Circular Mirror Research Articles

The One-Cushion Escape from Snooker in a Circular Table

Abstract The one-cushion escape from snooker in a circular table can be viewed as a ge-ometric problem involving the reflection of a light ray in a circular mirror. There are at most four escapes in any given configuration. We will obtain specific configurations in which there are exactly 0, 1, 2, 3 or 4 escapes. The details consist in determining the number of real solutions in the interval (−1; 1) of certain polynomial equations, of degrees two, three or four.

Computational analysis and optimization of daylight collector geometry for removal of hotspots in circular mirror light pipe

The illuminance patterns formed on the various surfaces of a tubular daylight guidance system (TDGS) were numerically measured and calculated for the beam sunlight input. For this study, the TDGS comprises a revolved parabolic profiled daylight collector geometry and a vertical MLP system for daylight guidance. TDGS is basically a non-imaging optical system that is designed to efficiently transmit available sunlight across the MLP (mirror light pipe) length. But while doing so the problematic hotspots are observed mainly on the diffuser placed at the exit aperture of cylindrical MLP which further results in non-uniform illumination in the daylit room. In this work, the use of a prismatic casing arranged sideways to the parabolic profiled collector and a sloped diffuser as a top cover shows a significant reduction in the hotspot problem on the exit aperture of MLP without compromising light transmission in TDGS. The ‘non-uniformity’ index value, Ir signifying the ratio of maximum illuminance to average illuminance on the diffuser surface dropped considerably for the proposed design signifying an increase in uniformity on the exit aperture of MLP. For 1 m long MLP (aspect ratio = 2.5), the maximum value of Ir was ∼ 19 and ∼ 37 for TDGS with dome collector and TDGS with parabolic collector having plane cover (TSA) respectively on midday timings of 21st June while for the proposed design the value was Ir < 5. For 2 m long MLP (aspect ratio = 5), the value was Ir < 4 much lower in comparison to Ir of ∼ 20 and ∼ 36 for TS with dome collector and TSA respectively. A considerable decrease in the severity of hotspots was realized from the results. The proposed collector design was also tested for the illuminance values on the work plane of the simulated room under beam sunlight, diffuse skylight, and overcast sky conditions. No compromise in the average illuminance values was observed when compared to the parabolic collector with transparent casing. Moreover, the proposed design gave enhanced values of illuminance under low altitude beam sunlight as well as under diffuse skylight for various timings of the day. Performance under the overcast sky was found slightly lesser in comparison to conventional collector designs though nominal levels of illuminance were observed for all the configurations of collectors due to the very less magnitude of light availability.

Generation of a radially polarized beam in a polycrystalline ceramic Yb:Lu2O3 thin-disk laser

We report on the generation of a continuous-wave (CW) radially polarized beam with an Yb:Lu2O3 polycrystalline ceramic disk in a thin-disk laser (TDL) oscillator. A circular grating-waveguide mirror (CGWM) with a high polarization discrimination given by a reflectivity difference between the two orthogonal polarization states of 44.6% was used as a polarization-selective cavity end-mirror. An output power of 175 W was achieved with an optical efficiency of 39.6%. A high degree of radial polarization of 96.2% and a beam propagation factor of M2hor. = 2.05 and M2ver. = 2.32 were measured at the maximum output power.

Nonimaging Behavior of Circular Trough Concentrators With Tubular Receivers

Abstract This paper presents a detailed analysis of the optical performance of circular trough concentrators with tubular receivers. First, a simple analytical formula for the achievable geometric concentration ratio as a function of the rim angle and acceptance angle is developed. Notably, the development reveals the existence of three distinct concentration ratio regimes: a first regime where the receiver is sized based on the reflection of the edge rays from the rim alone, a second regime where the receiver is sized based on the rim and the edge ray caustics, and a third regime where two reflections from the mirror are permitted. Several exemplary designs are proposed and further analyzed using Monte Carlo ray tracing to obtain transmission angle curves and receiver flux distributions. For an acceptance angle of 1 deg, the circular trough concentrator with circular receiver is found to achieve a maximum geometric concentration ratio of 7.695× with a peak flux of 30 suns. For large acceptance angles (10 deg), the circular trough achieves a geometric concentration ratio as high as 82% of that of a parabolic trough. This noteworthy performance, along with the fact that a circular mirror is amenable to an inflated polymer construction, makes this configuration promising for low-cost, low-concentration solar thermal applications.

Development of a design and optimization tool for axial mirror supports of large telescopes

The present paper describes a parametric design and optimization tool [Support Optimization and Design Tool (SODT)], used to evaluate passive axial support positions on circular solid meniscus mirrors. The developed tool avoids the intrinsic limitations of methodologies of the reference literature, based on analytical formulations. A parametric finite element model of the mirror is generated from the user inputs and the support distribution is optimized in terms of the root mean square of the surface error (SFE). The optimization process is based on a hybrid optimization algorithm combining genetic algorithms and a gradient-based approach. The results are compared to the ones presented in the literature, evidencing minor discrepancies that can be basically attributed to differences in methodology and structural formulation, as it is discussed in the text. Finally, the finite element and optical postprocessing results are verified against industry-grade software: MSC Nastran® and Sigmadyne SigFit®.

Hemispherical solar distiller with truncated circular cone-shaped reflector mirrors (TCC-RM): optimum inclination of reflector mirrors.

The present study aims to achieve the highest cumulative yield of the hemispherical distillers, by designing and constructing new reflector mirrors, which are truncated circular cone-shaped reflector mirrors (TCC-RM). To obtain the optimum inclination of TCC-RM that achieves the highest hemispherical distiller's performance, eight inclination angles (10°, 15°, 20°, 25°, 30°, 35°, 40°, and 45° with vertical) were experimentally studied. To achieve this, a series of experimental tests were carried out on the three hemispherical solar distillers: the first represents the reference distiller (traditional hemispherical solar distiller (THSD)) and the other two devices are the hemispherical solar distiller with truncated circular cone-shaped reflector mirrors (HSD-TCCRM) with different inclination angles. The experimental results indicate that utilizing TCC-RM with a 25° inclination angle achieves the maximum cumulative yield of 8.35 L/m2 with an improvement of 42.74% compared to THSD. While the utilization of TCC-RM with the inclination angles of 30°, 35°, 20°, 40°, and 15° achieves the cumulative yield of 7.9, 7.3, 7.05, 6.67, and 6.6 L/m2 compared with 5.85 L/m2 for THSD. On the contrary, adjusting the inclination angle of TCC-RM at 10° and 45° affects negatively the cumulative yield of the HSD with TCC-RM in comparison with THSD. Based on the data of cumulative yield, daily efficiency, and the economic analysis it is recommended to utilize TCC-RM with a 25° inclination angle to achieve the highest performance and minimum distillate cost of hemispherical solar distillers.

Concentration ratio for a solar trough concentrator with circular mirror and flat receiver

We present a simple analytical formula for the geometric concentration ratio of a circular trough optical concentrator coupled to a flat (planar) receiver. The receiver is sized to achieve full collection (no spillage) for any combination of acceptance and rim angle. The development reveals the existence of two concentration ratio regimes, one controlled by the edge ray caustics, and the other controlled by the intersection of the edge rays from the rim alone. Notably, we show that in the latter rim ray regime, the circular trough achieves the exact same geometric concentration ratio as a parabolic trough. The provided formula fills a gap towards the development of a complete catalogue of concentration ratio formulas for different concentrator/receiver geometries.

Rapid polishing process for the x ray reflector.

X ray mirrors are symmetrical workpieces along the length and width and are widely used in various optical systems. Unlike the center-symmetric circular mirror, it is more difficult to suppress the edge effect of the x ray mirror during the polishing process, which greatly limits the polishing accuracy and polishing efficiency. Based on this, the unique edge effect of x ray mirrors is investigated in depth in this paper. First, the causes and distribution laws of the edge effect of the x ray mirror were obtained by analyzing the inherent structure of the computer controlled optical surface (CCOS) and the motion trajectory of the polishing tool. Second, a mathematical model was established based on the material removal states of different regions on the x ray mirror. Finally, a combined polishing process based on the influence function of different shaped tools is proposed and experimentally verified. The results show that the edge effect on the x ray mirror is significantly weakened and its surface errors peak to valley (PV) and RMS are increased by 21.5 times and 47.9 times, respectively. This indicates that the combined polishing process has a good suppression effect on the edge effect of the x ray mirror.

Varifocal-Piston Micromirror With Quasi-Simply Supported Piecewise Linear Flexure

Micromirrors with variable focal length are critical components of various optical systems. However, due to the limitations of microfabrication and actuation mechanisms, it is very difficult to control accurately the surface shape of a varifocal mirror. In this study, a novel surface-micromachined varifocal piston micromirror is presented. By simulating quasi-simply-supported boundary conditions, an accurate focusing of the mirror was achieved. The mirror is controlled by a parallel-plate electrostatic actuator. When the micromirror is actuated, as the driving voltage increases, the micromirror moves and deforms in two stages. In the first stage, four beams that support the mirror bend, which produces the micromirror vertical translation. When the translation reaches its limit, the micromirror enters the second stage, during which it bends to a concave shape and thus can focus light. A prototype based on the proposed concept was fabricated using a commercially available surface micromachining process. An analytical formulation, finite element model, and experimental measurements were adopted to study the electromechanical and optical performances of the micromirror. The focus length could be adjusted from 79.8 mm to 2.03 mm with a residual rms error less than 15 nm by changing the driving voltage. When the deformation reached its maximum, the first 21 Zernike aberration coefficients were all less than 3 nm. The proposed concept is also applicable to circular mirrors.

Highly Linear and Wide Non-Resonant Two-Degree-of-Freedom Piezoelectric Laser Scanner.

Laser scanners with mechanically driven mirrors have exhibited increasing potential for various applications, such as displays and laser radar. Resonant scanners are the predominantly used scanners; however, non-resonant scanners are required for applications where point-to-point driving is desirable. Because a non-resonant drive cannot amplify the drive angle owing to the resonance phenomenon, high values are difficult to achieve for the main performance metrics of the scanners: mirror area, drive angle, and operating frequency. In this paper, we present a two-axis scanner with a piezoelectric actuator made of a piezoelectric single-crystal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 as the actuation force source. The scanner contains a circular mirror with a diameter of 7 mm and achieves an average static mechanical deflection angle amplitude of 20.8° in two axes with a resonant frequency of 559 Hz. It is equipped with a transmission mechanism that can decouple each axis to achieve high linearity; in our study, the nonlinearity error was less than 1°.

Comparative Additional Factor for Diffraction Loss On (TEM01) Mode from That of (TEM00) Mode

Comparative Additional Factor for Diffraction Loss On (TEM01) Mode from That of (TEM00) Mode

Multistate Nonvolatile Metamirrors with Tunable Optical Chirality

Compared with conventional mirrors that behave as isotropic electromagnetic (EM) reflectors, metamirrors composed of periodically aligned artificial meta-atoms exhibit increased degrees of freedom for EM manipulations. However, the functionality of most metamirrors is fixed by design, and how to achieve active EM control is still elusive. Here, we propose a multistate metamirror based on the nonvolatile phase change material Ge2Sb2Te5 (GST) with four distinct functionalities that can be realized in the infrared region by exploiting the temperature-activated phase transition. When varying the crystallinity of GST, the metamirror has the capability to perform as a right-handed circular polarization chiral mirror, a narrowband achiral mirror, a left-handed circular polarization chiral mirror, or a broadband achiral mirror, respectively. The inner physics is further explained by the construction or cancellation of extrinsic two-dimensional chirality. As a proof of concept, experimental verification is carried out and the measured results agree well with their simulated counterparts. Such a multifunctional tunable metamirror could address a wide range of applications from sensing and spectroscopy to analytical chemistry and imaging.

A New Thermal-Solar Field Configuration: The Rotatory Fresnel Collector or Sundial

A new type of Fresnel array has been devised and constructed as an answer to the need to reduce the investment costs of solar thermal collectors, without jeopardizing their efficiency in capturing solar radiation at high temperatures. The array of mirror bands is fixed onto a horizontal platform, which rotates around a virtual vertical axis, so that the sun is in the extrapolated vertical plane of symmetry of the array. The receptor central line is also placed in said plane, and it is physically made of at least one tube at each side of the plane. The geometrical relation between the mirrors and the receptor is therefore fixed. The platform rotates with the same speed as that of the sunlight’s azimuthal component. On the contrary, the angle of incidence of the sunlight on the mirrors changes as the sun rises and declines in its daily apparent motion, but this effect does not disturb the radiation concentration kinematics, although it induces a shift along the receptor. This is a new configuration based on the use of simple and cheap flat mirrors to obtain circular cylindrical mirrors. These mirrors are made of originally flat mirrors that are bent by applying an inexpensive and simple bending technique patented by our research group. The radius of curvature of each mirror is tuned to the distance from the mirror to the receiver central line. The integration of different scientific domains (such as structural analysis) and elementary technologies (such as 3D printing) in this innovative solar radiation concentrator and receiver can lead to a large reduction in costs. Nevertheless, the first experimental campaign has shown additional problems in the receiver configuration, which should be addressed in a next stage of research. This paper explains the methodology used and procedures in the development of the first prototype of the Sundial.

Geometric layout optimization of a large aperture thin elliptical mirror’s axial and lateral support

For passive support of large aperture telescopes, geometric layout optimization of the support structure is one of the most critical tasks because it determines the deformation of the mirror under gravity, which affects the wavefront aberration and image quality of the system. Due to a lack of symmetry, the optimization of an elliptical mirror support can be much more complex compared with circular mirrors. We optimize the geometric layout of axial and lateral support for the tertiary mirror of the Thirty Meter Telescope (TMT). Based on a theoretical analysis of the whiffletree principle, a parametric model of axial support is established based on the multi-point constraint equation. The mirror deformation SlopeRMS of the tertiary mirror under vertical gravity is used as the optimization target of the support points. The axial support point position is optimized by means of a simulated annealing algorithm and a mirror-deformed post-processing script written in Python. The TMT tertiary mirror lateral support also uses the whiffletree structure, and its in-plane layout affects the system's resonant modal frequency and the maximum load at each point. According to the dynamic equation and the static principle, the lateral support optimization model is established. The first-order resonant frequency and maximum load of the support point are the objective function. Through optimization of the axial and lateral support, the overall mirror distortion of the system is improved.

Исследования курганного могильника Станция Камышта-1 в 2021 году

The article presents preliminary data of the rescue archaeological works at Mound Kamyshta Station-1 located in the southwestern part of Khakassia-Minusinsk region. The site is situated in the Askyz District of the Republic of Khakassia on the second floodplain terrace of the ancient sector of the Abakan River valley. The excavations have shown that mound 2 is a distant stele of Mound 1 and is located 15 meters southwest of it. A rectangular kerb made of massive red Devonian grit slabs based upon piers on the outside was uncovered. Upright steles were erected in the middle of each kerb walls except the northeast one and at the corners; the steles are oriented toward sunrise with their narrow edges. The gate is attached to the northeastern side of the kerb. The kerb enclosed six tombs. Tombs 1, 2, and 3 are considered the main ones, the tomb 4 is subsidiary, tombs 5 and 6 were dug in from the overlying layer (inlets). All the burials were made either in earthen graves or in stone boxes covered with the ceilings of medium- rounded pebblestone. Some of the tombs remained intact (in situ). Tombs 1, 2, 3, 4, and 5 are typical for the Podgorny stage of the Tagarsky culture, whereas tomb 6 refers to the Tes (Tesinsky) stage. The grave good sets are culturally typical including flat-bottomed jar-shaped vessels, bronze daggers, chekan battle axes, knives, awls, circular mirrors with a loop on the backside, half-spherical discs, cylindrical beads, conic beads, and a bone comb with a circular ornamentation.

Analytical Solution for the Actuators Influence Functions of a Circular Deformable Mirror with Free Edge under Concentrated Loads

Analytical Solution for the Actuators Influence Functions of a Circular Deformable Mirror with Free Edge under Concentrated Loads

Closing the Distance or, The (Im)possible Politics of The Yield in Carrie Mae Weems’ Not Manet’s Type

Through the prism of a circular mirror, a lone female figure presses her lower body against the foot of a bedpost leaving her smooth, strong back to face us. If we follow her gaze, we never meet he...

Investigation of U-shaped microfiber temperature sensor using a combination of thermal expansion of a metal and reflectivity of a silver coated mirror

An optical temperature sensor using a U-shaped microfiber incorporated with the thermal expansion of a metal plate and the reflection of a silver coated mirror is demonstrated. A microfiber about 5.8 μm waist diameter is fabricated using the systematic flame brushing technique, and lately, U-shaped structure is made. The proposed sensing mechanism uses the expansion of the metal plate and the reflectivity of the silver-coated circular shape mirror and measures the average output power change with respect to temperature variations. Two types of metal are investigated in this study, namely Aluminum (Al) and Copper (Cu), which have different thermal expansion coefficients. Therefore, when heated, the expansion of the metals occurs in a different degree, which affects the sensing mechanism, and therefore, a difference has been observed in terms of power loss with respect to the temperature variation. The sensitivity of the U-shape microfiber by using Al and Cu metal plates are measured as 0.0018 dB m/ ºC and 0.0007 dB m/ ºC, respectively. Moreover, the effect of a reflective mirror has also been investigated by placing the mirror on the top of the metal plates. With the inclusion of the mirror in the experimental set-up, the sensitivity of the U-shape microfiber using Al and Cu metal plates are measured as 0.0019 dB m/ ºC and 0.0012 dB m/ ºC, respectively.

Does a Circular Convex Blind Spot Mirror Increase the Driver’s Field of View?

&#x0D; &#x0D; &#x0D; Many road traffic accidents occur in Malaysia every year. Road fatalities has been one of the main causes of death in Malaysia. More than half of these fatalities were among motorcyclists. An accident between a passenger car and a motorcycle might be caused by the blind spot of the car driver, in which the driver was unable to notice an incoming motorcycle from behind or the side. Blind spot monitoring system has been developed using recent technology. However, this active blind spot monitoring system is expensive and only available in luxury cars. Another type of blind spot monitoring is known as passive blind spot monitoring by means of a convex mirror. Many convex blind mirrors are being sold nationwide that come in various shapes. Nonetheless, the effectiveness of this convex mirror has never been quantified. This study aims to experimentally quantify the effectiveness of this mirror by using a spotlight, projecting a direct light to the side mirror. A circular convex mirror was placed at four different locations, one at a time. It is hypothesised that the reflection of the light on a flat, white wall indicates the driver’s field of view. The area of the reflection was calculated using image processing, and the values of all five cases were compared. It was found that the circular convex mirror increases the field of view by up to 211 %. The position of the convex mirror plays an important role to ensure a maximum field of view is achieved. This paper has demonstrated that the usage of a circular convex mirror does increase the driver's field of view.&#x0D; &#x0D; &#x0D;

A Multi-Cubic-Meter Ioffe Trap for Project 8

The Project 8 direct neutrino mass experiment requires a superconducting magnet of unusual scale and complexity. Project 8 will use atomic tritium held in a magnetic bottle of 10 to 100 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> to reach well beyond the sensitivity of the presentgeneration experiment. Project 8 is based on a new spectroscopic method, Cyclotron Radiation Emission Spectroscopy (CRES), that requires a highly uniform magnetic field in the fiducial volume at the center of the atom trap. The maximum fluctuation ΔB/B is nominally 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> . To meet these requirements, we propose a modified version of a Ioffe trap to confine the neutral tritium atoms and provide a large fiducial volume for CRES. The key change from the traditional topology is to replace the circular mirror coils that close the trap ends with pleated closures formed from the same conductors as the rest of the trap. This dramatically expands the fiducial volume of the trap. CRES achieves its best sensitivity with a particular particle density; for the highest event rate, all of these particles should be tritium atoms. Cooling is required to remove the atoms' radioactive decay heat and prevent them evaporating from the trap. We leave the magnetic bottle uncapped and maintain an equilibrium atom density by continuously supplying new, cold atoms to replace the warmer ones lost via the loading opening. Pleated trap ends, for certain choices of the number of Ioffe conductors, naturally transition to an extended quadrupole through which we load the trap. For a trapped atom population of ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> atoms at a density of ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , a trap volume of tens of cubic meters is required. Previous magnets have not simultaneously achieved the combination of high field strength, high uniformity, and large volume required for Project 8.