Mirror Shape Research Articles

Remote Measurement of Heliostat Reflectivity with the Backward Gazing Procedure

Concentrated solar power is a promising technique enabling renewable energy production with large scale solar power plants in the near future. Estimating quantitatively the reflectivity of a solar concentrator is a major issue, since it has a significant impact on the flux distribution formed at the solar receiver. Moreover, it is desirable that the mirrors can be measured during operation in order to evaluate environmental factors such as day/night thermal cycles or soiling and ageing effects at the reflective surfaces. For that purpose, a backward gazing method that was originally developed to measure mirror shape and misalignment error was developed. The method operates in quasi real-time without disturbing the heat production process. It was successfully tested at the Themis solar tower power plant in Targasonne, France. Its basic principle consists in acquiring four simultaneous images of a Sun-tracking heliostat, captured from different observation points located near the thermal receiver. The images are then processed with a minimization algorithm allowing the determination of the reflectance and slopes errors of the mirrors. In this communication, it is shown that the algorithm allows one to get quantitative reflectivity maps at the surface of the heliostat. The measurement is fully remote and is used to evaluate surface reflectivity that depends on optical coatings quality and soiling effects. Preliminary results obtained with a Themis heliostat are presented. They show that reflectivity measurements can be carried out within repeatability about ± 5% Peak-to-Valley (PTV) and 1% RMS. Ways to improving these numbers are discussed in the paper.

Variation in Reflected Beam Shape and Pointing Accuracy Over Time and Heliostat Field Position

Heliostats are typically constructed with fixed mirror shapes, which they move to varying angles to reflect sunlight onto a receiver. While heliostat facet curvatures and canting angles are selected to maximize a chosen performance criterion, these fixed shapes inevitably cannot maintain focus throughout widely varying solar incidence angles. Further, heliostat pointing accuracy generally exhibits error due to manufacturing and installation imperfections. In this paper we present a systematic study of how reflected beam shape and pointing accuracy vary with heliostat position, time of day, and time of year. We selected nine heliostats spanning the Sandia National Laboratories National Solar Thermal Test Facility (NSTTF) heliostat field, and measured their beam shape and required pointing corrections throughout the day, for six key dates spanning a solar year. We also present ray tracing analysis to aid understanding of the observed effects. The resulting data provide insight into the nature and magnitude of heliostat focus loss at various times, and clarify the nature of the problem faced when attempting to maximize heliostat field performance, especially for high-temperature industrial applications. We conclude that fixed heliostat fields canted with an off-axis strategy will lose significant performance away from the solar noon hour to which they are tuned, and that aim point corrections can vary widely, both between independent heliostats and over time for a given heiostat. This implies that multiple measurements of each heliostat are required to determine calibration pointing corrections.

Active-compensation of systematic error for the 1000 mm aperture flat interferometer

Large-aperture elements would induce unnegligible systematic errors due to material inhomogeneity, manufacturing or gravity, that are difficult to correct in an extreme large aperture flat interferometer and result in reference wavefront distortion. We propose an active-compensation method for systematic errors by employing a deformable mirror into the interferometer to modulate reference wavefront. A mapping relationship between sag of the deformable mirror and reference wavefront error is derived by theory of matrix optics, and two interferometer optical paths are designed for whether the deformable mirror is located at the pupil or not. The algorithm for calculating and controlling the sag of a deformable mirror can eliminate the need for the deformable mirror to be positioned at the pupil in order to achieve controllable modulation of the wavefront. This algorithm has been validated through the intentional introduction of systematic errors into the 1000 mm aperture flat interferometer for effective compensation. Moreover, the optimization algorithm in Ansys Zemax is utilized to calculate the optimal solution for surface shape of the deformable mirror, treating it as a nominal value. The algorithm error is on the order of 10−6 mm, falling within the acceptable tolerance range for the deformable mirror's surface shape.

Single-Image Super-Resolution Method for Rotating Synthetic Aperture System Using Masking Mechanism

The emerging technology of rotating synthetic aperture (RSA) presents a promising solution for the development of lightweight, large-aperture, and high-resolution optical remote sensing systems in geostationary orbit. However, the rectangular shape of the primary mirror and the distinctive imaging mechanism involving the continuous rotation of the mirror lead to a pronounced decline in image resolution along the shorter side of the rectangle compared to the longer side. The resolution also exhibits periodic time-varying characteristics. To address these limitations and enhance image quality, we begin by analyzing the imaging mechanism of the RSA system. Subsequently, we propose a single-image super-resolution method that utilizes a rotated varied-size window attention mechanism instead of full attention, based on the Vision Transformer architecture. We employ a two-stage training methodology for the network, where we pre-train it on images masked with stripe-shaped masks along the shorter side of the rectangular pupil. Following that, we fine-tune the network using unmasked images. Through the strip-wise mask sampling strategy, this two-stage training approach effectively circumvents the interference of lower confidence (clarity) information and outperforms training the network from scratch using the unmasked degraded images. Our digital simulation and semi-physical imaging experiments demonstrate that the proposed method achieves satisfactory performance. This work establishes a valuable reference for future space applications of the RSA system.

Optimization of the Reflective Surface Shape of a Variable Curvature Mirror

Optimization of the Reflective Surface Shape of a Variable Curvature Mirror

A hybrid surface shape control method for optimizing thermal deformation of FEL reflection mirror

The surface shape errors induced by thermal deformation of the free electron lasers (FEL) beamline reflection mirror directly affect the quality of FEL beam. In order to reduce the thermal deformation and meet the stringent requirements of surface shape error of the FEL reflection mirror, this paper proposes a surface shape control method that combines mirror bending and active thermal control (ATC) technique, aiming to minimize surface shape errors and enhance the overall performance of the FEL beamline. A bending mechanism has been designed to achieve a bending sensitivity of 60 nrad RMS/N using only one bending actuator. It does not obstruct the FEL beam with extremely small incident angle. This mechanism can compensate for thermal deformation by eliminating the cylindrical surface component of the thermal deformation. Additionally, a novel ATC algorithm is proposed based on the Tikhonov regularization method. When combined with the bending mechanism, it proves effective in controlling the surface shape of the reflection mirror. The simulation results indicate that this surface control method can effectively reduce the surface shape errors of the reflection mirror. Taking the 3 nm wavelength FEL as an example, the RMS value of surface slope error of the reflection mirror is substantially reduced from 17.1974 μrad (with heat load) to 0.0913 μrad after bending. Based on the bending result, the ATC technique further reduces the slope error to 0.0303 μrad RMS. For 1 nm and 2 nm wavelength FELs, the mirror slope errors ultimately reach 0.0147 μrad RMS and 0.0295 μrad RMS respectively. This surface shape control method ensures that the reflection mirror slope errors meet the beamline requirement, which is 0.05 μrad RMS, thereby guaranteeing the beam quality.

Investigation into the Co-Phase Detection Methodology for Segmented Plane Mirrors Utilizing Grazing Incidence Interferometry

Segmented plane mirrors constitute a crucial component in the self-aligned detection process for large-aperture space optical imaging systems. Surface shape errors inherent in segmented plane mirrors primarily manifest as tilt errors and piston errors between sub-mirrors. While the detection and adjustment techniques for tilt errors are well-established, addressing piston errors poses a more formidable challenge. This study introduces a novel approach to achieve long-range, high-precision, and efficient co-phase detection of segmented plane mirrors by proposing a segmented plane mirror shape detection method based on grazing incidence interferometry. This method serves to broaden the detection range of piston errors, mitigate the issue of the 2π ambiguity resulting from piston errors in co-phase detection, and extend the detection capabilities of the interferometer. By manipulating the incident angle of the interferometer, both rough and precise adjustments of the segmented plane mirrors can be effectively executed.

Visadapt: Catadioptric adaptive camera for scenes of variable density of visual information

This paper presents the design method of a multi-resolution camera, named Visadapt. It is made of a conventional compact camera with a sensor and a lens pointed to a new deformable mirror so that the mirror in a flat state is parallel to the image plane. The main novelty of the latter mirror, to our knowledge, is the ability to control automatically strokes of several millimeters. This allows Visadapt to capture scenes with a spatially variable density of visual information. A grid of linear actuators, set underneath the mirror surface, deforms the mirror to reach the desired shape computed to capture several areas of different resolutions. Mechanical simulations are allowed to iterate on Visadapt’s design, to reduce the geometrical distortions in the images. Evaluations made on an actual prototype of Visadapt show that, by adapting the mirror shape, this camera can magnify a scene object up to 20%, even off-centered in the field-of-view, while still perceiving the rest of the scene.

Evaluation of the effect of mirror shape distortions on the optical quality of radiation in unstable resonators

Evaluation of the effect of mirror shape distortions on the optical quality of radiation in unstable resonators

Soft-X-ray nanobeams formed by aberration-reduced elliptical mirrors with large numerical aperture.

X-ray focusing mirrors often employ the Kirkpatrick-Baez (KB) geometry, which sequentially crosses two elliptic-cylindrical mirrors in grazing-incidence configurations. However, KB mirrors do not satisfy the Abbe sine condition and thus potentially expand the focus size with severe coma aberration. Satisfying the Abbe sine condition complicates mirror shapes or increases the number of ultraprecision mirrors required. The present study shows that the focal length and mirror length of KB mirrors have to be shortened to simultaneously achieve a large numerical aperture and reduced aberration. Such ultracompact KB (ucKB) mirrors are examined using a simulation that combines ray tracing and wave propagation. The focus intensity distributions show that ucKB mirrors suppress the aberration produced by their rotation errors and that they robustly achieve diffraction-limited focusing. The simulation results are confirmed in a synchrotron radiation experiment. ucKB mirrors can be advantageous for soft-X-ray nanoprobes, which require focusing devices to achieve a large numerical aperture.

Convolutional neural networks for mode on-demand high finesse optical resonator design

We demonstrate the use of machine learning through convolutional neural networks to solve inverse design problems of optical resonator engineering. The neural network finds a harmonic modulation of a spherical mirror to generate a resonator mode with a given target topology (“mode on-demand”). The procedure allows us to optimize the shape of mirrors to achieve a significantly enhanced coupling strength and cooperativity between a resonator photon and a quantum emitter located at the center of the resonator. In a second example, a double-peak mode is designed which would enhance the interaction between two quantum emitters, e.g., for quantum information processing.

Fundamental study on optical performance of low-melting-point metal mirrors for space telescopes

The installation of telescopes with larger primary mirrors in outer space is required for the study of the early universe. However, the shipping, assembling and maintenance of the primary mirror are technical challenges. The primary mirror made of low-melting-point metal (LMPM) enables to simplify these procedures. The rotating liquid metal surface is shaped into a parabola and solidified on the site. The technological feasibility depends on the dynamic transformation of the parabolic LMPM mirror and its optical reflectance. The dynamic transformation of LMPM mirror was clarified by means of experiments with liquid gallium (Ga) which has a melting point of 302.91 K. The parabolic shape of solid Ga mirror was produced by the axial rotation and the solidification. The parabolic shape agreed with the theoretical curve obtained by a physical model. The reflectance spectra on the surface of various LMPMs solidified (i.e., Ga, lead (Pb), tin (Sn), bismuth (Bi), lead-bismuth eutectic (Pb-Bi) and Wood’s metal (Bi-Pb-Sn-Cd)) were measured. The reflectance of Ga solidified was approximately 70 % and was not degraded in the near-infrared wavelength due to the favorable optical characteristics. The reflectance both for p-polarized and s-polarized light of Ga solidified was measured by the spectrophotometer with the polarizer at the angle of incidence of 30°, 45°, 60° and 75°. The trend of measured reflectance agreed with theoretical prediction.

Hybrid ball-hinged secondary mirror assembly for high-precision surface shape maintenance.

As an essential part of optical telescope, the secondary mirror is subject to the influence of ambient temperature, which leads to temperature-induced distortion on the surface shape. A hybrid ball-hinged secondary mirror assembly (HSMA) is proposed to achieve thermal adaptation over a wide range of temperature. Simulation investigation on the temperature-induced surface shape distortion of the HSMA were carried out by using the finite element model. Simulation results show that the change of secondary mirror surface distortions over a wide range of temperature are minimal and negligible. For the wide ambient temperature range from -30°C to 70°C, the PV and RMS values of the maximum residual distortions can reach as small as 16.31 nm and 3.005 nm, respectively. Furthermore, the influence of gravity-induced distortion on the surface shape is also carried out. Both simulation and experiment results show that the HSMA is able to maintain high-precision surface shape of the secondary mirror over a wide range of temperature and at different attitudes from 0 to 90 ∘.

Shape optimization design of the offset mirror in FEL-1 beamline at S3FEL

Nowadays, due to the advantages of high peak power, high average power, ultra-short pulse, and fully coherent characteristics, the high-repetition-rate free-electron laser (FEL) is thriving in many countries around the world. The thermal load caused by high-repetition-rate FEL poses a great challenge to the mirror surface shape. Especially in the case of high average power, how to perfectly control the mirror shape to maintain the coherence of the beam has become a difficult problem in beamline design. In addition to multi-segment PZT, when multiple resistive heaters are used to compensate for the mirror shape, the heat flux (or power) generated by each heater must be optimized to obtain sub-nanometer height error. This article establishes MHCKF model for the mirror surface deformation under the combined effect of the mirror initial deformation, the thermal deformation caused by X-rays, and the deformation compensated by multiple heaters. By searching the perturbation term in the mathematical model, the least squares solution of the heat fluxes generated by all heaters can be obtained. This method can not only set multiple constraints on the heat fluxes but also quickly obtain their values when minimizing the mirror shape error. It overcomes the problem of time-consuming optimization processes encountered by traditional finite element analysis software, especially in the context of multi-parameter optimization. This article focuses on the offset mirror in the FEL-1 beamline at S3FEL. Using this method, the optimization of 25 heat fluxes generated by all resistive heaters was accomplished within a few seconds utilizing an ordinary laptop. The results indicate that the height error RMS decreased from 40 nm to 0.009 nm, and the slope error RMS reduced from 192.7nrad to 0.4nrad. Wave-optics simulations show that the wavefront quality has been significantly improved. In addition, some factors affecting mirror shape error, such as the number of heaters, higher repetition rate, film coefficient, and the length of copper tube, were analyzed. The results show that the MHCKF model and optimization algorithm can effectively solve the optimization problem of compensating for the mirror shape with multiple heaters.

Optimization study on the influence of rearview mirror and side window glass on interior noise

Based on the LES model, the compressible transient CFD simulation combined with the acoustic finite element method optimizes the effect of the rearview mirror and side window glass on in-vehicle noise from the perspective of sound source and transmission. The primary and secondary orders of the influence of different mirror shape and side window glass geometric parameters on the noise in the car were obtained through the design and analysis of orthogonal experiments, and the results of the flow and sound fields were compared. The following results are presented: acoustic source noise reduction from the rearview mirror is mainly affected by acoustic pressure excitation. The proportion of the mirror body of the rearview mirror, the angle of the lower edge, and the length of the mirror column affect the noise in the car in turn. The noise reduction control with PVB laminated glass as the transmission path is mainly limited by the low frequency turbulent pressure excitation. The inner and outer thicknesses of PVB laminated glass have different influences on the noise in the car under different frequency bands, and the results in the full frequency band are mainly affected by the low frequency band.

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines.

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

Surface figure correction with roughness reduction using carbon-doped platinum film for high-precision X-ray mirror fabrication.

To obtain the surface shape of an X-ray mirror with high precision, a differential deposition method was used instead of a direct removal method. To modify the mirror surface shape using the differential deposition method, it is necessary to coat it with a thick film, and the co-deposition method is used to suppress the increase in surface roughness. The addition of C to the Pt thin film, which is often used as an X-ray optical thin film, resulted in lower surface roughness compared with that with the Pt coating alone, and the stress change according to the thin film thickness was evaluated. Differential deposition controls the speed of the substrate during coating based on continuous motion. The stage was controlled by calculating the dwell time through deconvolution calculations based on the accurate measurement of the unit coating distribution and target shape. We successfully fabricated an X-ray mirror with high precision. This study indicated that an X-ray mirror surface could be manufactured by modifying the surface shape at a micrometer level through the coating. Changing the shape of existing mirrors can not only result in the manufacture of high-precision X-ray mirrors but also improve their performance.

ОБ ИНДИЙСКОМ ЗЕРКАЛЕ ИЗ РОГОЗИХИ-1 И ПРЕДВИДЕНИИ А. П. УМАНСКОГО

The «elephant scene» complex on the discovered by A. P. Umansky in 1985 rattle-mirror has been considered by many researchers. Alexey Pavlovich was particularly interested in it as well. In his opinion, the mirror shape and image semantics are connected with Hinduism religious mythology, and the scene is a solemn festive procession. Materials from Pakistan, India and Thailand support both of these provisions of A. P. Umansky. According to the summarised data, the back side of the rattle-mirrors with the cone and platens was a kind of Buddhist mandala variant with a conical projection in the center and concentric circles. The comparative analysis of the scenes on the mirror and a jar from Himachal Pradesh leaves no doubt about marches with musicians, dancers and elephants depiction. Such real or virtual processions content in North India in the second half of the I thousand BC may have varied considerably, but it was usually based on religious beliefs. It is possible that they were connected with the afterlife as A. P. Umansky envisaged.

Геодезическое обеспечение выверки формы отражающей поверхности главного зеркала радиотелескопа с применением лазерных трекеров

The article discusses the possibilities of coordinate-determining technology using high-precision geodetic instruments for alignment of reflecting surface shape of the radio telescope main mirror. It’s important for adjustment of reflecting surface shape and consequently performance of radio astronomy observations. The article provides general information about radio telescopes and consideres the existing classical geodesic and non-geodesic methods used in the process of solving the problem of shape alignment. The text describes the method of geodetic work on the form alignment using high-precision laser trackers. The methodology includes several stages from designing the geodetic control network and tracker location stations and processing and interpreting the measurement results. The conditions for performing high-precision measurements are given in the thesis. Mathematical processing of measurement results is performed in the Spatial Analyzer and based on coordinate systems transformation.

Data-driven modeling and control of an X-ray bimorph adaptive mirror.

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.