Curvature Of Mirror Research Articles

Design and application of omnidirectional mirror for catadioptric optical system dedicated to high-speed video registration of lightning

Omnidirectional optical mirrors are widely used in many scientific, industrial and military applications but there is still a lot to do to improve their projection characteristics. The paper presents design method for a novel class of omnidirectional mirrors characterized by their settable reflection angle and 3D/2D image projection. Such approach can effectively improve the mirrored image distribution on matrix of optical sensor. A complex mirror curvature was manufactured with application of computerized numerical control milling machines and Physical Vapor Deposition technique. Three prototypes with 15°, 30° and 45° vertical top view angles were tested. Mirrors were applied to get a set of wide range cloud-to-ground lightning video registrations. Analysis of the high-speed video confirmed design assumptions, and using lightning location system data, enabled dimensioning and measurement of the lightning channel geometry in 3D. Proposed method can be easily implemented in other applications involving omnidirectional observation and photogrammetry.

Manufacturability-based optical design optimization for advanced Kirkpatrick–Baez X-ray focusing mirrors

The advanced Kirkpatrick–Baez (AKB) mirror setup is an effective and compelling solution to provide stable X-ray nano-focusing for synchrotron radiation or free-electron laser beamlines. We propose an AKB mirror design optimization approach to mitigate the difficulties associated with mirror fabrication by minimizing the total slope ranges of the four curved mirrors while achieving the expected focusing performance. In the optimization, we have considered geometry constraints to ensure the beam acceptance with the required clear aperture, the diffraction-limited focal size with the adequate numerical aperture, and the desired mirror gaps for adjustment and the necessary working distance for the sample stage. Additionally, practical constraints linked to mirror metrology and fabrication, such as mirror length limits and curvature uncertainty in measurement, are taken into account. Furthermore, progressive objective optimization eliminates the need for any initial guess, fully automating the AKB optimization process. This approach facilitates the development of an elegant Wolter-I or Wolter-III type AKB design solution that satisfies these multiple constraints. In cases where constraints cannot be simultaneously satisfied, the optimization results provide valuable insights into areas where trade-offs need to be considered. Simulations with ray tracing and wavefront propagation validate the optimized AKB design showing high tolerance to the beam incident angle.

Optimization of the Reflective Surface Shape of a Variable Curvature Mirror

Optimization of the Reflective Surface Shape of a Variable Curvature Mirror

Исследование трехмерного отражения от криволинейных зеркал с применением инструментов компьютерной алгебры

This article is a continuation of the study of the process of reflection of various objects from curved mirrors. So, earlier in the works [18; 20], a geometric method of constructing the results of reflections was described, which was implemented mathematically in the article [38] using the principles of analytical geometry [6; 11–14; 30]. The obtained analytical equations of the reflection results were visualized in the Wolfram Mathematica [24] program with the ability to dynamically change the parameters of the mirror and the reflected object. However, in the listed works, only cases of reflection on the plane were considered. In this study, attention is paid to a more complex case — reflection in three-dimensional space.
 
 The article considered the reflection of a point from surfaces of the second order: a cylinder, a cone, a single-cavity and double-cavity hyperboloids, a sphere, elliptical and hyperbolic paraboloids, and from a torus — a surface of the fourth order. As before, the reflection result obtained in each of the cases is accompanied by a program code for Wolfram Mathematica, which allows the reader to independently simulate the reflection process with different initial parameters.
 
 In addition, the relationships between the results obtained were analyzed — both the relationships between the results of various three-dimensional reflections, and the relationship of the results of three-dimensional reflections with the results of similar plane reflections. In particular, on the basis of this, a hypothesis was formulated about the relationship between the curvature of the Gaussian mirror and the dimension of the object obtained as a result of reflection.
 
 Based on the results of the work, conclusions were drawn and prospects for further research were outlined. One of them is to obtain an analytical mechanism for describing complex geometric surfaces using a set of simpler objects. This feature will increase the efficiency of specialists when working with reflections from complex surfaces in areas such as aircraft construction (for creating aerodynamic surfaces and air ducts), medicine [40], shipbuilding [7; 31; 42], etc.

Optimal design of a gravitational wave telescope system for the suppression of stray light.

For gravitational wave detection, the telescope is required to have an ultra-low wavefront error and ultra-high signal-to-noise ratio, where the power of the stray light should be controlled on the order of less than 10-10. In this work, we propose an alternative stray light suppression method for the optical design of an off-axis telescope with four mirrors by carefully considering the optimal optical paths. The method includes three steps. First, in the period of the optical design, the stray light caused by the tertiary mirror and the quaternary mirror is suppressed by increasing the angle formed by the optical axes of the tertiary mirror and the quaternary mirror and reducing the radius of curvature of the quaternary mirror as much as possible to make sure the optical system provides a beam quality with a wavefront error less than λ/80. Next, the stray light could satisfy the requirement of the order of 10-10 when the level of roughness reaches 0.2nm, and the pollution of mirrors is controlled at the level of CL100. Finally, traditional stray light suppression methods should also be applied to mechanics, including the use of the optical barrier, baffle tube, and black paint. It can be seen that the field stop can efficiently reduce stray light caused by the secondary mirror by more than 55% in the full field of view. The baffle tube mounted on the position of the exit pupil can reduce the overall stray light energy by 5%, and the difference between the ideal absorber (absorption coefficient is 100%) and the actual black paint (absorption coefficient is 90%) is 3.2%. These simulation results are confirmed by the Monte Carlo method for a stray light analysis. Based on the above results, one can conclude that the geometry structure of the optical design, the quality of mirrors, and the light barrier can greatly improve the stray light suppression ability of the optical system, which is vital when developing a gravitational wave telescope with ultra-low stray light energy.

High Repetition Frequency Solid-State Green Laser with Large Stable Area for Water Jet Guided.

This paper presents the design and experimental results of a long cavity length Nd:YAG laser with a large stable zone for water jet-guided laser (WJGL) applications. The design is based on the light transmission matrix and resonator stability conditions, aiming to achieve a large stable zone and a short cut-off thermal focal length (CTFL). A folded concave resonator is researched to enhance the cavity length, and the influence of the tunable cavity arm length on the oscillating beam in the resonator and in the YAG crystal is theoretically studied. Moreover, the effects of the output mirror curvature and the cavity arm length on the range of the stable area and the cut-off thermal focal length are also investigated. Experimental results show that a stable green laser output is obtained after second harmonic generation (SHG) with a pulse width ranging from 43 to 143 ns within the laser operating frequency range of 5-20 kHz. At an operation frequency of 10 kHz, the output power is 21.33 W, and the instability of the output power within 400 min is 0.88%. The laser source achieves a maximum power of 25.7 W at 20 kHz, and the maximum single pulse energy reaches 2.7 mJ at 6 kHz. Finally, this is used as the laser source to couple with a water jet with a diameter of 100 microns, achieving a lossless water conductivity transmission over 60 mm length. These results demonstrate the suitability of the designed laser source for WJGL technology research. In precision machining applications, this technology exhibits processing advantages of low thermal damage (~2 μm) and large depth (>10 mm), for 7075 aluminum alloy.

Adjustable rotation of multiple vortices produced by diode-pumped Nd:YVO4 lasers using intracavity second harmonic generation.

The criteria for achieving adjustable rotation of optical vortices are analyzed and used to design a diode-pumped solid-state laser that incorporates intracavity second harmonic generation within a concave-flat cavity to produce frequency-doubled Hermite-Gaussian (FDHG) modes. These FDHG modes are subsequently employed to generate various structured lights containing 2, 4, and 6 nested vortices using an external cylindrical mode converter. Through theoretical exploration, we propose that increasing the radius of curvature of the concave mirror and extending the cavity length can enhance the rotational angles of multiple vortices by expanding the adjustable range of phase shift for FDHG modes. Moreover, theoretical analyses assess vortex rotation concerning the positions of a nonlinear medium, successfully validating the experimental observations and elucidating the phase structures of the transformed beams.

Optical characterization of high performance mirrors based on cavity ringdown time measurements with 6 degrees of freedom mirror positioning.

An instrument capable of measuring optical losses, transmission, and the radius of curvature of high reflectivity mirrors is presented. The measurement setup consists of two remote controlled hexapod systems with 6 degrees of freedom placed inside a vacuum enclosure. Mirror loss measurements are performed via the cavity ring-down time method using a linear resonant two-mirror Fabry-Perot cavity configuration. The use of high-precision positioning systems enables cavity loss mapping by transversely scanning the position of the cavity end mirror. Mirror surfaces of up to 30mm in diameter can be scanned, and the cavity length can be tuned by 120mm.

Design and Manufacture of Polarization-Independent 3D SOI Vertical Optical Coupler.

An optical coupler is a key input/output (I/O) device in a photonic integrated circuit (PIC), which plays the role of light-source import and modulated light output. In this research, a vertical optical coupler consisting of a concave mirror and a half-cone edge taper was designed. We optimized the structure of mirror curvature and taper through finite-difference-time-domain (FDTD) and ZEMAX simulation to achieve mode matching between SMF (single-mode fiber) and the optical coupler. The device was fabricated via laser-direct-writing 3D lithography, dry etching and deposition on a 3.5 µm silicon-on-insulator (SOI) platform. The test results show that the overall loss of the coupler and its connected waveguide at 1550 nm was 1.11 dB in transverse-electric (TE) mode and 2.25 dB in transverse-magnetic (TM) mode.

Research on output spot evolution of multi-pass gain Tm:YLF slab laser based on multi-transverse mode competition

In this paper, the multi-transverse mode competition rate equation model of the Tm:YLF slab laser is established based on the cavity structure of multi-pass gain. As the pump power increased, the changing trend of the number of particles in each mode is analyzed. The direction of beam quality change is also mastered, verified by the three-pass gain laser with the evolution of pump power. Due to the limited compression capacity of the x-axial output spot of the three-pass gain laser, the output spot changes significantly under different cavity lengths and output mirror curvatures. By discussing the output spot evolution, it is known that the large curvature output mirror and the appropriate cavity length can optimize the output spot. Finally, under the pump power of 72 W, the four-pass gain laser obtains a laser output of 1.8 W. It’s beam quality is MX2 = 1.77;MY2 = 1.99, the optical–optical conversion efficiency is 2.5 %, and the slope efficiency is 15 %. The beam quality of a three-pass gain laser is MX2 = 2.67; MY2 = 1.70, the optical–optical conversion efficiency is 3.2 %, and the slope efficiency is 11 %. It is verified that the compression of the four-pass gain laser is stronger than that of the three-pass gain laser on the x-axis, laying the foundation for developing a compact multi-pass gain laser.

In-situ residual deformation field analysis of laser repaired metal components by coherent gradient sensing method

Directed Energy Deposition (DED) technology plays an important role in metal additive manufacturing and remanufacturing. However, the quality and repeatability of DED products are still regarded as a challenge that hinders their widespread applications, especially in cutting-edge sectors. As a promising approach to meet that challenge, the in-situ monitoring of mechanical quantities during DED process, such as deformation and stress, has attracted extensive attention in both academic and engineering fields. In this study, a coherent gradient sensing (CGS) system that matches DED equipment is developed and used for in-situ monitoring the residual deformation of DED repaired metal components. The accuracy of the CGS system has been verified by measuring the curvature of a spherical mirror, and the relative error of the curvature is within 2.5% as a whole. Then, through single-layer/double-layers repair experiments, the influence of dwell time between adjacent tracks, cooling process between adjacent layers, and scanning path of the second layer on the residual deformation are analyzed. In single-layer repair experiment, the value of residual deformation increases with the dwell time, while its distribution characteristic almost keeps the same. In double-layers repair experiment, the anisotropy of residual deformation field is mainly influenced by the deposition direction of the second layer. Compared with parallel deposition path in double-layer repair experiment, the orthogonal deposition path results in a reduction of both the anisotropy and the maximum value of residual deformation field. Moreover, in the cooling process of orthogonal deposition, the residual deformation increases while the distribution characteristic remains unchanged. In conclusion, the feasibility of residual deformation measurement by CGS method in DED repairing process is verified, which provides both data support and tool for the future industrial application.

Active Optics—Progress in Modeling of Tulip-like Variable Curvature Mirrors

We present new results obtained from the modeling of a tulip-like variable curvature mirror (VCM) in the case of a central force that reacts to its contour. From Nastran finite element analysis, we shows that 3-D optimizations, using non-linear static flexural option, with an appropriate solution sequence, provide an accurate tulip-like VCM thickness distribution. This allows us to take into account boundary conditions, including the thin outer collarette and its link to a rigid ring. Modeling with a quenched stainless steel chromium substrate provides diffraction-limited optical surfaces. Rayleigh’s quarter-wave criterion is performed over a zoom range from flat up to f/3.5 convexity over a 13 mm clear aperture and 10 daN central force. The optical testing results of a prototype tulip-like VCM elaborated from the previous analytic theory, show quasi-diffraction-limited figures for a zoom range up to f/5. The present modeling results should significantly help in the future construction of such VCMs with a zoom range extended up to f/3.5.

CATADIOPTRIC IMAGE DENOISING: A SPATIALLY VARIANT APPROACH

A catadioptric camera uses a conventional camera in conjunction with a quadratic mirror for capturing an omnidirectional field of view in real-time. The resolution of catadiop- tric images, however, is non-uniform due to the mirror curvature. A widely used approach to processing catadioptric images is to apply classical methods to them directly or via a trans- formed domain. The aim of this work is to demonstrate that for the task of image denoising, an appropriate approach is to modify classical methods so that they become spatially adaptive with the non-uniform resolution of catadioptric images. To this end, we modify the famous Rudin-Osher-Fatemi (ROF) denoising model by introducing a space-variant regularizer. The proposed model comprises a spatially varying total variation term, which adjusts the edge- preservation and the noise reduction abilities in the whole image domain. We carry out an empirical evaluation of the performance of the proposed model compared with the widely used methods for processing catadioptric images. The results reveal that, despite its simplic- ity, our model improves the performance of the original method in terms of both quantitative and qualitative aspects.

Miniature Deformable MEMS Mirrors for Ultrafast Optical Focusing.

Here, we introduce ultrafast tunable MEMS mirrors consisting of a miniature circular mirrored membrane, which can be electrostatically actuated to change the mirror curvature at unprecedented speeds. The central deflection zone is a close approximation to a parabolic mirror. The device is fabricated with a minimal membrane diameter, but at least double the size of a focused optical spot. The theory and simulations are used to predict maximum relative focal shifts as a function of membrane size and deflection, beam waist, and incident focal position. These devices are demonstrated to enable fast tuning of the focal wavefront of laser beams at ≈MHz tuning rates, two to three orders of magnitude faster than current optical focusing technologies. The fabricated devices have a silicon membrane with a 30-100 μm radius and a 350 nm gap spacing between the top and bottom electrodes. These devices can change the focal position of a tightly focused beam by ≈1 mm at rates up to 4.9 MHz and with response times smaller than 5 μs.

1: A Miniaturized Polarization‐multiplexed Dual‐plane Head‐mounted Display System for Augmented Reality

A dual-plane head-mounted display system based on polarization-multiplexing is proposed. A metal wire grid polarizer is employed to separate the two orthogonal polarizations to different optical paths due to its excellent polarization-selective characteristics within large angle and spectrum ranges. System parameters including the curvatures of the reflective mirrors and the aspheric lens have been optimized to achieve good image quality within a field of view of ~50 degrees at different focal depths. Our system could provide correct depths for full-color 3D images, so that the vergence-accommodation conflict and visual fatigue problems could be solved.

Theory of Dronized Laser Source for Next Generation of Optical Wireless Power Transmission

A theory of dronized laser resonator source which can be applied effectively to achieve an efficient remote wireless optical power transmission (WOPT) for the next 6G mobile communications, internet of things (IoT) devices, and continuous flying unmanned aerial vehicles (UAV) is proposed. The proposed laser resonator composes mainly of mirrors and a gain element that can be carried individually by drones to form a relatively long cavity. The airborne components can be assembled according to a specified formation flight of drones to configure a flying laser cavity that exposes its output towards the corresponding target. The stability of the proposed device is theoretically analyzed in terms of main important intracavity parameters, such as length, g-geometrical parameters, and radius of curvature of mirrors. Accordingly, the performance of the confocal symmetric laser resonator is determined in terms of mode size, beam waist size, and beam divergence angle of the fundamental mode in presence of refractive power variation. Simulation results have shown that a stable operation over a wide range of refractive power of confocal long laser resonator can be obtained when the value of curvature of mirror approaches resonator length. In addition, an acceptable fundamental mode size at gain element and mirrors is obtained with an expected efficient gain medium excitation and low diffraction loss.

Laser Profilometry on Micro-PTC

Profilometry is useful in detecting surface faults on solar concentrators, which can be imperfectly manufactured, thus affecting system performance. Profilometric analyses are performed on a micro-parabolic trough collector (m-PTC), with reduced sizes and greater mirror curvature than a usual PTC. The peculiar dimensions and shape of this micro-PTC request to develop a specific configuration of laser profilometry. It includes a laser diode with a converging lens placed in front of it, ensuring that the mirror curvature does not affect the beam reflection. A new method to calculate the spot position furnishes the reflected beam center even if it lies outside the target, giving it a virtual expansion. The profile is assessed with an iterative calculation, starting from a first point, physically measured. The results are the 3D profile reconstruction of the parabolic mirror and a map of the slope error for each mirror point. It also estimates the intercept factor, a parameter fundamental to optimize the m-PTC system, whose value is in agreement with a structured light measurement on the same object. This intercept factor was obtained averaging the local intercept factor calculated for each mirror point, which individuates the mirror portions not focusing the sunrays on the tube.

P‐68: Student Poster: A Miniaturized Polarization‐multiplexed Dual‐plane Head‐mounted Display System for Augmented Reality

A dual‐plane head‐mounted display system based on polarization‐multiplexing is proposed. A metal wire grid polarizer is employed to separate the two orthogonal polarizations to different optical paths due to its excellent polarization‐selective characteristics within large angle and spectrum ranges. System parameters including the curvatures of the reflective mirrors and the aspheric lens have been optimized to achieve good image quality within a field of view of ~ 50 degrees at different focal depths. Our system could provide correct depths for full‐color 3D images, so that the vergence‐accommodation conflict and visual fatigue problems could be solved.

Active Optics—Advances of Cycloid-like Variable Curvature Mirrors for the VLTI Array

Elasticity theory and active optics led us to the discovery of three geometrical configurations of variable curvature mirrors (VCMs) that are either cycloid-like or tulip-like thickness distributions. Cycloid-like VCMs are generated by a uniform load—air pressure—applied over the mirror rear surface, and reacts without any bending moment along its circular contour. This particular VCM configuration is of practical interest because it smoothly generates accurate optical curvatures, varying from plane at rest to spherical curvatures up to f/2.9 over 16-mm aperture under 6.5-bar air pressure. Starting from the thin plate theory of elasticity and modeling with NASTRAN finite element analysis, one shows that 3-D optimizations—using a non-linear static flexural option—provide an accurate cycloid-like thickness distribution. VCM elasticity modeling in quenched stainless steel–chromium substrates allows the obtaining of diffraction-limited optical surfaces: Rayleigh’s criterion is achieved over a zoom range from flat to f/3.6 over 13-mm clear aperture up to 6-bar loading. These VCMs were originally developed and built at the Marseille Observatory in 1975 and implemented as a cat’s-eye mirror of IR Fourier-transform interferometers for laboratory recording of fast events in gas molecular spectroscopy. Later, for high-angular resolution astronomy with the ESO VLTI array—an interferometer made of 8 m Unit Telescopes (UTs) and 1.8 m Auxiliary Telescopes (ATs)—such VCMs were inevitable components to provide in a 3″ co-phased field-of-view since 1998. They were implemented (1) as cat’s eye mirrors of the height delay-lines beam recombination lab and (2) as ATs mirror-pair for output pupil conjugation of the movable x–y baseline. From the ESO-AMU approved convention of making 10 VCM spares up to 2024, the present modeling should provide a diffraction-limited extended field-of-view. It is pure coincidence that present results from modeling with an outer collarette are identical to results from analytic theory without collarette.

Variable Curvature Mirror with Variable Thickness and Its Application in Space-Borne Optical Camera

Variable Curvature Mirror with Variable Thickness and Its Application in Space-Borne Optical Camera