different colors were selected for the verification of measurement accuracy, and their mean relative bias of BRDF measurement was found to be as low as 2.5%.

Conceptual design and analysis of remote steering system for CFETR ECRH system

In order to optimize the operational safety and reliability of the upper launcher for the CFETR ECRH system, a design of the launcher based on the remote steering concept is currently being carried out for comparison with the front steering equivalent. This paper presents the remote steering system's conceptual design and simulation analysis. A Square Corrugated Waveguide (SCW) of 65 × 65 mm has been designed with an optimized length of 9.35 m. By changing the relative length of the waveguide, the transmission efficiency of the SCW is optimized within the range of steering angles ±12°. Different error factors are investigated in detail, and corresponding acceptable error ranges are provided. Considering these error factors and ignoring ohmic losses and thermal effects, the relative transmission efficiency of the SCW is estimated to be >98 % within the steering angle range. A matching steering unit for the SCW is designed, which consists of an ellipsoidal focusing mirror and a steerable flat mirror. The detailed design of the steerable mirror motion trajectory is presented. Also, the influence of the possible beam incident errors caused by the steering unit on the transmission efficiency is analyzed in detail.

Mutual optical intensity propagation through non-ideal two-dimensional mirrors.

The mutual optical intensity (MOI) model is a partially coherent radiation propagation tool that can sequentially simulate beamline optics and provide beam intensity, local degree of coherence and phase distribution at any location along a beamline. This paper extends the MOI model to non-ideal two-dimensional (2D) optical systems, such as ellipsoidal and toroidal mirrors with 2D figure errors. Simulation results show that one can tune the trade-off between calculation efficiency and accuracy by varying the number of wavefront elements. The focal spot size of an ellipsoidal mirror calculated with 100 × 100 elements gives less than 0.4% deviation from that with 250 × 250 elements, and the computation speed is nearly two orders of magnitude faster. Effects of figure errors on 2D focusing are also demonstrated for a non-ideal ellipsoidal mirror and by comparing the toroidal and ellipsoidal mirrors. Finally, the MOI model is benchmarked against the multi-electron Synchrotron Radiation Workshop (SRW) code showing the model's high accuracy.

Statistical perception of the chaotic fabrication error and the self-adaptive processing decision in ultra-precision optical polishing.

Subaperture polishing is a key technique for fabricating ultra-precision optics. However, the error source complexity in the polishing process creates large fabrication errors with chaotic characteristics that are difficult to predict using physical modelling. In this study, we first proved that the chaotic error is statistically predictable and developed a statistical chaotic-error perception (SCP) model. We confirmed that the coupling between the randomness characteristics of chaotic error (expectation and variance) and the polishing results follows an approximately linear relationship. Accordingly, the convolution fabrication formula based on the Preston equation was improved, and the form error evolution in each polishing cycle for various tools was quantitatively predicted. On this basis, a self-adaptive decision model that considers the chaotic-error influence was developed using the proposed mid- and low-spatial-frequency error criteria, which realises the automatic decision of the tool and processing parameters. An ultra-precision surface with equivalent accuracy can be stably realised via proper tool influence function (TIF) selection and modification, even for low-deterministic level tools. Experimental results indicated that the average prediction error in each convergence cycle was reduced to 6.14%. Without manual participation, the root mean square(RMS) of the surface figure of a ϕ100-mm flat mirror was converged to 1.788 nm with only robotic small-tool polishing, and that of a ϕ300-mm high-gradient ellipsoid mirror was converged to 0.008 λ. Additionally, the polishing efficiency was increased by 30% compared with that of manual polishing. The proposed SCP model offers insights that will help achieve advancement in the subaperture polishing process.

Development of a laser-based angle-resolved-photoemission spectrometer with sub-micrometer spatial resolution and high-efficiency spin detection.

Angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution (μ-ARPES), has become a powerful tool for studying quantum materials. To achieve sub-micrometer or even nanometer-scale spatial resolution, it is important to focus the incident light beam (usually from synchrotron radiation) using x-ray optics, such as the zone plate or ellipsoidal capillary mirrors. Recently, we developed a laser-based μ-ARPES with spin-resolution (LMS-ARPES). The 177nm laser beam is achieved by frequency-doubling a 355nm beam using a KBBF crystal and subsequently focused using an optical lens with a focal length of about 16mm. By characterizing the focused spot size using different methods and performing spatial-scanning photoemission measurement, we confirm the sub-micron spatial resolution of the system. Compared with the μ-ARPES facilities based on the synchrotron radiation, our LMS-ARPES system is not only more economical and convenient, but also with higher photon flux (>5 × 1013 photons/s), thus enabling the high-resolution and high-statistics measurements. Moreover, the system is equipped with a two-dimensional spin detector based on exchange scattering at a surface-passivated iron film grown on a W(100) substrate. We investigate the spin structure of the prototype topological insulator Bi2Se3 and reveal a high spin-polarization rate, confirming its spin-momentum locking property. This lab-based LMS-ARPES will be a powerful research tool for studying the local fine electronic structures of different condensed matter systems, including topological quantum materials, mesoscopic materials and structures, and phase-separated materials.

Current status of ECE system on EAST tokamak

The electron cyclotron emission (ECE) diagnostic on the experimental advanced superconducting tokamak (EAST) has had a major upgrade since 2020, when EAST heating system also went through a significant upgrade, including one NBI system changed from counter-current to co-current (moving from port F to port D), and the antenna and the installation port of LHW and ICRF system have also been changed. The quasi-optical (QO) antenna of P port ECE system has been redesigned, the main purpose of which is to add one oblique ECE view. The angle with respect to perpendicular to the magnetic field is about 10°, which will facillitate measurement of the electron velocity distribution altered by LHW system. The ellipsoidal mirror has also been moved close to the plasma, about 70 cm away from the plasma center, and the poloidal beam waist radius in the plasma has been optimised to be less than 3 cm. The CECE system has also been moved from port G to port C. The frequency coverage of the CECE system has been upgraded to 104-132 GHz by adding one radio frequency (RF) module. Also in the intermediate frequency (IF) module, 8 narrow-band filters have been added to improve the spacial coverage of the system. On port F, a new superheterodyne radiometer with narrow-band filters in IF module has been installed. It consists of eight channels, the radial coverage is about 8 cm, the main purpose of this new system is to study the fine structure of magnetic island.

Abrasive slurry jet machining system using polyurethane@silica core-shell particles for internal surfaces of axisymmetric x-ray mirrors.

Abrasive machining has been used for inner surface processing of various hollow components. In this study, we applied an in-air fluid jet as a precision machining method for the inner surface of an axisymmetric x-ray mirror whose inner diameter was less than 10mm. We employed an abrasive with a polyurethane@silica core-shell structure, which has a low density of about 1.2 g/cm3 and a relatively large particle size of about 15 µm. By using this abrasive, a practical removal rate and a smooth machined surface were simultaneously obtained. We performed figure corrections for an axisymmetric mirror and improved the circumferential figure accuracy to a sub-10nm root mean square level. To evaluate the machining performance in the longitudinal direction of the ellipsoidal surface, we also performed periodic figure fabrication on the inner surface of a 114 mm-long nickel ellipsoidal mirror. X-ray ptychography, an optical phase retrieval method, was also employed as a three-dimensional figure measurement technique of the mirror. The wavefield of the x-ray beam focused by the processed ellipsoidal mirror was observed with the ptychographic system at SPring-8, a synchrotron radiation facility. The retrieval calculations for the wavefront error confirmed that a sinusoidal waveform with a period of 12mm was fabricated on the mirror surface. These experimental results suggest that a nanoscale figure fabrication cycle for the inner surface consisting of jet machining and wavefront measurement has been successfully constructed. We expect this technique to be utilized in the fabrication of error-free optical mirrors and various parts having hollow shapes.

Design of an ellipsoidal mirror assisted oblique plane microscopy

Using one objective for excitation and detection simultaneously, oblique plane microscopy (OPM) provides a mounting-friendly approach for optical sectioning. Unfortunately, the original OPM has three major defects: the mechanical constraints when placing the objectives, the phase loss and the resulting anisotropy of the point spread function (PSF). In order to alleviate the above defects, an ellipsoidal mirror assisted oblique plane microscopy (EM-OPM) was proposed. By inserting an ellipsoidal mirror into the optical path to help collect the light beam, the problem of placing the objectives was solved. The numerical calculation results showed that EM-OPM can obtain higher relative light intensity and larger effective area of exit pupil than OPM when the tilt angle of the light sheet becomes larger. The imaging simulation results showed that EM-OPM effectively solves the problem of resolution reduction in the Y direction of OPM. In addition, optimization of the higher-order terms of the ellipsoidal mirror further improved the imaging ability of EM-OPM in large field of view (FOV).

Optical Design of a Solar Simulator With Large Irradiation Surface and High Irradiation Uniformity

Aiming at the problem of low irradiation uniformity in existing solar simulators with large irradiation surface, a new optical design method of off-axis TMA (three-mirror anastigmat) solar simulators with large irradiation surface high uniformity was proposed. Three groups of short arc xenon lamps and non-coaxial ellipsoid mirror are used as composite light sources, the causes of stray light in optical integrator are clarified, and the optimization design method of integrator based on anti-crosstalk diaphragm is proposed. The light propagation matrix model of the optical system of the solar simulator is established to effectively suppress stray light in the integrator, and the influence of the aberration of the collimating system on the irradiation uniformity was analyzed. A optical system of object side telecentric off-axis TMA was designed to achieve high uniform illumination with large irradiation area. The results show that in the Φ500 mm irradiation surface, the irradiance of the system is better than 1S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (1367 w/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), up to 1656 w/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , irradiation uniformity is 98.29%, this research can provide accurate and reliable solar radiation for space environment experiment of satellite load and make up for the limitation of low irradiation uniformity of traditional solar simulators with large irradiation surface.

Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle.

Ellipsoidal and plane-elliptical surfaces are widely used as reflective, point-to-point focusing elements in many optical systems, including X-ray optics. Here the classical optical path function approach of Fermat is applied to derive a closed-form expression for these surfaces that are uniquely described by the object and image distances and the angle of incidence at a point on a mirror surface. A compact description facilitates design, modeling, fabrication, and testing to arbitrary accuracy. Congruent surfaces in two useful coordinate systems - a system centered on the ellipsoid's axes of symmetry and a mirror-centered or `vertex' system with the surface tangent to the xy plane at the mirror's center - are presented. Expressions for the local slope and radii of curvature are derived from the result, and the first several terms of the Maclauren series expansion are provided about the mirror center.

Photoacoustic microscopy with subwavelength resolution and enhanced spatial isotropy by using an aspheric acoustic mirror group

Photoacoustic microscopy (PAM) is an emerging biomedical imaging modality, combining good acoustic resolution in deep tissue and rich functional biomedical information. Spatial resolution and spatial isotropy are two of the most important indexes of a PAM. In this study, we propose a PAM scheme based on an aspheric acoustic mirror group to achieve the subwavelength resolution and enhance the spatial isotropy. The mirror group consists of an ellipsoid acoustic mirror and a parabolic acoustic mirror. The ellipsoid acoustic mirror expands the cone angle of signal collection, and the parabolic acoustic mirror reduces the cone angle of the PA beam. Their combination equivalently expands the numerical aperture of acoustic detection. Phantom experiments demonstrate that the proposed scheme can achieve the subwavelength resolution. Simultaneously, its spatial isotropy is improved from 48.2% to 96.7%. An in vivo mouse brain imaging experiment examines the biomedical practicability of the method. This method may be found wide potential applications in biomedicine.

An Easy Technique for Focus Characterization and Optimization of XUV and Soft X-ray Pulses

For many applications of extreme ultraviolet (XUV) and X-ray pulses, a small focus size is crucial to reach the required intensity or spatial resolution. In this article, we present a simple way to characterize an XUV focus with a resolution of 1.85 µm. Furthermore, this technique was applied for the measurement and optimization of the focus of an ellipsoidal mirror for photon energies ranging from 18 to 150 eV generated by high-order harmonics. We envisage a broad range of applications of this approach with sub-micrometer resolution from high-harmonic sources via synchrotrons to free-electron lasers.

Laboratory system for optical coherence tomography (OCT) using a laser plasma source of soft x-rays and extreme ultraviolet and focusing ellipsoidal optics.

Optical coherence tomography (OCT) with the use of soft x-rays (SXR) and extreme ultraviolet (EUV) has been recently demonstrated [Fuchs et al. Sci. Rep.6, 20658 (2016)10.1038/srep20658; Fuchs et al. Optica4, 903 (2017)10.1364/OPTICA.4.000903]. This new imaging technique, named XCT, makes it possible to obtain cross-sectional and tomographic images of objects with nanometer spatial resolution. The article presents a newly developed laboratory system for XCT using a compact laser plasma light source operating in the SXR and EUV spectral ranges. The source is based on a gas puff target containing Kr gas or a Kr/Xe gas mixture irradiated with nanosecond laser pulses from an Nd:YAG laser. The use of the gas puff target enables efficient emission of SXR and EUV radiation without generating target debris associated with laser ablation when using a solid target. The system is equipped with an ellipsoidal mirror to collect radiation from the source and focus on the imaged object. The XCT measurements are made by processing the spectrum of the radiation reflected from the object recorded with a transmission grating spectrometer equipped with an identical focusing mirror and a CCD camera. The paper presents the characterization and optimization of the new XCT system and its application to the measurements of layered nanostructures.

A potential way of detecting circulating tumor cells via laser scanning

Circulating tumor cells (CTCs) are generally considered as seeds for metastases, serving as a clinical biomarker for cancer diagnosis. Due to their low content in the blood, detection of CTCs normally requires an antibody-mediated biological enrichment process, which is rather complicated and time-consuming. In this work, we demonstrate a potential, fast, and cost-effective way of detecting CTCs. That is, CTCs are physically isolated by size using filtration and imaged optically via laser scanning. The filtered and stained blood sample, which is placed on a moving and spinning stage, is illuminated by a 405 nm diode laser. Scattered optical signals are collected by using an ellipsoidal reflective mirror for dark-field imaging. Then CTCs in dark-field images are screened and counted by the clustering algorithm. Our method possesses the advantages of antibody-free and low cost, holding great promise for early diagnosis and prognosis prediction of cancer patients.

Near-optimal intense and powerful terahertz source by optical rectification in lithium niobate crystal

Using a 400 μJ ytterbium laser combined with a novel pulse compression technique, we demonstrate a state-of-the-art terahertz (THz) source from the tilted-pulse front pumping scheme in lithium niobate at room temperature with record efficiency of 1.3% capable of generating 74 mW of average power and 400 kV/cm at focus. Key points of this demonstration include the use of a pump pulse duration of 280 fs in combination with a stair-step echelon mirror and an off-axis ellipsoidal mirror. This source has unmatched characteristics of generating intense and powerful THz pulses at the same time and remains highly scalable as compared to existing Ti:sapphire-based THz sources pumped in the millijoule range.

Realizing mutual occlusion in a wide field-of-view for optical see-through augmented reality displays based on a paired-ellipsoidal-mirror structure

Mutual occlusion is an essential feature for augmented reality (AR) displays for allowing the virtual content to be clearly perceived under an excessively illuminated environment. Although a few works have been done to facilitate the performance of occlusion-capable optical see-through augmented reality (OC-OST-AR) displays, the realization of mutual occlusion in a wide field-of-view (FOV) is still challenging. Divergent from typical hard-edge occlusion and soft edge-occlusion designs, we propose the paired-ellipsoidal-mirror (PEM) structure. The proposed system is allowed to support either hard-edge occlusion or enhanced soft-edge occlusion in a wide FOV by optionally fixing a spatial light modulator (SLM) before the entrance pupil or at an inner focal plane. The numerical aperture (NA) of the system is efficiently increased by the combination of paired ellipsoidal mirror imaging and aperture stop restriction. With proof-of-concept prototypes built, virtual display in a FOV of H160°×V74° and mutual occlusion in a FOV of H122°×V74° are demonstrated with a basic design, respectively. Furthermore, a mixed FOV of H95.3°×V52.9° is demonstrated by an optimized design with vertical parallax reduction and virtual display improvement.

Copper electroforming replication process for soft x-ray mirrors.

We developed a copper electroforming replication (CER) process to fabricate precise ellipsoidal mirrors for soft x-ray focusing. Some applications of ellipsoidal mirrors in x-ray microscopy require that all components that are close to samples, including the mirrors, are made of non-magnetic materials. In this study, a non-magnetic copper ellipsoidal mirror was fabricated by replicating a figured and super-polished quartz glass mandrel using an electroforming technique. It was found that the CER process has a high replication accuracy of 8 nm. The focusing performance of the mirror was characterized using a soft x-ray free-electron laser with a photon energy of 100 eV. A small focus size of 370 × 400 nm2 was achieved with a high reflectivity of 65%.