Mirror Telescope Research Articles

Method for the design of nonaxially symmetric optical systems using free-form surfaces (Erratum)

We made an error of scale in section six of our paper [Opt. Eng., 57(10), 101704 (2018). doi: https://doi.org/10.1117/1.OE.57.10.101704] that resulted in an inappropriate comparison. After properly scaling and optimizing our three mirror telescope design the averaged over the field RMS spot size is 10.4 μm and this represents an improvement of about 26% and not of 40%. We find that the Zf(r) surfaces, the XY polynomial surfaces, and the NURBS surfaces are able to model the mirror system with similar RMS spot size performance.

Correction of wind bias for the lidar on board Aeolus using telescope temperatures

Abstract. The European Space Agency (ESA) Earth Explorer satellite Aeolus provides continuous profiles of the horizontal line-of-sight wind component globally from space. It was successfully launched in August 2018 with the goal to improve numerical weather prediction (NWP). Aeolus data have already been successfully assimilated into several NWP models and have already helped to significantly improve the quality of weather forecasts. To achieve this major milestone the identification and correction of several systematic error sources were necessary. One of them is related to small fluctuations of the temperatures across the 1.5 m diameter primary mirror of the telescope which cause varying wind biases along the orbit of up to 8 m s−1. This paper presents a detailed overview of the influence of the telescope temperature variations on the Aeolus wind products and describes the approach to correct for this systematic error source in the operational near-real-time (NRT) processing. It was shown that the telescope temperature variations along the orbit are due to changes in the top-of-atmosphere reflected shortwave and outgoing longwave radiation of the Earth and the related response of the telescope's thermal control system. To correct for this effect ECMWF model-equivalent winds are used as a reference to describe the wind bias in a multiple linear regression model as a function of various temperature sensors located on the primary telescope mirror. This correction scheme has been in operational use at ECMWF since April 2020 and is capable of reducing a large part of the telescope-induced wind bias. In cases where the influence of the temperature variations is particularly strong it was shown that the bias correction can improve the orbital bias variation by up to 53 %. Moreover, it was demonstrated that the approach of using ECMWF model-equivalent winds is justified by the fact that the global bias of model u-component winds with respect to radiosondes is smaller than 0.3 m s−1. Furthermore, this paper presents the alternative of using Aeolus ground return winds which serve as a zero-wind reference in the multiple linear regression model. The results show that the approach based on ground return winds only performs 10.8 % worse than the ECMWF model-based approach and thus has a good potential for future applications for upcoming reprocessing campaigns or even in the NRT processing of Aeolus wind products.

Piston detection in segmented telescopes via multiple neural networks coordination of feature-enhanced images

High-precision piston detection within a large capture range is a key for segmented telescopes. In this paper, we propose a simple and efficient piston detection method based on multiple neural networks coordination. By setting a mask with a sparse multi-subpupil configuration at conjugate plane of the segmented mirror, a new dataset that is extremely sensitive to the piston is created. And two kinds of neural networks are built for different stages of detection, which ensures the method is of both large-scale and high-precision. Simulation shows that the piston can be detected in the range of the coherence length of the operating light with a sub-nanometer scale precision by this method. This method is robust and does not require complex hardware. It can be widely applied in segmented and deployable primary mirror telescopes.

Design and Numerical Analysis of an Infrared Cassegrain Telescope Based on Reflective Metasurfaces.

Reflective imaging systems such as Cassegrain-type telescopes are widely utilized in astronomical observations. However, curved mirrors in traditional Cassegrain telescopes unavoidably make the imaging system bulky and costly. Recent developments in the field of metasurfaces provide an alternative way to construct optical systems, possessing the potential to make the whole system flat, compact and lightweight. In this work, we propose a design for a miniaturized Cassegrain telescope by replacing the curved primary and secondary mirrors with flat and ultrathin metasurfaces. The meta-atoms, consisting of SiO2 stripes on an Al film, provide high reflectance (>95%) and a complete phase coverage of 0~2π at the operational wavelength of 4 μm. The optical functionality of the metasurface Cassegrain telescope built with these meta-atoms was confirmed and studied with numerical simulations. Moreover, fabrication errors were mimicked by introducing random width errors to each meta-atom; their influence on the optical performance of the metasurface device was studied numerically. The concept of the metasurface Cassegrain telescope operating in the infrared wavelength range can be extended to terahertz (THz), microwave and even radio frequencies for real-world applications, where metasurfaces with a large aperture size are more easily obtained.

Three-sided pyramid wavefront sensor, part 1: simulations and analysis for astronomical adaptive optics

The Giant Segmented Mirror Telescopes (GSMTs) including the Giant Magellan Telescope (GMT), the Thirty Meter Telescope (TMT), and the European Extremely Large Telescope (E-ELT), all have extreme adaptive optics (ExAO) instruments planned that will use pyramid wavefront sensors (PWFS). The ExAO instruments all have common features: a high-actuator-count deformable mirror running at extreme speeds (>1 kHz); a high-performance wavefront sensor (WFS); and a high-contrast coronagraph. ExAO WFS performance is currently limited by the need for high spatial sampling of the wavefront which requires large detectors. For ExAO instruments for the next generation of telescopes, alternative architectures of WFS are under consideration because there is a trade-off between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront control. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS), which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to read noise. Here we develop a mathematical formalism based on the diffraction theory description of the Foucault knife-edge test that predicts the intensity pattern after the PWFS. Our formalism allows us to calculate the intensity in the pupil images formed by the PWFS in the presence of phase errors corresponding to arbitrary Fourier modes. We use these results to motivate how we process signals from a 3PWFS. We compare the raw intensity (RI) method, and derive the Slopes Maps (SM) calculation for the 3PWFS, which combines the three pupil images of the 3PWFS to obtain the X and Y slopes of the wavefront. We then use the Object Oriented MATLAB Adaptive Optics toolbox (OOMAO) to simulate an end-to-end model of an AO system using a PWFS with modulation and compare the performance of the 3PWFS to the 4PWFS. In the case of a low read noise detector, the Strehl ratios of the 3PWFS and 4PWFS are within 0.01. When we included higher read noise in the simulation, we found a Strehl ratio gain of 0.036 for the 3PWFS using RI over the 4PWFS using SM at a stellar magnitude of 10. At the same magnitude, the 4PWFS RI also outperformed the 4PWFS SM, but the gain was only 0.012 Strehl. This is significant because 4PWFS using SM is how the PWFS is conventionally used for AO wavefront sensing. We have found that the 3PWFS is a viable WFS that can fully reconstruct a wavefront and produce a stable closed-loop with correction comparable to that of a 4PWFS, with modestly better performance for high read-noise detectors.

The Ground-based Experiment of the Prototype of Planetary (& Lunar) Rotation Monitor Telescope

The scientific objective of the Planetary (& Lunar) Rotation Monitor (PRM) telescope is to study the terrestrial planet's (the Moon's) rotation and its interior structure and physics by in-situ observation. In order to verify the brand new principle of observations and the data processing method, the prototype of the telescope is designed and manufactured. The prototype's optical system consists of a commercial telescope and trihedron mirror set placed at the entrance of its light path to realize the capability of observing three fields of view (FOVs) simultaneously. The ground-based validation observation began in 2017, and the images containing the stars from three FOVs were achieved. Star images from different FOVs are initially mixed together, but they can be classified into the three FOVs respectively by calculating the displacement of star images on the CCD plate between two adjacent exposures, to make the observational effect be identical with three independent observations of the three FOVs respectively. After image processing, from the orientation variation of the three FOVs simultaneously in space due to the Earth's rotation, the direction of the rotation axis of the Earth in space can be derived. Its deviation from the theoretical value is about 1″ in average, indicating that the working principle and data processing method are effective. The main errors in observations are discussed, including the atmospheric refraction, the thermal deformation of the commercial telescope tube, the low optical resolution caused by the short focal length, the optical aberration in the multi-FOV observation, etc. It is indicated that the spatial resolution of the telescope can be enhanced with a longer focal length, and the observational reliability can be improved by optimizing the thermal deformation control. Improving the optical design in the simultaneous observation of multiple FOVs will also be helpful to the accuracy enhancement.

The Mysterious Lives of Speckles. I. Residual Atmospheric Speckle Lifetimes in Ground-based Coronagraphs

High-contrast imaging observations are fundamentally limited by the spatially and temporally correlated noise source called speckles. Suppression of speckle noise is the key goal of wavefront control and adaptive optics (AO), coronagraphy, and a host of post-processing techniques. Speckles average at a rate set by the statistical speckle lifetime, and speckle-limited integration time in long exposures is directly proportional to this lifetime. As progress continues in post-coronagraph wavefront control, residual atmospheric speckles will become the limiting noise source in high-contrast imaging, so a complete understanding of their statistical behavior is crucial to optimizing high-contrast imaging instruments. Here we present a novel power spectral density method for calculating the lifetime, and develop a semi-analytic method for predicting intensity PSDs behind a coronagraph. Considering a frozen-flow turbulence model, we analyze the residual atmosphere speckle lifetimes in a MagAO-X-like AO system as well as 25–39 m giant segmented mirror telescope scale systems. We find that standard AO control shortens atmospheric speckle lifetime from ∼130 ms to ∼50 ms, and predictive control will further shorten the lifetime to ∼20 ms on 6.5 m MagAO-X. We find that speckle lifetimes vary with diameter, wind speed, seeing, and location within the AO control region. On bright stars lifetimes remain within a rough range of ∼20 ms to ∼100 ms. Due to control system dynamics there are no simple scaling laws which apply across a wide range of system characteristics. Finally, we use these results to argue that telemetry-based post-processing should enable ground-based telescopes to achieve the photon-noise limit in high-contrast imaging.

High-accuracy electrohydraulic control system for the position and orientation of the primary mirror for a large telescope

High-accuracy electrohydraulic control system for the position and orientation of the primary mirror for a large telescope

Mathematical simulation of a 3D scanner for controlling the mirror system of the Millimetron Observatory

We develop an original system for controlling the mirror geometry of the Millimetron observatory as a part of the on-board scientific equipment. The system is designed to monitor the quality of the space telescope's mirror system and use the data received as feedback signals for presetting and adjusting the telescope's optical system in outer space. The system aims to determine a multi-dimensional vector of unknown parameters that define the state of the telescope's mirror system by indirect measurements of the telescope with a 3D scanner. An unparalleled mathematical model has been created, numerically describing a process of pre-measurement of the mirror system of the Millimetron Observatory using optical control marks on the surface of the mirror system. Using the mathematical model created and the geometric optics approximation, we numerically simulate the performance of the on-board 3D scanner in the course of preliminary measurements of the mirror system of the Millimetron Observatory using optical control marks applied on the mirror surfaces. A new effective method of pre-estimation of the displacement of elements of the AP telescope by indirect (implicit) measurements performed with the 3D scanner has been created. The method is based on the mathematical transformation of indirect measurements of deviations of the position of the telescope's mirror control marks from their reference position, which provides an easy-to-use list of estimates of the offsets of the unknown parameters of the mirror system elements. A possibility to measure the telescope's mirror system with the aim to pre-configure it using a 3D scanner on board the spacecraft is shown. Estimates of acceptable deviations of the mirror system component needed to ensure the telescope's functionality are given.

Distortion mapping correction in the AIMS primary mirror testing by a computer-generated hologram

The National Solar Observatory is currently developing the Accurate Infrared Magnetic Field Measurements of the Sun (AIMS). The primary mirror of the AIMS solar telescope is an off-axis parabolic with a diameter of 1 m and with a large off-axis amount of 1 m. Due to the surface figure of the primary mirror under the used state is directly related to image quality of the whole system, a computer-generated hologram (CGH) is carried out to test the primary mirror, and the test results are used to polish the mirror to a higher surface accuracy. However, the fact that the distortion exists in the testing results leads to the failure of a further guide to deterministic optical processing. In this paper, a distortion correction method is proposed, which uses an orthogonal set of vector polynomials to mapping the coordinates of the mirror and the pixels of fringes, and then an interpolation method is adopted to obtain the corrected results. The testing accuracy by using CGH is also verified by an auto-collimate test experiment. According to the distorted corrected results, the root-mean-square of the surface figure is about 1/50λ (λ = 632.8 nm) after polishing.

Critical processing temperature for high-performance protected silver mirrors

Silver (Ag) mirrors for astronomical telescopes consist of multiple metallic and dielectric thin films. Furthermore, the topmost surface of such Ag mirrors needs to be covered by a protection coating. While the protection coating is often deposited at room temperature and the entire mirrors are also handled at room temperature, various thin film deposition techniques offer protection coatings with improved characteristics when carried out at elevated temperatures. Thus, in this work, high-performance Ag mirrors were designed and fabricated with a new benchmark. The resulting Ag mirrors were annealed (i.e., post-fabrication annealing) at various temperatures to investigate the viability of introducing thermal processes during and/or after fabrication in improving overall optical performance and durability of protected silver mirrors. In our experiments, Ag mirror samples were deposited by electron-beam evaporation and subsequently annealed at various temperatures in the range from 60 {\deg}C to 300 {\deg}C, and then the mirror samples underwent an environmental stress test at 80 {\deg}C and 80% humidity for 10 days. While all the mirror samples annealed below 200 {\deg}C showed negligible corrosion after undergoing the stress testing, those annealed below 160 {\deg}C presented spectral reflectivity comparable to or higher than that of as-deposited reference samples. In contrast, the mirror samples annealed above 200 {\deg}C exhibited significant degradation after the stress testing. The comprehensive analysis indicated that delamination and voids caused by the growth of Ag grains during the annealing are the primary mechanisms of the degradation.

Comparisons between an on-axis three-mirror anastigmat telescope and an off-axis one: polarization aberrations.

Due to the ability to achieve a wide-diffraction-limited field of view, three-mirror anastigmat (TMA) telescopes are widely used in many applications that demand high imaging quality and detection accuracy, in which polarization aberrations play increasingly important roles. In this paper, polarization properties of on-axis elements and those of off-axis elements are analyzed and compared via polarization aberration theory. Then, an on-axis TMA (OTMA) telescope and an off-axis TMA (FTMA) telescope are designed and optimized to be diffraction-limited systems in parallel. Their constructional parameters and first-order parameters are set to be identical. Via polarization ray tracing, polarization aberrations of the 2 telescopes are obtained and compared in terms of diattenuation map, retardance map, Jones pupil, Pauli pupil, and amplitude response matrix. Results demonstrate that polarization aberrations are closely related to the structural features of mirrors and telescopes. The diattenuation and retardance maps of power mirrors in the OTMA telescope are rotationally symmetric, while those in the FTMA telescope are not. A Maltese cross appears in off-diagonal elements of the Jones pupil of the OTMA telescope and disappears in the FTMA telescope. Amplitude response matrices of polarization crosstalk components in the OTMA telescope are with a four-peak structure, while those in the FTMA telescope are with a two-peak structure. After quantitative comparisons, it is found that diattenuation in the OTMA telescope is smaller than that in the FTMA telescope as well as in the cases of retardance and polarization crosstalk. There are also similarities between the 2 TMA telescopes. Polarization aberrations of secondary mirrors (SM) are greater than those of both primary mirrors (PM) and tertiary mirrors (TM). What is more, polarization aberrations of TM are so small that they can be ignored safely. The numerical sum of Pauli coefficients of PM, SM, and TM is nearly identical to the cumulative Pauli coefficients. Hence, the TMA telescopes can be treated as weak polarization elements. This work compares polarization aberration performance of on- and off-axis TMA telescopes and can provide important references for designing and optimizing telescopes in which polarization aberrations matter.

High-power laser-induced optical aberrations on beam director mirrors

We present a full-scale numerical study of thermally induced optical aberrations on the primary mirror of a beam director telescope. In particular, we investigate high-power laser-induced deformations, resulting monochromatic aberrations, and their effects on imaging and laser focusing performance of primary telescope mirrors in shared aperture beam director systems. As a practical example, we consider a system based on 6 × 4 kW single-mode high-power laser sources and a primary mirror having a 500 mm circular clear aperture. A detailed comparison of the monochromatic aberrations and their implications on the optical performance is provided for borosilicate and Zerodur® substrates having identical reflective coatings for potential laser beam director applications. Our analyses show that high-power lasers can be efficiently directed with negligible imaging degradation using athermal substrates (i.e., Zerodur®) with high reflective coatings (>99.9 % ) for primary mirrors. On the other hand, substrates with a relatively higher coefficient of thermal expansion (i.e., borosilicate) can only be used effectively under a strictly controlled ambient temperature.

Simultaneous estimation of segmented telescope phasing errors and non-common path aberrations from adaptive-optics-corrected images

ABSTRACT We investigate the focal plane wavefront sensing technique, known as Phase Diversity, at the scientific focal plane of a segmented mirror telescope with an adaptive optics (AO) system. We specifically consider an optical system imaging a point source in the context of (i) an artificial source within the telescope structure and (ii) from AO-corrected images of a bright star. From our simulations, we reliably disentangle segmented telescope phasing errors from non-common path aberrations (NCPA) for both a theoretical source and on-sky, AO-corrected images where we have simulated the Keck/NIRC2 system. This quantification from on-sky images is appealing, as it is sensitive to the cumulative wavefront perturbations of the entire optical train; disentanglement of phasing errors and NCPA is therefore critical, where any potential correction to the primary mirror from an estimate must contain minimal NCPA contributions. Our estimates require a 1-min sequence of short-exposure, AO-corrected images; by exploiting a slight modification to the AO-loop, we find that 75 defocused images produce reliable estimates. We demonstrate a correction from our estimates to the primary and deformable mirror results in a wavefront error reduction of up to 67 per cent and 65 per cent for phasing errors and NCPA, respectively. If the segment phasing errors on the Keck primary are of the order of ∼130 nm RMS, we show we can improve the H-band Strehl ratio by up to 10 per cent by using our algorithm. We conclude our technique works well to estimate NCPA alone from on-sky images, suggesting it is a promising method for any AO-system.

Study of linear phase shift algorithms and application to deflectometry

For a number of optical methods, including deflectometry, information is encoded in fringe patterns. To extract the phase data from intensity values, a number of phase shift algorithms have been designed. In deflectometry, the nonlinearity of the fringe display implies that the displayed fringe pattern presents a harmonic content even if the input pattern is perfectly sinusoidal. The propagation of these harmonics through phase shift algorithms creates parasitic fringe patterns, reminiscent of the initial fringe pattern on the estimated phase. This phenomenon, known as print-through, has been identified as a serious performance limitation.In this paper, we revisit Surrel’s work on harmonic insensitive phase shift algorithms and demonstrate that the class of Discrete Fourier Transform (DFT) phase shift algorithms he defines is very appropriate for the field of deflectometry. We show how to choose the most suitable one depending on the application by performing a complete modeling of the harmonic print-through phenomenon for these DFT algorithms and studying the error propagation for shot noise and temporal perturbations. In a deflectometry context, we demonstrate by means of simulations that carefully chosen DFT algorithms can simultaneously be robust to print-through and perform better with respect to noise than the state of the art nonlinear phase shift algorithms.Lastly, by comparing experimental mirror shape measurements of the matrix of the secondary mirror of the European Extremely Large Telescope made on the one hand by DFT deflectometry and on the other hand by phase shift interferometry, we demonstrate that the use of DFT algorithms can substantially improve the high spatial frequency measurement capabilities of a deflectometry setup, without the need for a calibration of the display’s nonlinearities.

Risk assessment for landslide of FAST site based on GIS and fuzzy hierarchical method

In the context of circular high steep slopes within a 500-m aperture spherical radio telescope (FAST) site in Pingtang, Guizhou Province in southwest China, a pertinent small-area karst landslide risk assessment is carried out based on geographic information system and fuzzy analytical hierarchy process. Results show the following: (a) The AUC value of hazard assessment is 0.826, which means a good adaptability and a relatively higher accuracy, and the AUC value of risk assessment is 0.803, which means the accuracy of landslide risk assessment is within acceptable level. (b) The slopes of FAST area are generally at the medium or low-hazard level, with high-hazard region accounting for only 3.17% of the total area. High-hazard regions are primarily found in two locations, one is located in nearby the Guangmingding slope where the dangerous rock masses were basically cleared away, the other is located in nearby feed tower 5H where potentially unstable rock masses were reinforced to improve the stability of slope. (c) High-vulnerability area of FAST accounts for approximately 43.62%. As a direct result, the high-risk area of FAST site accounts for 34.36% based on the overlap of vulnerability and hazard. The high risk is concentrated in the surrounding areas such as the feed tower, support pillar, and telescope mirror, and the high-risk area overlaps most of the fault fracture zone in the study area. Our findings provide meaningful references for landslide prevention and monitoring of FAST areas and are instructive in theory and practice.

Об осесимметричном нагружении пластины на локальной опоре в рамках теории Родионовой – Титаева – Черных

The problem of an axisymmetric bending of a plate with constant thickness under its own weight is considered. The plate has a circular support. The problem is solved in an axisymmetric statement using a nonclassical shell theory of Rodionova-Titaev-Chernykh (RTCh), which takes plate compression in thickness into account. The solution for this theory is obtained using Godunov's orthogonal sweep method. This solution is compared with the solution obtained using the general three-dimensional theory of elasticity, implemented in an open-source package Code_Aster using axisymmetric finite elements. The motivation for this study is the description of a stress-strain state of some variants of primary mirrors of large optical telescopes under the action of gravity. The obtained results characterizing the optical quality of the mirror surface are: the peak value (PV) and the root-mean square (RMS) of its displacement. A parametric study was carried out, i.e., the thickness of the plate and the half-width of the support were varied. The two methods were compared. It is shown that, as the plate thickness increases or the half-width of the support decreases, non-physical behaviour of the mirror surface takes place within the limits of the nonclassical theory of RTCh. A criterion of its applicability is therefore proposed.

Jacques Beckers (1934–2021)

Beckers’ interests included many aspects of solar physics and a variety of topics in astronomical instrumentation. His appointments included leadership positions at the Multiple Mirror Telescope, the National New Technology Telescope project, and the National Solar Observatory.

Alignment of the active secondary mirror of a space telescope using model-based wavefront sensorless adaptive optics.

The precise alignment of the space telescope with an active secondary mirror (ASM) is essential to high-quality imaging. The traditional alignment methods either require a dedicated wavefront sensor or a lot of iterations to optimize a metric function, which is not suitable for on-orbit instant alignment. A model-based wavefront sensorless adaptive optics method is proposed for the alignment of the ASM of a wide field-of-view space telescope. In our method, the aberration is estimated by introducing a series of modal biases successively into the system using the ASM. Unlike the traditional wavefront sensing methods that intend to measure all aberration modes, only five aberration modes that can be compensated by the ASM are estimated. Two alignment schemes either using single-field or multi-field images are proposed to calculate the control signals of the ASM, depending on if the aberration is mainly caused by the ASM. Simulations are made to evaluate the performance of our method under different scenarios. The influence of image sampling frequency, image size, and image noise on alignment are also investigated.

Симуляционная модель системы адаптивного управления сегментами составного зеркала космического телескопа и ее метрологическая аттестация

The paper concerns a measurement problem of identifying inadequacy in a mathematical model of an adaptive control system driving segments of a deformable mirror in a large telescope. This is necessary to assess the validity of this model. A dual-axis servo drive unit utilising permanent magnet synchronous machines controls the mirror segments. The servo unit rotates each segment of the deformable mirror with respect to its axis of symmetry and tilts each segment relative to the fixed central reference segment. The paper provides general descriptions of the model structure and the feedback in the current control loop employing phase current measurement and coordinate transformations. We present initial data sets for metrological certification of the model. We used the MMK-stat M software to perform the metrological certification so that we could check empirical equations, determine the scope of application for the model and validate it. The metrological certification allowed us to confirm that the model of an adaptive control system for a segmented deformable telescope mirror is valid, and to find the model structure that ensures a more accurate description of the measurement problem that concerns controlling the spatial position of the object simulated