Tip-tilt Errors Research Articles

Co-Phase Error Detection for Segmented Mirrors Based on Far-Field Information and Transfer Learning

The resolution of a telescope is closely related to its aperture size; however, the aperture of a single primary mirror telescope cannot be indefinitely enlarged due to design and manufacturing constraints. Segmented mirror technology can achieve the same resolution as a single primary mirror of equivalent aperture, provided that the segments are co-phased correctly. This paper proposes a method for high-precision detection of piston errors in segmented mirror telescope systems, based on far-field information and transfer learning. By training a ResNet-18 network model, this method can predict piston errors with high precision within 10 ms of a single-frame far-field diffraction image. Simulation results demonstrate that the method is robust to tip-tilt errors, wavefront aberrations, and noise. This approach is simple, fast, highly accurate in detection, and resistant to noise, providing a new solution for piston error detection in segmented mirror systems.

Effect of Panel Misalignment Error Distribution on the Radiation Pattern of Leighton Chajnantor Telescope’s Antenna

The Leighton dish formerly at the Caltech Submillimeter Observatory will be reassembled to become the Leighton Chajnantor Telescope (LCT). It will be required to demonstrate high surface accuracy and controlled radiation patterns at high frequency, which are largely limited by surface error due to panel misalignment on the primary reflector. Not only the surface rms error but also the error distribution has effect on the radiation pattern of the antenna. Therefore, analyzing the effect of error distributions resulting from various panel misalignments on the radiation pattern of the antenna will facilitate better compensation of surface errors during the reassembly process. To acquire the radiation pattern of LCT’s antenna with panel misalignments, we first propose a simulation method based on physical optics and the physical theory of diffraction, which offers precise results but is time-consuming, especially at high frequencies. Then, we propose a rapid computation method that combines the method of calculating the optical path difference (OPD), the OPD fitting method, and the aperture integration method for segmented reflectors. Experimental results demonstrate that the rapid computation method is highly efficient and accurate compared to the simulation method. In order to show the effect of error distributions due to two typical panel misalignments (i.e., piston and tip-tilt) on radiation patterns, experiments are conducted using the two proposed methods for various error distributions. These experiments indicate that for the same surface rms error, smaller panel errors at smaller normalized aperture radii are more conducive to achieving improved characteristics of the radiation patterns, such as reduced peak gain losses and lower sidelobe levels. Additionally, comparison experiments also reveal that variations in piston error have a greater impact on the radiation patterns than variations in tip-tilt error under the same surface rms error.

Design and Experimental Analysis of an Optical Fiber Coupling System for a Ground-based Telescope with Adaptive Optics

Astronomy photonics has opened up a new era for the application of astronomical optical instruments. The fiber coupling system serves as the crucial link between the telescope and photonic devices. This paper explores a beam shaping method that utilizes a coupled lens to enhance the efficiency of coupling light into an optical single mode fiber. Compared to directly coupling the telescope beam into the fiber, this approach offers improved coupling efficiency and greater adjustment tolerance. The laboratory-based optical fiber coupling system described in this study comprises an imaging component with an F/50 ratio and a fiber coupling component. Theoretical analysis indicates that optimal coupling efficiency is achieved when the diameter of the focusing spot, limited by diffraction, matches the fiber core size. Any axial error, position error, or tip-tilt error between the lens and the fiber will reduce the coupling efficiency. Experimental results confirm that the coupling system achieves an efficiency of approximately 70%, which is close to the theoretical limit of 78%. These findings underscore the effectiveness of the fiber coupling method.

Co-phase error detection for segmented mirrors with ptychography

Co-phase error detection has been extensively studied as a key technology to achieve diffraction-limited imaging for telescopes with segmented primary mirrors. This paper provides a novel method to simultaneously detect piston, tip–tilt, and decenter errors of sub-mirrors based on an extended ptychographic iterative engine (ePIE). The main components of the detection system are a transmissive specimen and a detector near the focal plane of the segmented system. The specimen is mechanically moved across the stationary beam from the telescope with adjacent positions sufficiently overlapped, and the detector then records the diffraction patterns. After retrieving the wavefront aberration of the segmented primary mirror using ePIE, the decenter errors can be calculated based on the displacement of the pupil centers of sub-mirrors and the piston and tip–tilt errors can be computed by the least square method According to a series of numerical simulations, the root mean square errors (RMSEs) of the residual co-phase errors are below 0.01 λ. The results of preliminary experiments show that the relative errors of piston error detection and decenter error detection are 1.20% and 2.08% , respectively, which validates the effectiveness of our proposed method.

Model-based fine phasing of segmented mirror using Chebyshev segmented piston-tip-tilt modes.

On-orbit cophasing is essential for high-resolution imaging of space telescopes with a segmented primary mirror. A model-based fine phasing method for a segmented mirror is proposed and demonstrated in this Letter. The tip-tilt error is related to the second moment of spot intensity, and the piston error is related to the Strehl ratio. Chebyshev segmented piston-tip-tilt (CSPTT) modes are used to express cophasing errors to suppress the effect of imaging noises. The CSPTT modal coefficients are estimated by the "2N + 1" algorithm that introduces bidirectional biases for each mode's estimation. The proposed method is proved robust to image noises and figure errors.

Redundant apodization for direct imaging of exoplanets

Context. Telescope pupil fragmentation from spiders generates specific aberrations that have been observed at various telescopes and are expected on the 30-meter class telescopes under construction. This is known as the island effect, and it induces differential pistons, tips, and tilts on the pupil petals, deforming the instrumental point spread function (PSF); it is one of the main limitations to the direct detection of exoplanets with high-contrast imaging. These petal-level aberrations can have different origins such as the low-wind effect or petaling errors in the adaptive optics reconstruction. Aims. In this paper, we propose a method for alleviating the impact of the aberrations induced by island effects on high-contrast imaging by adapting the coronagraph design in order to increase its robustness to petal-level aberrations. Methods. Following a method first developed and applied on robustness to errors due to primary mirror segmentation (e.g., segment phasing errors, missing segments), we developed and tested redundant apodized pupils (RAP): apodizers designed at the petal-scale, then duplicated and rotated to mimic the pupil petal geometry. Results. We applied this concept to the ELT architecture, made of six identical petals, to yield a 10−6 contrast in a dark region from 8 to 40λ/D. Both amplitude and phase apodizers proposed in this paper are robust to differential pistons between petals, with minimal degradation to their coronagraphic PSFs and contrast levels. In addition, they are also more robust to petal-level tip-tilt errors than classical apodizers designed for the whole pupil, with which the limit of contrast of 10−6 in the coronagraph dark zone is achieved for constraints up to 2 rad RMS of these petal-level modes. Conclusions. In this paper the RAP concept proves its robustness to island effects (low-wind effect and post-adaptive optics petaling), with an application to the ELT architecture. It can also be considered for other 8- to 30-m class ground-based units such as VLT/SPHERE, Subaru/SCExAO, GMT/GMagAO-X, and TMT/PSI.

Adaptive Youla–Kučera parametric control of unknown tip-tilt disturbance rejection in image stabilization systems

We propose a new, to the best of our knowledge, adaptive control method to attenuate beam jitter in image stabilization systems, which breaks the restrictions of existing adaptive control methods in terms of time consumption and control stability, and then provides an innovative way for tip-tilt disturbance rejection. In this approach, disturbance rejection could be converted to optimize error attenuation through the parameters design of the Youla-Kučera (YK) parametric controller, which are determined by a new on-line power spectrum density (PSD) estimation of tip-tilt errors to identify the frequency and amplitude of unknown disturbances. Experimental results demonstrate that the proposed method working in an adaptive correction process can attenuate the beam jitter to approximately 1/3 less than the original control error.

Redundant apodization for direct imaging of exoplanets

Context. Direct imaging and spectroscopy of Earth-like planets and young Jupiters require contrast values up to 106−1010 at angular separations of a few dozen milliarcseconds. To achieve this goal, one of the most promising approaches consists of using large segmented primary mirror telescopes with coronagraphic instruments. While they are able to reach high contrast at small angular separations, coronagraphs are highly sensitive to wavefront errors, however. The segmentation itself is responsible for phasing errors and segment-level vibrations that have to be controlled at a subnanometric accuracy. Aims. We propose an innovative method for a coronagraph design that allows a consequent relaxation of the segment phasing and stability constraints for low segment-count mirrors and generates an instrument that is more robust to segment-level wavefront errors. Methods. This method is based on an optimization of the coronagraph design that includes a segment-level apodization. This is repeated over the pupil to match the segmentation redundancy and improves the contrast stability beyond the minimum separation set by the single-segment diffraction limit. Results. We validate this method on a Giant Magellan Telescope (GMT)-like pupil (seven circular segments) for two coronagraph types: apodized pupil Lyot coronagraphs, and apodizing phase plate coronagraphs. For the apodized pupil Lyot coronagraphs, redundant apodization enables releasing the piston phasing constraints by a factor of 5-20 compared to classical designs. For the apodizing phase plate coronagraphs, the contrast remains almost constant up to 1 radian RMS of the phasing errors. We also show that redundant apodizations increase the robustness of the coronagraph to segment tip-tilt errors, as well as to missing segment errors. Conclusions. Redundant apodization enables reducing or even removing any constraints on the primary mirror segment phasing at the price of larger angular separations and lower throughputs. This method cannot be applied to higher-segment count mirrors such as the ELT or the TMT, but it is particularly suitable for low segment-count mirrors (fewer than ~20 segments) such as the GMT aperture. These mirrors aim for high-contrast imaging of debris disks or exoplanets down to 100 mas.

High-precision co-phase method for segments based on a convolutional neural network

In order to achieve the resolution comparable to the resolution of a monolithic primary mirror telescope and make the imaging quality of the imaging system reach or approach to the diffraction limit, the submirrors of the segments telescope should ensure co-phase splicing. To solve the problem of phase error detection, a high-precision piston error detection method is proposed based on convolutional neural network (CNN). By setting a mask with a sparse multi-subpupil configuration on the exit pupil of the imaging system, a point spread function (PSF) image dataset that is extremely sensitive to the piston error is constructed. According to the characteristics of this dataset, a high-performance CNN model is built. And the best detection range of CNN is tested. The simulation results show that a single network can accurately output the piston error of one or more submirrors in the capture range slightly less than one wavelength. When the single network is applied to the six-submirror imaging system, the detection precision of the piston error reaches an RMS value of 0.0013<i>λ</i> (here, RMS stands for root mean square). And the method has good robustness to residual tip-tilt error, wavefront aberration, and CCD noise, light source bandwidth. The method is simple and fast, and can be widely used to detect the piston error of the segments.

Deep learning wavefront sensing for fine phasing of segmented mirrors.

Segmented primary mirror provides many crucial important advantages for the construction of extra-large space telescopes. The imaging quality of this class of telescope is susceptible to phasing error between primary mirror segments. Deep learning has been widely applied in the field of optical imaging and wavefront sensing, including phasing segmented mirrors. Compared to other image-based phasing techniques, such as phase retrieval and phase diversity, deep learning has the advantage of high efficiency and free of stagnation problem. However, at present deep learning methods are mainly applied to coarse phasing and used to estimate piston error between segments. In this paper, deep Bi-GRU neural work is introduced to fine phasing of segmented mirrors, which not only has a much simpler structure than CNN or LSTM network, but also can effectively solve the gradient vanishing problem in training due to long term dependencies. By incorporating phasing errors (piston and tip-tilt errors), some low-order aberrations as well as other practical considerations, Bi-GRU neural work can effectively be used for fine phasing of segmented mirrors. Simulations and real experiments are used to demonstrate the accuracy and effectiveness of the proposed methods.

Design considerations of photonic lanterns for diffraction-limited spectrometry

The coupling of large telescopes to astronomical instruments has historically been challenging due to the tension between instrument throughput and stability. Light from the telescope can either be injected wholesale into the instrument, maintaining high throughput at the cost of point-spread function (PSF) stability, or the time-varying components of the light can be filtered out with single-mode fibers (SMFs), maintaining instrument stability at the cost of light loss. Today, the field of astrophotonics provides a potential resolution to the throughput-stability tension in the form of the photonic lantern (PL): a tapered waveguide that can couple a time-varying and aberrated PSF into multiple diffraction-limited beams at an efficiency that greatly surpasses direct SMF injection. As a result, lantern-fed instruments retain the stability of SMF-fed instruments while increasing their throughput. To this end, we present a series of numerical simulations characterizing PL performance as a function of lantern geometry, wavelength, and wavefront error (WFE), aimed at guiding the design of future diffraction-limited spectrometers. These characterizations include a first look at the interaction between PLs and phase-induced amplitude apodization (PIAA) optics. We find that Gaussian-mapping beam-shaping optics can enhance coupling into 3-port lanterns but offer diminishing gains with larger lanterns. In the y and J band (0.97–1.35 µm) region, with moderately high WFE ( ∼ 10 % Strehl ratio), a 3-port lantern in conjunction with beam-shaping optics strikes a good balance between pixel count and throughput gains. If pixels are not a constraint, and the flux in each port will be dominated by photon noise, then larger port count lanterns will provide further coupling gains due to a greater resilience to tip-tilt errors. Finally, we show that lanterns can maintain high operating efficiencies over large wavelength bands where the number of guided modes at the lantern entrance drops, if care is taken to minimize the attenuation of weakly radiative input modes.

Global piston restoration of segmented mirrors with recurrent neural networks

Recurrent neural networks are usually used for processing sequential data. They have been employed in this paper to deal with the sequence of diffraction subimages created by every intersection from a segmented mirror. Every subimage is first processed by a convolutional neural network that extracts a set of features from each of them. It was attained superior prediction accuracy with the recurrent approach than with convolution layers alone. Furthermore, a consistency test was added to detect wrong predictions before computing the global piston values. The final system predicts global piston values with rms = 7.34 nm, high reliability, and capture range of [ − 21λ, 21λ]. Atmospheric seeing, polishing and tip-tilt residual errors were also added in the simulations.

The Single-mode Complex Amplitude Refinement (SCAR) coronagraph

We present the monochromatic lab verification of the newly developed SCAR coronagraph that combines a phase plate (PP) in the pupil with a microlens-fed single-mode fiber array in the focal plane. The two SCAR designs that have been measured, create respectively a 360 degree and 180 degree dark region from 0.8–2.4λ∕D around the star. The 360 SCAR has been designed for a clear aperture and the 180 SCAR has been designed for a realistic aperture with central obscuration and spiders. The 360 SCAR creates a measured stellar null of 2–3 × 10−4, and the 180 SCAR reaches a null of 1 × 10−4. Their monochromatic contrast is maintained within a range of ±0.16λ∕D peak-to-valley tip-tilt, which shows the robustness against tip-tilt errors. The small inner working angle and tip-tilt stability makes the SCAR coronagraph a very promising technique for an upgrade of current high-contrast instruments to characterize and detect exoplanets in the solar neighborhood.

The Single-mode Complex Amplitude Refinement (SCAR) coronagraph

Context. The recent discovery of an Earth-mass exoplanet around the nearby star Proxima Centauri provides a prime target for the search for life on planets outside our solar system. Atmospheric characterization of these planets has been proposed by blocking the starlight with a stellar coronagraph and using a high-resolution spectrograph to search for reflected starlight off the planet. Aims. Due to the large flux ratio and small angular separation between Proxima b and its host star (≲10−7 and ≲2.2λ/D respectively; at 750 nm for an 8 m-class telescope) the coronagraph requires high starlight suppression at extremely-low inner working angles. Additionally, it must operate over a broad spectral bandwidth and under residual telescope vibrations. This allows for efficient use of spectroscopic post-processing techniques. We aim to find the global optimum of an integrated coronagraphic integral-field spectrograph. Methods. We present the Single-mode Complex Amplitude Refinement (SCAR) coronagraph that uses a microlens-fed single-mode fiber array in the focal plane downstream from a pupil-plane phase plate. The mode-filtering property of the single-mode fibers allows for the nulling of starlight on the fibers. The phase pattern in the pupil plane is specifically designed to take advantage of this mode-filtering capability. Second-order nulling on the fibers expands the spectral bandwidth and decreases the tip-tilt sensitivity of the coronagraph. Results. The SCAR coronagraph has a low inner working angle (∼1λ/D) at a contrast of < 3 × 10−5 for the six fibers surrounding the star using a sufficiently-good adaptive optics system. It can operate over broad spectral bandwidths (∼20%) and delivers high throughput (> 50% including fiber injection losses). Additionally, it is robust against tip-tilt errors (∼0.1λ/D rms). We present SCAR designs for both an unobstructed and a VLT-like pupil. Conclusions. The SCAR coronagraph is a promising candidate for exoplanet detection and characterization around nearby stars using current high-resolution imaging instruments.

Suppressions of vibration in the Tip-Tilt mirror control system by add-on controller

Tip-Tilt mirrors play an important role in astronomical telescopes requiring the tracking performance at the level of microradian or sub-microradian. However, the closed-loop performance suffers a lot from the low-sample rate and time delay of image sensors. Especially, this issue is under the condition of vibrations, because dynamic behaviors are complex and the models are difficult to be obtained accurately. Another challenging issue comes from the measurement of vibrations and its extraction for the closed-loop control. This paper proposes a new method based on an add-on controller of the Tip-Tilt mirror to mitigate telescope vibrations. The proposed method only uses Tip-Tilt errors from an image sensor to implement a disturbance observer, which is not being restricted by an accurate model. As a result, the closed-loop performance can be optimized by designing of a proper Q-filter. To suppress the low-frequency and high-frequency vibrations, a novel Q-filter combining a lowpass filter and a bandpass filter is proposed here. The improved control method is validated by both simulation and experiment in the tip-tilt mirror control system under the condition of vibrations.

Analysis of errors in polarimetry using a rotating waveplate.

Modulation using a rotating waveplate is the most popular way in astronomy to obtain radiation polarization states and thus the physical condition of celestial bodies. Modulation error analysis of the rotating quarter-waveplate polarimeter is presented in this paper. In terms of geometric dimensions, three modulation error sources are analyzed: the waveplate axial error, waveplate rotation axis tip-tilt error (zenithal error), and position error of the waveplate fast axis (azimuthal error). The dispersion deviation, as another dimension of modulator error, is also studied in this paper. In theory, two factors affect the accuracy of polarization measurement using waveplate polarimetry: retardance $ \delta $δand fast axis position $ \theta $θ. The temperature property of the waveplate, which represents the axial error, the waveplate mounting tip-tilt error, which represents the zenithal error, and the wavelength-based retardance characteristic, which represents the dispersion property of the waveplate, belong to the retardance error. The motorized rotary stage home position error and the random sample rotating position error, representing the azimuthal error, belong to the fast axis position error. These factors will be analyzed in detail here. Based on these analyses, the maximum allowable upper limits for each error source under $ 1 \times {10^{ - 4}} $1×10-4 polarization measurement accuracy are presented. Also, feasible solutions are proposed to address these errors.

High-bandwidth tip-tilt vibration compensation in telescope systems

Mechanical vibrations resulting from wind, ground vibrations and actuator imperfections lower the performance of optical telescope systems used for astronomical applications, as well as free-space optical communication. This paper proposes a high-bandwidth tip-tilt compensation system for optical telescopes, in order to reduce the influence of these vibrations. A typical, high precision, motorized telescope system is used as a base for this evaluation. By utilization of a tip-tilt sensor, the resulting tip-tilt errors are measured and analyzed in the frequency domain. A fast steering mirror integrated into the optical path allows to compensate for the measured tip-tilt errors. The performance of the fast steering mirror based system is compared to the original, uncompensated system, as well as to a compensation loop, which uses the telescope mount to counteract measured errors. Experiments demonstrate a significant reduction of the tip-tilt errors due to vibrations by a factor of 5 (altitude axis) and by a factor of 4.6 (azimuth axis) utilizing a compensation bandwidth of up to 810 Hz.

A portable picometer reference actuator with 100 µm range, picometer resolution, subnanometer accuracy and submicroradian tip-tilt error for the characterization of measuring instruments at the nanoscale

We present the realization and the characterization of a picometer reference actuator (PRA), a metrological instrument based on a precision linear actuator capable of 100 µm range with subnanometer accuracy, picometer resolution, and submicroradian tip-tilt pointing control. The PRA relies on an integrated multiple reflections homodyne interferometer as a high resolution and accurate internal reference, on a multiple reflection based angle sensor for the control of the movement straightness, and on a versatile mirrors configuration to transfer the metrological traceability to an external device. As an example case we report the use of the PRA for the characterization of the non-linearities of the INRIM heterodyne interferometer dedicated to the calibration of capacitive sensors.

衍射主镜面外拼接误差分析

衍射主镜面外拼接误差分析

Design, fabrication, and testing of a Shack-Hartmann sensor with an automatic registration feature.

In this research, design, construction, and testing of an innovative Shack-Hartmann sensor are described. As the most critical component, a polymer microlens array is injection molded and mounted on a board-level CMOS camera such that the focal plane of the microlens array is on the camera's image plane. To allow for automatic registration of the spots of the measured area, a diffusing surface was created at the center of the lens array in the same diamond machining process in an uninterrupted operation. This unique diffusing surface does not generate an image spot. The no-spot feature functions as the reference in the measurement on the camera's image plane. Using this unique feature, large global tip-tilt error can be detected and eliminated. In this research, both experiments and simulation have shown that the Shack-Hartmann sensor built using low cost components is capable of precision wavefront detection. This research also demonstrated that automatic registration based on the diffusing surface is simple and reliable.