Paraboloidal Mirror Research Articles

Regiomontanus angle maximization for catadioptric sensors with paraboloidal mirrors

Dioptric cameras with conventional perspective projection have well established analytical properties. However, they suffer from perspective distortions and only have a limited field of view. Catadioptric cameras offer panoramic imaging. Their extensive field of view together with projection specific image analysis, can simplify many computer vision tasks. Several properties of catadioptric projection for geometric primitives such as points and lines have been addressed and have also been used for calibration. However, higher order geometric properties are yet to be investigated. Such analysis is complicated by the specifics of the warping of the scene by catadioptric projection. One such property, that is the subject of this work, is the Regiomontanus angle maximization relative to the effective viewpoint of the sensor. This work considers catadioptric sensors with paraboloidal mirrors, that is, paracatadioptric sensors. Analytical ray tracing of a simplified 1D world object gives its projection in the image and an expression for its length. The optimization of the length of the projection results in a third degree equation for the Regiomontanus distance that can be solved explicitly. The Khayyam geometric solution of this equation provides the Regiomontanus distance of maximum subtended projection for these cameras. Applications of these results in various contexts are presented and discussed.

Unfiltering of the EarthCARE Broadband Radiometer (BBR) observations: the BM-RAD product

Abstract. The methodology to determine the unfiltered solar and thermal radiances from the measured EarthCARE Broadband Radiometer (BBR) shortwave (SW) and total-wave (TW) filtered radiances is presented. Within the EarthCARE ground processing, the correction for the effect of the BBR spectral responses, the unfiltering, is performed by the so-called BM-RAD processor which produces the level-2 BM-RAD product. The BM-RAD product refers to unfiltered broadband radiances that are derived from the BBR and the Multi-Spectral Imager (MSI) instruments on board the forthcoming EarthCARE satellite. The method is based on theoretical regressions between filtered and unfiltered radiances, as is done for the Clouds and the Earth's Radiant Energy System (CERES) and the Geostationary Earth Radiation Budget (GERB) instruments. The regressions are derived from a large geophysical database of spectral radiance curves simulated using radiative transfer models. Based on the radiative transfer computations, the unfiltering error, i.e., the error introduced by the small spectral variations of the BBR instrument response, is expected to remain well below 0.5 % in the shortwave (SW) and 0.1 % in the longwave (LW), at 1 standard deviation. These excellent performances are permitted by the very simple optics used in the BBR instrument: a telescope with a single paraboloid mirror. End-to-end verification of the unfiltering algorithm has been performed by running the BM-RAD processor on modelled level-1 BBR radiances obtained for three EarthCARE orbits simulated by an integrated forecasting and data assimilation system. The resulting unfiltered radiances are eventually compared to the solar and thermal radiances derived by radiative transfer simulations over the three EarthCARE orbits. In addition, this end-to-end verification has provided further evidence on the high accuracy of the unfiltered radiance process, with accuracies better than 0.5 % for SW and better than 0.1 % for LW.

Spatio-temporal characterization of tightly focused femtosecond laser fields formed by paraboloidal mirrors with different F-numbers.

The focusing spatiotemporal property of a femtosecond laser pulse is presented under tight focusing conditions by using the frequency-resolved incident electric field and vector diffraction formulas with the wavefront correction term. In the ideal case, the focused laser intensity reaches its maximum at the F-number of ∼0.35 due to the strong diffraction effect under extremely tight focusing conditions. In spatio-temporal coupling distortion cases, their spatiotemporal Strehl ratios show a trend of improvement as the F-number decreases and this phenomenon is mainly concentrated along the y-direction. Based on the numerical calculation method used in this work, the precise information of tightly focused ultra-intense femtosecond laser fields can be obtained, which is crucial for assessing a focused intensity and describing the motion of charged particles under an extremely strong electric field. Moreover, the evolution law of focal fields with spatiotemporal distortions found in this paper can offer some theoretical guidance for realizing ultrahigh laser intensity in the near future.

Novel high-flux indoor solar simulator for high temperature thermal processes

A novel 32 kWe high flux solar simulator compound of eight xenon arc lamps coupled with a truncated paraboloid mirror and a secondary paraboloid mirror was designed, built, and tested. Collimated rays from a set of xenon arc lamps emulating outdoor solar radiation were reflected by a secondary set of paraboloid mirrors to a common system focus. Relative irradiance measurements were performed to obtain the xenon arc lamp radiation spectrum. Thermal power delivered by each lamp was evaluated by using a heat flux gauge mounted at the system focus. Concentrated thermal power was estimated by the heat superposition method, which allowed us to quantify both the total and the concentrated peak power along with the heat flux mapping. A 10.2% energy conversion efficiency was achieved. Experimental results determined a 3.0 kW total concentrated power on a 100 mm spot diameter resulting in a 1028 kWm−2 peak flux at the center; a lamp total thermal radiant power average of 615 W was achieved, and the lamp spectrum was compared with the 6200 K blackbody radiation spectrum.

Continuous wave operation of terahertz metasurface quantum-cascade VECSEL with a long intra-cryostat cavity

We report continuous wave (cw) operation of a terahertz quantum-cascade vertical-external-cavity surface-emitting laser with an external cavity length of approximately 30 mm, benefited by an intra-cryostat focusing cavity. Compared to previous plano–plano cavities, an off-axis paraboloid mirror is introduced into the external cavity as a focusing element to reduce the diffraction loss and to enable cw lasing using small-area metasurfaces and long cavity lengths. The device shows lasing operation in the cw mode up to 111 K, and cw output power up to 11.5 mW at 77 K (0.5% wall-plug efficiency). A circular, directive beam pattern is collected, and free-running linewidths on the order of tens of kHz are measured over tens of seconds.

First light of BEaTriX, the new testing facility for the modular X-ray optics of the ATHENA mission

Aims. The Beam Expander Testing X-ray facility (BEaTriX) is a unique X-ray apparatus now operated at the Istituto Nazionale di Astrofisica (INAF), Osservatorio Astronomico di Brera (OAB), in Merate, Italy. It has been specifically designed to measure the point spread function (PSF) and the effective area (EA) of the X-ray mirror modules (MMs) of the Advanced Telescope for High-ENergy Astrophysics (ATHENA), based on silicon pore optics (SPO) technology, for verification before integration into the mirror assembly. To this end, BEaTriX generates a broad, uniform, monochromatic, and collimated X-ray beam at 4.51 keV. The beam collimation is better than a few arcseconds, ensuring reliable tests of the ATHENA MMs, in their focus at a 12 m distance. Methods. In BEaTriX, a micro-focus X-ray source with a titanium anode is placed in the focus of a paraboloidal mirror, which generates a parallel beam. A crystal monochromator selects the 4.51 keV line, which is expanded to the final size by a crystal asymmetrically cut with respect to the crystalline planes. An in-house-built Hartmann plate was used to characterize the X-ray beam divergence, observing the deviation of X-ray beams from the nominal positions, on a 12-m-distant CCD camera. After characterization, the BEaTriX beam has the nominal dimensions of 170 mm × 60 mm, with a vertical divergence of 1.65 arcsec and a horizontal divergence varying between 2.7 and 3.45 arcsec, depending on the monochromator setting: either high collimation or high intensity. The flux per area unit varies from 10 to 50 photons s−1 cm−2 from one configuration to the other. Results. The BEaTriX beam performance was tested using an SPO MM, whose entrance pupil was fully illuminated by the expanded beam, and its focus was directly imaged onto the camera. The first light test returned a PSF and an EA in full agreement with expectations. As of today, the 4.51 keV beamline of BEaTriX is operational and can characterize modular X-ray optics, measuring their PSF and EA with a typical exposure of 30 min. Another beamline at 1.49 keV is under development and will be integrated into the current equipment. We expect BEaTriX to be a crucial facility for the functional test of modular X-ray optics, such as the SPO MMs for ATHENA.

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS)

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) is a sounding rocket instrument that flew on July 30, 2021 from the White Sands Missile Range, NM. The instrument was designed to address specific science questions that require differential emission measures of the solar soft X-ray spectrum from 6 – 25[Formula: see text]Å(0.5 – 2.1[Formula: see text]keV). MaGIXS comprises a Wolter-I telescope, a slit-jaw imaging system, an identical pair of grazing incidence paraboloid mirrors, a planar grating and a CCD camera. While implementing this design, some limitations were encountered in the production of the X-ray mirrors, which ended up as a catalyst for the development of a deterministic polishing approach and an improved meteorological technique that utilizes a computer-generated hologram (CGH). The opto-mechanical design approach addressed the need to have adjustable and highly repeatable interfaces to allow for the complex alignment between the optical sub-assemblies. The alignment techniques employed when mounting the mirrors and throughout instrument integration and end-to-end testing are discussed. Also presented are spatial resolution measurements of the end-to-end point-spread-function that were obtained during testing in the X-ray Cryogenic Facility (XRCF) at NASA Marshall Space Flight Center. Lastly, unresolved issues and off-nominal performance are discussed.

Analytic descriptions of parabolic X-ray mirrors.

On X-ray beamlines and telescopes, glancing-incidence mirrors with parabolic profiles are used to collimate, focus, and collect light. Here, analytic descriptions for paraboloidal, plane-parabolic, and parabolic cylindrical mirrors in several congruent geometries that are commonly used in fabrication, metrology, and modeling are provided. The exact expressions are derived directly from Fermat's principle, without coordinate transformations, in several mirror-centered coordinate systems, including one with the surface tangent to the central point of intersection. Coefficients for a sixth-order polynomial series approximation are calculated for that coordinate system.

Steam and electrical power generation by a hybrid photovoltaic/parabolic dish concentrator using beam splitter technology

The parabolic dish is considered the most performant concentrating solar power (CSP) technology since it fits a wide range of domestic and industrial processes and offers better modular deployment than other CSP technologies such as thermal power receivers. The parabolic dish has been widely employed to produce steam and electricity especially when it works in conjunction with Stirling engines; however, the extreme complexity of the latter makes the power generation cost of this technology unfavorable against other competing solutions. In this paper, a comprehensive and detailed optical and thermal performance analysis and optimization study of a hybrid photovoltaic/parabolic dish concentrator with a conical thermal receiver using a beam splitter filter (PV/PDC-CTR-BSF) are carried out. A complete modeling module is developed to assess and optimize the overall yields of the PV/PDC-CTR-BSF. The present work is unique since it encompasses a sophisticated simulation tool enabling performance potential assessment of a novel PV/PDC-CTR-BSF system coupled with a novel conical-shaped helical coiled-tube heat exchanger for steam production and paves the avenue for higher electrical yield using single-junction PV cells mounted over the tip surface area of the paraboloid mirrors. The concentrated solar density (CSD) distribution, optical efficiency, temperature distribution, and steam fraction have particular interest in the performance assessment of the innovative PV/PDC-CTR-BSF package system. As a result, the maximum value of the CSD at the conical cavity receiver and the PV cells is 40 and 8 kW/m2, respectively. The optical efficiency of the proposed design has a breakthrough in the record of the typical hybrid designs reaching the value of 67%. Moreover, the maximum surface solar cells temperature was 80°C, while the temperature reached 170°C at the conical cavity receiver. The optical new hybrid design has maximized the steam productivity up to a steam volume fraction of 98%.

HDROmni: Optical Extension of Dynamic Range for Panoramic Robot Vision

This paper presents the design method to optically extend the perceptible dynamic range of panoramic vision for robotics. The large range of scene radiance is captured in real-time by a combination of paraboloidal mirrors, a telecentric lens and neutral density filters. The first prototype made of 4 mirrors and 3 neutral density filters increases 100 times the perceptible dynamic range of the used camera. Results in various challenging scenes compare the new camera to low dynamic range ones. They show that the dynamic range quality of images doubles, on average. They also show significant benefit for feature-based approaches, i.e. much more matched features, and direct ones, i.e. much higher positioning accuracy of direct visual servoing.

Heat accumulation temperature measurement in ultrashort pulse laser micromachining

Ultrashort pulse laser micromachining is affected by the heat accumulation resulting from the residual heat from previous laser pulses on the sample surface. Up to now, most of the works analysed the accumulation by numerical modelling. The present work focussed on development and application for the first time of a measurement system of heat accumulation temperature directly during the processes in nanosecond and microsecond time ranges. The measurement system was based on the infrared radiometry and contained liquid nitrogen cooled fast HgCdTe photodetector and paraboloid mirrors. Micromachining of grooves was done using a 14 W picosecond laser with different pulse energies, repetition frequencies and scanning speeds. Calibration of the measurement system was done in order to obtain temperatures from the measured signal. The calibration was not straightforward due to very small laser spot (25 μm), small signal and changing of the size of the heated area for low scanning speeds. Obtained heat accumulation temperature ranged from 300°C to 2600°C for scanning speeds from 8 m/s to 0.07 m/s and pulse energies from 0.1 µJ to 100 µJ. According to the scanning electron microscope (SEM) images, the material was already partially melted (small droplets on boarders) for low scanning speeds. Surface roughness and ablation rate were determined by 3D confocal laser microscope. Good correlation was found between the roughness and the heat accumulation temperature, thus confirming the validity of calibration. Measured heat accumulation temperature was surprisingly the highest for the most efficient ablation parameters and at the same time low surface roughness was achieved.

In-situ deflectometric measurement of optical surfaces for precision manufacturing

The in-situ measurement of complex optical surfaces is a challenging task in precision engineering. The phase measuring deflectometry is a powerful measuring method for complex specular surfaces, and it has higher measuring efficiency, stability and dynamic range compared to interferometry. Consequently it is promising to widespread applications in various fields. Deflectometry is essentially a calibration problem, and the measuring accuracy is directly determined by the quality of geometrical calibration. An in-situ deflectometric measuring system is designed based on the single point diamond turning machine. A self-calibration method is developed to specify the relative positions of the camera and screen. Ray tracing is conducted at two positions of an auxiliary reflecting mirror, which is mounted on an air bearing spindle. The accuracy of the geometrical positions can be improved by an order of magnitude by minimizing the deviations of the traced points with respect to the true correspondences. According to the statistical properties of the deviations in reverse ray tracing, the form errors and the position errors can be separated, and the positioning error of the workpiece can be corrected accordingly. Henceforth, the nominal shape of the fabricated workpiece can be fully utilized, and the conventional one-way position-form mapping can be converted into a two-way mapping problem. As for the complex shapes, the whole surface can be covered by sub-aperture measurement. Precise localization of a local region under test is achieved by multi-position imaging, so that correct convergence of the iterative reconstruction process can be guaranteed. Several typical optical surfaces including an off-axis paraboloid mirror are measured, and the measuring accuracy of the proposed method is proved better than 150 nm RMS.

Deployment dynamics for flexible deployable primary mirror of space telescope with paraboloidal and laminated structure by using absolute node coordinate method

A nonlinear dynamic modeling method for primary mirror of Flower-like Deployable Space Telescope (F-DST) undergoing large deployment motion is proposed in this paper. To ensure pointing accuracy and attitude stability of the paraboloidal primary mirror, the mirror is discretized into equal thickness shell elements by considering shell curvature. And the material nonlinear constitutive relation of flexible mirror is acquired using Absolute Nodal Coordinate Formulation (ANCF). Furthermore, the primary mirror of F-DST can be regarded as a clustered multi-body system, and its dynamic equations of elastic deformation and deployment motion are established by virtual work principle. Finally, the deployment motion of primary mirror by different driving conditions are simulated, the results show that the vibrations of mirrors that driven by elastic hinge device are more than that driven by servo motor. In addition, single sub-mirror deployment process will perturb the pointing accuracy of primary mirror, and the multiple sub-mirrors simultaneously deploying will seriously affect all the sub-mirrors surface accuracy because of the coupling effect. Thus, there are theoretical value and practical significance for the controlling surface accuracy and attitude accuracy of space telescope.

Measurement and Compensation of Tool Contour Error Using White Light Interferometry for Ultra-Precision Diamond Turning of Freeform Surfaces

In ultra-precision diamond turning of freeform optics, it is necessary to obtain submicron-level form accuracy with high efficiency. In this study, we proposed a new method for the quick measurement and compensation of tool contour errors to improve the form accuracy of the workpiece. In this method, the nanometer-scale contour error of a diamond tool is quickly and precisely measured using a white light interferometer and then compensated for, before machining. Results showed that the contour of a diamond tool was measured with an error less than 0.05 μm peak-to-valley (P-V) and the feasibility of error compensation was verified through cutting experiments to create a paraboloid mirror and a microlens array. The form error decreased to 0.2 μm P-V regardless of the contour error of the diamond tools when cutting the paraboloid mirror, and that of the microlens array was reduced to 0.15 μm P-V during a single machining step.

Development and in-orbit performance evaluation of multi-layered nested grazing incidence optics

On November 10, 2016, China launched an X-ray pulsar navigation test satellite (XPNAV-1) to investigate the X-ray pulsar navigation technology, and a lot of scientific observation data have been obtained. The X-ray grazing incidence optics is a critical component of the focusing pulsar telescope. It plays an important role in increasing the effective area and enhancing the sensitivity of the telescope. It is also the first grazing incidence optics verified in orbit in China. According to the characteristic that the times of arrival (TOA) of X-ray photons are measured in pulsar navigation, the grazing incidence focusing optics based on single-reflection paraboloid mirror is designed, and manufacturable mirror design parameters are obtained through theoretical calculation and derivation. The theoretical effective area of the designed optics is 15.6 cm<sup>2</sup> at 1 keV. The designed optics is then simulated to evaluate its focusing performance. It meets the focusing requirement in the full field of view. The electroforming nickel replication process used for manufacturing the mirrors for XMM-Newton and eRosita missions is investigated. A super-smooth mandrel is firstly fabricated and used for follow-up replication. An about-100 nm-thick gold layer is deposited on the mandrel, and serves as the reflection and release layer of the mirror. The nickel substrate of the mirror is electroformed on the gold layer. The mirror is finally obtained by releasing the nickel and gold layer from the mandrel. The patterns and roughness of the mandrel are then replicated onto the inner surface of the mirror. The 4-layered mirror is fabricated for the optics. The reflectivity for each layer of the 4-layered mirror is then measured with a dedicated facility on 4B7B beamline of BSRF. The effective area of the optics based on the above-measured reflectivity is 13.2 cm<sup>2</sup> at 1 keV. Finally, according to the in-orbit observation data, the effective area of the optical system is evaluated to be a typical value of 4.22 cm<sup>2</sup> at 1 keV, which is less than the ground-tested value. The reason for this is analyzed and it turns out to be due to the thermal deformation of mechanical structure and contamination of the mirrors. Therefore, in our future work, we will strictly control the environmental factors and implement space environmental adaptability design, while increasing the accuracy of the optics.

DETERMINATION OF THE DENSITY VALUE SPECIFICALLY AT THE FOCAL POINT OF THE MIRROR CONCENTRATING SYSTEM

When designing mirror concentrating systems, it is necessary to determine in advance the optical-geometric and optical-energy characteristics of the installation. One is required to choose the mirrors with a reflection coefficient to satisfy the expected energy distribution in the focal area and to pay attention to the accuracy of the reflective surfaces of the mirrors, to the accuracy of the tracking system of the heliostats to the trajectory of the apparent motion of the Sun, to the partial shading to the reflective surfaces, etc. Based on these data, it is necessary to calculate the irradiance distribution in the focal zone of the installation. During installation and utilization of the equipment it is necessary to measure and monitor these parameters and, if necessary, to recalculate the energy distribution taking into account the new parameters.The methods for calculating the density distribution of the radiant flux in the focal zone of mirror-concentrating systems have been developed in parallel with the requirements of exploitation. They do not always correctly reflect the true picture formed in the focus of the heliostat. In this paper, the analysis presents the existing methods for calculating paraboloid concentrators based on the Gaussian distribution of energy in the focal plane. Developing the method of fallen and reflected elementary cone beam and on the basis of generated scattered optical images of the Sun and of the visible angular size (2γо = 32 angle of minutes) of the Sun, which shows non-Gaussian nature of the resulting distribution in the focal plane due to the influence of aberration of the optical paraboloidal surface depending on the change of the aperture angle 2U, we obtained an analytical calculation formula to determine the value of the concentrated radiant flux specifically at the focal point of a paraboloid mirror concentrating system.

EXERGY ANALYSIS OF DIRECT SUN RADIATION CONCENTRATION

In the article substantiates that the exergy method of thermodynamic analysis, along with the entropy method, makes it possible to determine the locations of the most significant thermodynamic losses in energy conversion processes. It is shown that the use of exergy analysis makes it possible to estimate the thermodynamic losses at each stage of the energy conversion scheme and to reduce them. It is proved that exergetic analysis of the concentration of solar radiation in solar installations with paraboloid mirrors, as well as in optical systems of tower solar thermal plants with horizontal fields of flat heliostats and thermal power plants with horizontal parabolic cylindrical mirrors will allow to increase the energy of these transformations. Exergy analysis of the concentration of solar radiation was performed. For the first time, solar radiation is treated as radiant heat flux, which is characterized by its own temperature, and its exergy is determined within the canonical Carnot cycle. On the basis of the new interpretation of the temperature of the radiant flux, an analytical expression was obtained for the radiation temperature of the thermal radiation of the Sun, both for direct radiation and for diffuse. The dependence of the direct solar radiation density on the mass of the atmosphere is found. The above formulas allow to calculate the radiation temperature of solar radiation and the density of exergy flux on the Earth's surface and in the focus of the concentrator mirror.

Design and testing of an externally-coupled planar waveguide photobioreactor

Waveguides can be used to deliver light deep into algal photobioreactors, allowing the growth of algal biofilms with high areal yield. A current drawback of these reactors is their dependency upon artificial illumination. A more practical approach would be to use direct sunlight to illuminate the waveguide photobioreactor. In this paper a novel optical system is designed to grow algal biofilm using waveguides illuminated with external light using 3D-printed paraboloidal mirrors. It was found that the polygonal approximation of a compound parabolic trough was an effective mechanism for focusing external natural light, which could be constructed easily. It is also demonstrated that algae biofilm biomass productivity on the waveguide increases by a factor of 2.5 when operated in conjunction with mirrored troughs.

Mirror Surface Assessment in Solar Power Applications by 2-D Coded Light

Concentrative mirrors are typically used to provide the reliable thermal source in solar thermal power applications. Their geometrical optical characteristics are of essential importance to the sun-to-electricity conversion efficiency. However, there is a lack of cost-effective approach for measuring these characteristics in field applications. In this article, we propose a color-coded grid pattern-based method to extract optical properties of paraboloidal mirrors. Comparing with the existing techniques, our assessment system only consists of a digital camera, a color-coded grid plane, and a flat mirror with chess-board pattern, and no additional equipments are required. In our system, the image of the grid pattern is captured by the camera through the reflection of the test mirror. Benefiting from the representation of grid positions with colors, the image points can be easily paired with their source points on the grid plane. Applying ray-tracing and reflection principle, the normal vectors of the reflecting points on the test mirror surface can be determined. These normals facilitate to construct the surface model in the form of a second-order polynomial. The gradient descent algorithm is used to minimize the discrepancy between the measured normals and those calculated from a guess model, by which we improve the accuracy of the model parameters and, finally, obtain the optical properties of the test mirror. The accuracy and efficiency of the proposed method are verified by a set of numerical simulations with respect to mirrors with known parameters. Also, for a real concentrative mirror, the proposed method helps to retrieve quantities of interest and show little dependence on mirror position.

Radiative properties of scattering media containing directionally controlled nanofibers

Directional control of radiation could be useful in a range of scientific and industrial applications. This study evaluated the possibility of directional control of radiation using nanofibers. Herein, scattering media containing directionally controlled nanofibers were assembled, and their relative directional radiative intensity was measured by constructing an optical system comprising a paraboloidal mirror and a charge-coupled device (CCD) camera. The influence of polarized light on relative light intensity was confirmed and compared to the theoretical result of a single nanofiber. The scattering direction of the scattered light was found to differ based on the material and size of the nanofibers. In addition, the scattering direction of the scattered light changed according to the incident angle of the irradiated light. Therefore, the results of this study suggest that radiation can be directionally controlled using a scattering medium containing nanofibers with controlled orientations.