Performance evaluation of ground layer adaptive optics based on layer correction efficiency.

Ground layer adaptive optics (GLAO) has been widely employed in wide-field observations with ground-based telescopes. However, the present evaluation of GLAO performance lacks a criterion in terms of turbulence layer correction. This deficiency results in a significant gap in understanding the effectiveness of GLAO correction at different heights of the turbulence layer, thereby hindering the optimization of GLAO system performance. To bridge this gap, this Letter introduces a new, to the best of our knowledge, performance criterion for GLAO, termed layer correction efficiency (LCE). This criterion is formulated to quantify the effective compensation of the GLAO system for a specific altitude layer of turbulence, providing support for the further enhancement of GLAO performance. The simulation results indicate that the LCE has high applicability in GLAO performance analysis.

Phase unwrapping algorithm based on phase diversity wavefront reconstruction and virtual Hartmann-Shack technology.

Phase unwrapping (PU) algorithms play a crucial role in various phase measurement techniques. Traditional algorithms cannot work well in strong noise environments, which makes it very difficult to obtain the accurate absolute phase from the noisy wrapped phase. In this Letter, we introduce a novel, to the best of our knowledge, phase unwrapping algorithm named PD-VHS. This algorithm innovatively employs point spread function (PSF) filtering to eliminate noise from the wrapped phase. Furthermore, it combines a phase diversity (PD) wavefront reconstruction technology with a virtual Hartmann-Shack (VHS) technology for phase reconstruction and phase unwrapping of the filtered PSFs. In simulations, hundreds of random noise wrapped phases, containing the first 45 Zernike polynomials (excluding piston and the two tilt terms) and the wavefront RMS = 0.5λ and 1λ, are used to compare the classical quality-map guided algorithm, the VHS algorithm with decent noise immunity, with our PD-VHS algorithm. When signal-to-noise ratio (SNR) drops to just 2 dB, the mean root mean square errors (RMSEs) of the residual wavefront between the unwrapped result and the absolute phase of the quality-map guided algorithm and the VHS algorithm are up to 3.99λ, 0.44λ, 4.29λ, and 0.85λ, respectively; however, our algorithm RMSEs are low: 0.11λ and 0.17λ. Simulation results demonstrated that the PD-VHS algorithm significantly outperforms the quality-map guided algorithm and the VHS algorithm under large-scale noise conditions.

MWDNs: reconstruction in multi-scale feature spaces for lensless imaging.

Lensless cameras, consisting of only a sensor and a mask, are small and flexible enough to be used in many applications with stringent scale constraints. These mask-based imagers encode scenes in caustic patterns. Most existing reconstruction algorithms rely on multiple iterations based on physical model for deconvolution followed by deep learning for perception, among which the main limitation of reconstruction quality is the mismatch between the ideal and the real model. To solve the problem, we in this work learned a class of multi Wiener deconvolution networks (MWDNs), deconvoluting in multi-scale feature spaces with Wiener filters to reduce the information loss and improving the accuracy of the given model by correcting the inputs. A comparison between the proposed and the state-of-the-art algorithms shows that ours achieves much better images and performs well in real-world environments. In addition, our method takes greater advantage of the computational time due to the abandonment of iterations.

Dispersed fringe cophasing method based on principal component analysis.

With the success of the Webb telescope, dispersed fringe sensing (DFS), with the significant merit of a large capture range, is proving to be a promising cophasing approach for a large-aperture segmented telescope. In this Letter, a novel, to the best of our knowledge, piston error extraction method based on principal component analysis (PCA) technology is proposed. In this method, all the one-dimension intensity distributions along the dispersion axis for different interference positions are regarded as a set of random phase-shifted interference signals. PCA technology is utilized to obtain its corresponding continuous principal phase and the piston error could be directly estimated proportionally from the slope of the phase-wavenumber line. This method avoids nonlinear operations, similar to Shi's traditional framework; no active move is needed for fine cophasing, and the method is also free of characteristic constant calibration in sidelobe peak displacement- and slope-based methods. Preliminary simulations of the method's coarse-then-fine cophasing ability with high accuracy are presented here to show its potential.

No-Reference Quality Assessment of Extended Target Adaptive Optics Images Using Deep Neural Network.

This paper proposes a supervised deep neural network model for accomplishing highly efficient image quality assessment (IQA) for adaptive optics (AO) images. The AO imaging systems based on ground-based telescopes suffer from residual atmospheric turbulence, tracking error, and photoelectric noise, which can lead to varying degrees of image degradation, making image processing challenging. Currently, assessing the quality and selecting frames of AO images depend on either traditional IQA methods or manual evaluation by experienced researchers, neither of which is entirely reliable. The proposed network is trained by leveraging the similarity between the point spread function (PSF) of the degraded image and the Airy spot as its supervised training instead of relying on the features of the degraded image itself as a quality label. This approach is reflective of the relationship between the degradation factors of the AO imaging process and the image quality and does not require the analysis of the image's specific feature or degradation model. The simulation test data show a Spearman's rank correlation coefficient (SRCC) of 0.97, and our method was also validated using actual acquired AO images. The experimental results indicate that our method is more accurate in evaluating AO image quality compared to traditional IQA methods.

Polarization imaging based on time-integration by a continuous rotating polarizer.

Polarimeter by rotating polarizer is one of the well-known and classic division of time polarimeter (DoTP). It is generally acknowledged that this kind of polarimeter is time consuming for each measurement although it has simple, accurate and compact performances. In this paper we present a time-integration polarimeter by using a continuous rotating polarizer. The basic principle and the corresponding mathematical expressions are derived. Numeric analysis and experiments are also made in this paper. Experimental results validate the precision and feasibility of the proposed imaging polarization and state of polarization retrieve theory. The frame-frequency of polarization image is 80fps which is limited mainly by the speed of the photodetector in our experiments, and its maximum frame-frequency can achieve over 270fps in theory for some special applications. That may give this kind of classic polarimeter new attractive prospects and life.

Analytical calibration of slope response of Zernike modes in a Shack-Hartmann wavefront sensor based on matrix product.

The Shack-Hartmann wavefront sensor (SH-WFS) is widely used as a slope-based wavefront sensing device. The modal method is favored for wavefront reconstruction from SH-WFS output because of its excellent performance. In this case, the calibration of modal (commonly Zernike modes) slope is required in advance. Traditional numerical or symbolic integral-based methods are not satisfactory because of their low accuracy or efficiency, particularly when an extremely large number of microlenses are involved. In this Letter, a novel method based on matrix product is proposed in which two key matrix operators are utilized. The first, namely the derivative matrix operator, is used to obtain the derivative of the Zernike modes; the second, that is, the transformation matrix operator, is then used to map the Zernike derivative defined in the original, whole circular pupil into modes defined in a scaled, translated circle pupil enveloping a specific microlens. With these two operators, the evaluation of slope response of Zernike modes could be unified into a matrix-product framework, which contributes its high efficiency. Numerical simulations show the superior advantages of the proposed method in accuracy and efficiency over traditional ones.

Region-correlation algorithm with improved dynamic range and reconstruction accuracy for extended object wavefront sensing.

The correlation Shack-Hartmann wavefront sensor (SHWFS) is widely used in many fields in addition to solar adaptive optics. The requirement for the SHWFS dynamic range increases with the diameter of the telescope, which means a larger detector array is needed. However, the size of the detector would be restricted by the high frame rate needed for the solar observation. To solve this problem, a new, to the best of our knowledge, method called the region-correlation algorithm (RCA) is proposed. In this method, the sub-image array is divided into several regions, and the slopes of sub-apertures are calculated by referring to a selected sub-image in each region. Note that the final slope over a sub-aperture is obtained by combining the relative slopes between the selected sub-image in different regions. The dynamic range in each region is similar to the conventional correlation algorithm, and the final dynamic range of the RCA would be accumulated from those of the regions. The reconstruction accuracy under large aberration would also be improved due to the extended dynamic range. Meanwhile, the RCA does not require any extra device and the increase in calculation time resulting from the RCA is acceptable. The results of numerical simulation and experiment, compared with conventional correlation algorithm, confirm the advantages in the performance of the RCA as well.

Constrained least-squares algorithm for active optics correction of a primary mirror.

Active optics technology improves the performance and image quality of large telescopes. To effectively compensate for optical aberrations, the constrained least-squares (CLS) algorithm, which considers the characteristics of the resultant moment, the force budget, and the local force smoothness, is proposed to optimize the force distribution. First, the constraint of the resultant moment is used to decouple the shape control and location control. Then, through the force budget, the surface residual and force amplitude can be balanced. At last, the local smooth constraint is proposed to reduce the mirror's internal stress. Simulations were conducted on a 4 m thin mirror to compare the force distributions obtained by the least-squares, bending modes (BMs), and CLS algorithms. The results show that under equivalent residuals, the proposed algorithm is superior to the BM algorithm and performs better on local force smoothness.

Unified analytical method for Zernike coefficient transformation of scaled, rotated, and translated pupils based on Shack's vector multiplication.

Zernike polynomials play an essential role in characterizing and analyzing wavefront aberrations. Transformation of weighted coefficients for Zernike modes is required when pupil scaling, rotation, and/or translation exist. Here, a novel method based on Shack's vector multiplication is first proposed to derive the transformation relation. The derived modes resulting from pupil scaling, rotation, and/or translation for each individual mode are easily indicated via this method; thus, the effect of each kind of pupil change could be studied qualitatively and quantitatively. Its remarkable computational efficiency against the direct integral is demonstrated by simulation. The method introduced here provides a generalized methodology to analyze the relationship between weighted coefficients for different description basis sets.

Sub-Millisecond Phase Retrieval for Phase-Diversity Wavefront Sensor.

We propose a convolutional neural network (CNN) based method, namely phase diversity convolutional neural network (PD-CNN) for the speed acceleration of phase-diversity wavefront sensing. The PD-CNN has achieved a state-of-the-art result, with the inference speed about 0.5 ms, while fusing the information of the focal and defocused intensity images. When compared to the traditional phase diversity (PD) algorithms, the PD-CNN is a light-weight model without complicated iterative transformation and optimization process. Experiments have been done to demonstrate the accuracy and speed of the proposed approach.

Solar multi-conjugate adaptive optics based on high order ground layer adaptive optics and low order high altitude correction.

Multi-conjugate adaptive optics (MCAO) is the most promising technique currently developed to enlarge the corrected field of view of adaptive optics for astronomy. In this paper, we propose a new configuration of solar MCAO based on high order ground layer adaptive optics and low order high altitude correction, which result in a homogeneous correction effect in the whole field of view. An individual high order multiple direction Shack-Hartmann wavefront sensor is employed in the configuration to detect the ground layer turbulence for low altitude correction. Furthermore, the other low order multiple direction Shack-Hartmann wavefront sensor supplies the wavefront information caused by high layers' turbulence through atmospheric tomography for high altitude correction. Simulation results based on the system design at the 1-meter New Vacuum Solar Telescope show that the correction uniform of the new scheme is obviously improved compared to conventional solar MCAO configuration.

Compact single-shot radial shearing interferometer with random phase shift.

We propose a compact phase-shifting radial shearing interferometer based on a pixelated micro-retarder array (MRA). The MRA is made of a thin birefringence plate, and is composed of identical units that have pixels of four different thicknesses. We demonstrate that pixelated phase delay between two shearing beams can be introduced by applying the fast axis of birefringence plate in the horizontal or vertical orientation. We also present an approach to extract the wavefront under test with random phase shift, which dramatically reduces the machining difficulty of the MRA. The feasibility and accuracy of the proposed method are further validated through our numerical analysis. With the advantages of vibration immunity, simultaneous phase stepping, and broad spectral range, the presented interferometer is expected to be of potential use in a variety of applications, such as the detection of moving objects and dynamic processes.

Dispersed-fringe-accumulation-based left-subtract-right method for fine co-phasing of a dispersed fringe sensor.

In this paper, a dispersed-fringe-accumulation (DFA)-based left-subtract-right (LSR) piston estimation method (DFA-LSR), in which the dispersed fringe image is accumulated in the dispersed direction, and then the LSR method is used to estimate the piston error, is proposed for dispersed fringe sensors (DFS) in the fine co-phasing stage. The DFS is usually used to detect the piston errors (optical path difference) between different segmented mirrors or synthetic aperture telescopes. The DFA-LSR makes up for the shortcomings of the main peak position (MPP) method, which suffers from the constant offset in the pixel counts. The analysis and experiment results show that the proposed method can keep relatively better performance even at the condition of poor signal-to-noise ratio, compared with the MPP method in fine co-phasing stage.

First on-sky demonstration of the piezoelectric adaptive secondary mirror.

We propose using a piezoelectric adaptive secondary mirror (PASM) in the medium-sized adaptive telescopes with a 2-4 m aperture for structure and control simplification by utilizing the piezoelectric actuators in contrast with the voice-coil adaptive secondary mirror. A closed-loop experimental setup was built for on-sky demonstration of the 73-element PASM developed by our laboratory. In this Letter, the PASM and the closed-loop adaptive optics system are introduced. High-resolution stellar images were obtained by using the PASM to correct high-order wavefront errors in May 2016. To the best of our knowledge, this is the first successful on-sky demonstration of the PASM. The results show that with the PASM as the deformable mirror, the angular resolution of the 1.8 m telescope can be effectively improved.

[The Aberration Corrected Grating Spectrometer Based on Adaptive Optics].

To study the thermodynamics properties of the solar atmosphere with different height distribution, the imaging grating spectrometer with excellent image quality is one of the important tools to achieve this goal. However, the atmosphere turbulence can not be avoided for the imaging grating spectrometer installed in the ground-based solar telescope, and the imaging properties of the grating spectrometer will influenced by the wavefront aberration generalized by the atmosphere turbulence and the wavefront aberration generalized by the optical system adjusting errors and the optical element manufacturing errors. The atmospheric turbulence can be effectively compensated by the Adaptive Optics. To correct the wavefront aberrations of the optical system, a correction method based on Adaptive Optics is proposed, and the experiment validation is carried out to verify the feasibility of the method. The results demonstrate that the correction method proposed can effectively correct the wavefront aberration generalized by the atmosphere turbulence and the optical system aberration. The RMS value is roughly equal to 0.025λ after the Adaptive Optics correction. Besides, it has the virtue of lower the requirement of optical system adjusting errors and optical elements manufacturing errors.

Quantitative evaluation on internal seeing induced by heat-stop of solar telescope.

heat-stop is one of the essential thermal control devices of solar telescope. The internal seeing induced by its temperature rise will degrade the imaging quality significantly. For quantitative evaluation on internal seeing, an integrated analysis method based on computational fluid dynamics and geometric optics is proposed in this paper. Firstly, the temperature field of the heat-affected zone induced by heat-stop temperature rise is obtained by the method of computational fluid dynamics calculation. Secondly, the temperature field is transformed to refractive index field by corresponding equations. Thirdly, the wavefront aberration induced by internal seeing is calculated by geometric optics based on optical integration in the refractive index field. This integrated method is applied in the heat-stop of the Chinese Large Solar Telescope to quantitatively evaluate its internal seeing. The analytical results show that the maximum acceptable temperature rise of heat-stop is up to 5 Kelvins above the ambient air at any telescope pointing directions under the condition that the root-mean-square of wavefront aberration induced by internal seeing is less than 25nm. Furthermore, it is found that the magnitude of wavefront aberration gradually increases with the increase of heat-stop temperature rise for a certain telescope pointing direction. Meanwhile, with the variation of telescope pointing varying from the horizontal to the vertical direction, the magnitude of wavefront aberration decreases at first and then increases for the same heat-stop temperature rise.

Heat-stop structure design with high cooling efficiency for large ground-based solar telescope.

A heat-stop is one of the most important thermal control devices for a large ground-based solar telescope. For controlling the internal seeing effect, the temperature difference between the heat-stop and the ambient environment needs to be reduced, and a heat-stop with high cooling efficiency is required. In this paper, a novel design concept for the heat-stop, in which a multichannel loop cooling system is utilized to obtain higher cooling efficiency, is proposed. To validate the design, we analyze and compare the cooling efficiency for the multichannel and existing single-channel loop cooling system under the same conditions. Comparative results show that the new design obviously enhances the cooling efficiency of the heat-stop, and the novel design based on the multichannel loop cooling system is obviously better than the existing design by increasing the thermal transfer coefficient.

Speckle image reconstruction of the adaptive optics solar images.

Speckle image reconstruction, in which the speckle transfer function (STF) is modeled as annular distribution according to the angular dependence of adaptive optics (AO) compensation and the individual STF in each annulus is obtained by the corresponding Fried parameter calculated from the traditional spectral ratio method, is used to restore the solar images corrected by AO system in this paper. The reconstructions of the solar images acquired by a 37-element AO system validate this method and the image quality is improved evidently. Moreover, we found the photometric accuracy of the reconstruction is field dependent due to the influence of AO correction. With the increase of angular separation of the object from the AO lockpoint, the relative improvement becomes approximately more and more effective and tends to identical in the regions far away the central field of view. The simulation results show this phenomenon is mainly due to the disparity of the calculated STF from the real AO STF with the angular dependence.

Multichannel-Hadamard calibration of high-order adaptive optics systems.

we present a novel technique of calibrating the interaction matrix for high-order adaptive optics systems, called the multichannel-Hadamard method. In this method, the deformable mirror actuators are firstly divided into a series of channels according to their coupling relationship, and then the voltage-oriented Hadamard method is applied to these channels. Taking the 595-element adaptive optics system as an example, the procedure is described in detail. The optimal channel dividing is discussed and tested by numerical simulation. The proposed method is also compared with the voltage-oriented Hadamard only method and the multichannel only method by experiments. Results show that the multichannel-Hadamard method can produce significant improvement on interaction matrix measurement.