Compressive Shack-Hartmann Wavefront Sensor based on Deep Neural Networks
College of Physics and Optoelectronics, Taiyuan University of Technology（太原理工大学物理与光电工程学院）；Department of Physics, Durham University（杜伦大学物理系）；College of Information and Computer Science, Taiyuan University of Technology（太原理工大学信息与计算机学院）
Peng Jia, Mingyang Ma, Dongmei Cai, Weihua Wang, Juanjuan Li, Can Li
The Shack-Hartmann wavefront sensor is widely used to measure aberrations induced by atmospheric turbulence in adaptive optics systems. However if there exists strong atmospheric turbulence or the brightness of guide stars is low, the accuracy of wavefront measurements will be affected. In this paper, we propose a compressive Shack-Hartmann wavefront sensing method. Instead of reconstructing wavefronts with slope measurements of all sub-apertures, our method reconstructs wavefronts with slope measurements of sub-apertures which have spot images with high signal to noise ratio. Besides, we further propose to use a deep neural network to accelerate wavefront reconstruction speed. During the training stage of the deep neural network, we propose to add a drop-out layer to simulate the compressive sensing process, which could increase development speed of our method. After training, the compressive Shack-Hartmann wavefront sensing method can reconstruct wavefronts in high spatial resolution with slope measurements from only a small amount of sub-apertures. We integrate the straightforward compressive Shack-Hartmann wavefront sensing method with image deconvolution algorithm to develop a high-order image restoration method. We use images restored by the high-order image restoration method to test the performance of our the compressive Shack-Hartmann wavefront sensing method. The results show that our method can improve the accuracy of wavefront measurements and is suitable for real-time applications.
Three centroiding techniques to estimate the position of the spots in a Shack Hartmann sensor: Normalized Centre of Gravity (CoG), Iteratively Weighted Centre of Gravity (IWCoG) and Intensity Weighted (IWC) centroiding are studied in comparison. The spot pattern at the focal plane of a Shack Hartmann sensor was simulated by including the effect of a background noise. We present the results of optimization of the performance of each of the centroiding techniques as a function of Signal to Noise Ratio (SNR) at different experimental conditions.
The precise reconstruction of the turbulent volume is a key point in the development of new-generation Adaptive Optics systems. We propose a new Cn2 profilometry method named CO-SLIDAR (COupled Slope and scIntillation Detection And Ranging), that uses correlations of slopes and scintillation indexes recorded on a Shack-Hartmann from two separated stars. CO-SLIDAR leads to an accurate Cn2 retrieval for both low and high altitude layers. Here, we present an end-to-end simulation of the Cn2 profile measurement. Two Shack-Hartmann geometries are considered. The detection noises are taken into acco…
Context. Solar Shack-Hartmann wavefront sensors measure differential wavefront tilts as the relative shift between images from different subapertures. There are several methods in use for measuring these shifts. Aims. We evaluate the inherent accuracy of the methods and the effects of various sources of error, such as noise, bias mismatch, and blurring. We investigate whether Z-tilts or G-tilts are measured. Methods. We test the algorithms on two kinds of artificial data sets, one corresponding to images with known shifts and one corresponding to seeing with different r_0. Results. Our results…
The Max-Planck institutes for astronomy (MPIA) and for extraterrestrial physics (MPE) run an adaptive optics (AO) system with a laser guide star at the 3.5 m telescope on Calar Alto, Spain. This system, called ALFA, produces now scientific results and works ex- cellent with natural guide stars (NGS) as faint as 13th magnitude in R-band. The ultimate goal however is to achieve similar performances with the laser guide star (LGS) which is faint and extended. We introduce the Shack-Hartmann wavefront sensor implemented in ALFA and present our efforts in increasing its sensitivity by using advance…
We investigate the improvements in Shack-Hartmann wavefront sensor image processing that can be realised using total variation minimisation techniques to remove noise from these images. We perform Monte-Carlo simulation to demonstrate that at certain signal-to-noise levels, sensitivity improvements of up to one astronomical magnitude can be realised. We also present on-sky measurements taken with the CANARY adaptive optics system that demonstrate an improvement in performance when this technique is employed, and show that this algorithm can be implemented in a real-time control system. We conc…
The Shack-Hartmann Wavefront Sensor (WFS) is well-known in the fields of optical metrology, wavefront sensing in astronomy, and ophthalmologic control applications. The purpose of this communication is to bring new insights on the historical Hartmann test and to compare it with the less known reverse Hartmann test, where the locations of the pupil mask and observed image planes are exchanged. Both tests can actually be interpreted by using the formalism of Fourier optics, i.e. Fraunhofer diffraction for the Shack-Hartmann and Fresnel diffraction in the reverse configuration. The principles of …
Real-time seeing estimation at the focus of a telescope is nowadays strongly emphasized as this knowledge virtually drives the dimensioning of adaptive optics systems and instrument operational aspects. In this context we study the interest of using active optics Shack-Hartmann (AOSH) sensor images to provide accurate estimate of the seeing. The AOSH practically delivers long exposure spot PSFs -- at the critical location of the telescope focus -- being directly related to the atmospheric seeing in the line of sight. Although AOSH sensors are not specified to measure spot sizes but slopes, we …
Cn2 profile monitoring usually makes use of wavefront slope correlations or of scintillation pattern correlations. Wavefront slope correlations provide sensitivity to layers close to the receiving plane. In addition, scintillation correlations allow a better sensitivity to high turbulence layers. Wavefront slope and scintillation correlations are therefore complementary. Slopes and scintillation being recorded simultaneously with a Shack-Hartmann wavefront sensor (SHWFS), we propose here to exploit their correlation to retrieve the Cn2 profile. The measurement method named COupled SLodar scIDA…
In recent years, detectors with sub-electron readout noise have been used very effectively in astronomical adaptive optics systems. Here, we compare readout noise models for the two key faint flux level detector technologies that are commonly used: EMCCD and scientific CMOS (sCMOS) detectors. We find that in almost all situations, EMCCD technology is advantageous, and that the commonly used simplified model for EMCCD readout is appropriate. We also find that the commonly used simple models for sCMOS readout noise are optimistic, and recommend that a proper treatment of the sCMOS rms readout no…
The use of Adaptive Optics in Extremely Large Telescopes brings new challenges, one of which is the treatment of Shack-Hartmann Wavefront sensors images. When using this type of sensors in conjunction with laser guide stars for sampling the pupil of telescopes with 30+ m in diameter, it is necessary to compute the centroid of elongated spots, whose elongation angle and aspect ratio are changing across the telescope pupil. Existing techniques such as Matched Filter have been considered as the best technique to compute the centroid of elongated spots, however they are not good at coping with the…
Adaptive optics (AO) systems using tomographic estimation of three-dimensional structure of atmospheric turbulence requires vertical atmospheric turbulence profile, which describes turbulence strength as a function of altitude as a prior information. We propose a novel method to reconstruct the profile by applying Multi Aperture Scintillation Sensor (MASS) method to scintillation data obtained by a Shack-Hartmann wavefront sensor (SH-WFS). Compared to the traditional MASS, which uses atmospheric scintillation within 4 concentric annular apertures, the new method utilizes scintillation in sever…
The ability to position multiple miniaturized wavefront sensors precisely over large focal surfaces are advantageous to multi-object adaptive optics. The Australian Astronomical Observatory (AAO) has prototyped a compact and lightweight Shack-Hartmann wavefront-sensor that fits into a standard Starbug parallel fibre positioning robot. Each device makes use of a polymer coherent fibre imaging bundle to relay an image produced by a microlens array placed at the telescope focal plane to a re-imaging camera mounted elsewhere. The advantages of the polymer fibre bundle are its high-fill factor, hig…
Shack Hartmann Sensor (SHS) is inflicted with significant background noise that deteriorates the wave-front reconstruction accuracy. In this paper, a simple method to remove the back ground noise with the use of Zernike polynomials is suggested. The images corresponding to individual array points of the SHS at the detector, placed at the focal plane are independently reconstructed using Zernike polynomials by the calculation of Zernike moments. Appropriate thresholding is applied on the images. It is shown with computational experiments that using Zernike Reconstructor along with usual thresho…
Shack-Hartmann wavefront sensors using wound fibre bundles are desired for multi-object adaptive optical systems to provide large multiplex positioned by Starbugs. The use of the large-sized wound fibre bundle provides the exibility to use more sub-apertures wavefront sensor for ELTs. These compact wavefront sensors take advantage of large focal surfaces such as the Giant Magellan Telescope. The focus of this paper is to study the wound fibre image bundle structure defects effect on the centroid measurement accuracy of a Shack-Hartmann wavefront sensor. We use the first moment centroid method …
Sodium Laser Guide Stars (LGSs) are elongated sources due to the thickness and the finite distance of the sodium layer. The fluctuations of the sodium layer altitude and atom density profile induce errors on centroid measurements of elongated spots, and generate spurious optical aberrations in closed--loop adaptive optics (AO) systems. According to an analytical model and experimental results obtained with the University of Victoria LGS bench demonstrator, one of the main origins of these aberrations, referred to as LGS aberrations, is not the Centre-of-Gravity (CoG) algorithm itself, but the …
The estimation of atmospheric turbulence parameters is of relevance for: a) site evaluation & characterisation; b) prediction of the point spread function; c) live assessment of error budgets and optimisation of adaptive optics performance; d) optimisation of fringe trackers for long baseline optical interferometry. The ubiquitous deployment of Shack-Hartmann wavefront sensors in large telescopes makes them central for atmospheric turbulence parameter estimation via adaptive optics telemetry. Several methods for the estimation of the Fried parameter and outer scale have been developed, most of…
Over the last few years increasing consideration has been given to the study of Laser Guide Stars (LGS) for the measurement of the disturbance introduced by the atmosphere in optical and near-infrared astronomical observations from the ground. A possible method for the generation of a LGS is the excitation of the Sodium layer in the upper atmosphere at approximately 90 km of altitude. Since the Sodium layer is approximately 10 km thick, the artificial reference source looks elongated, especially when observed from the edge of a large aperture. The spot elongation strongly limits the performanc…
CO-SLIDAR is a very promising technique for the metrology of near ground $C_n^2$ profiles. It exploits both phase and scintillation measurements obtained with a dedicated wavefront sensor and allows profiling on the full line of sight between pupil and sources. This technique is applied to an associated instrument based on a mid-IR Shack-Hartmann wavefront sensor, coupled to a 0.35 m telescope, which observes two cooperative sources. This paper presents the first comprehensive description of the CO-SLIDAR method in the context of near ground optical turbulence metrology. It includes the presen…
Shack-Hartmann wavefront sensing relies on accurate spot centre measurement. Several algorithms were developed with this aim, mostly focused on precision, i.e. minimizing random errors. In the solar and extended scene community, the importance of the accuracy (bias error due to peak-locking, quantisation or sampling) of the centroid determination was identified and solutions proposed. But these solutions only allow partial bias corrections. To date, no systematic study of the bias error was conducted. This article bridges the gap by quantifying the bias error for different correlation peak-fin…
An important factor which affects performance of solar adaptive optics (AO) systems is the accuracy of tracking an extended object in the wavefront sensor. The accuracy of a centre-ofmass approach to image shift measurement depends on the parameters applied in thresholding the recorded image; however, there exists no analytical prediction for these parameters for extended objects. Motivated by this we present a new method for exploring the parameter space of image shift measurement algorithms, and apply this to optimize the parameters of the algorithm. Using a thresholded, windowed centre of m…
Real-time seeing and outer scale estimation at the location of the focus of a telescope is fundamental for the adaptive optics systems dimensioning and performance prediction, as well as for the operational aspects of instruments. This study attempts to take advantage of multiwavelength long exposure images to instantaneously and simultaneously derive the turbulence outer scale and seeing from the full-width at half-maximum (FWHM) of seeing-limited images taken at the focus of a telescope. These atmospheric parameters are commonly measured in most observatories by different methods located awa…
The Shack-Hartman wavefront sensor designed for final acceptance of 2.5m SAI telescope allows to measure the shape of the wavefront on exit pupil of the telescope using a bright star. The reference laser source on wavelength 532 nm is used for measurements. During testing the device at different telescopes it was found out what it's probable to estimate some properties of air streams in the dome. Such estimations have been made for three domes: 1.5 m AZT-22 and 1.0 m Zeiss telescope of Maidanak Observatory, Uzbekistan and for 2.6 m telescope ZTSh of Crimean observatory, Ukraine. The following …
Laser guide stars (LGS) are used in many adaptive optics systems to extend sky coverage. The most common wavefront sensor used in combination with a LGS is a Shack-Hartmann wavefront sensor (SHWFS). The Shack-Hartmann has a major disadvantage for extended source wavefront sensing because it directly samples the image. In this proceeding we propose to use the generalized-Optical Differentation Wavefront Sensor (g-ODWFS) a wavefront sensor for wavefront sensing of LGS. The g-ODWFS uses only 4 pixels per sub-aperture, has little to no aliasing noise and therefore no spurious low-order errors and …
Shack-Hartmann wavefront sensors for both solar and laser guide star adaptive optics (with elongated spots) need to observe extended objects. Correlation techniques have been successfully employed to measure the wavefront gradient in solar adaptive optics systems and have been proposed for laser guide star systems. In this paper we describe a method for synthesising reference images for correlation Shack-Hartmann wavefront sensors with a larger field of view than individual sub-apertures. We then show how these supersized reference images can increase the performance of correlation wavefront s…
Shack Hartmann wavefront sensor is a two dimensional array of lenslets which is used to detect the incoming phase distorted wavefront through local tilt measurements made by recording the spot pattern near the focal plane. Wavefront reconstruction is performed in two stages - (a) image centroiding to calculate local slopes, (b) formation of the wavefront shape from local slope measurement. Centroiding accuracy contributes to most of the wavefront reconstruction error in Shack Hartmann sensor based adaptive optics system with readout and background noise. It becomes even more difficult in atmos…
Australian National University（澳大利亚国立大学）；School of Computing（计算机学院）；Research School of Astronomy and Astrophysics（天文与天体物理研究学校）；Advanced Instrumentation Technology Centre（先进仪器技术中心）
Atmospheric turbulence degrades the quality of astronomical observations in ground-based telescopes, leading to distorted and blurry images. Adaptive Optics (AO) systems are designed to counteract these effects, using atmospheric measurements captured by a wavefront sensor to make real-time corrections to the incoming wavefront. The Fried parameter, r0, characterises the strength of atmospheric turbulence and is an essential control parameter for optimising the performance of AO systems and more recently sky profiling for Free Space Optical (FSO) communication channels. In this paper, we devel…
The differential Optical Transfer Function (dOTF) is a focal plane wavefront sensing method that uses a diversity in the pupil plane to generate two different focal plane images. The difference of their Fourier transforms recovers the complex amplitude of the pupil down to the spatial scale of the diversity. We produce two simultaneous PSF images with diversity using a polarizing filter at the edge of the telescope pupil, and a polarization camera to simultaneously record the two images. Here we present the first on-sky demonstration of polarization dOTF at the 1.0m South African Astronomical …
We describe the concept of splitting spatial frequency perturbations into some kind of pupil planes wavefront sensors. Further to the existing approach of dropping higher spatial frequency to suppress aliasing effects (the so-called spatial filtered Shack-Hartmann), we point out that spatial frequencies splitting and mixing of these in a proper manner, could be handled in order to exhibit some practical or fundamental advantages. In this framework we describe the idea behind such class of concepts and we derive the relationship useful to determine if, by which extent, and under what kind of me…
Wavefront sensing in solar adaptive-optics is currently done with correlating Shack-Hartmann sensors, although the spatial- and temporal-resolutions of the phase measurements are then limited by the extremely fast computing required to correlate the sensor signals at the frequencies of daytime atmospheric-fluctuations. To avoid this limitation, a new wavefront-sensing technique is presented, that makes use of the solar brightness and is applicable to extended sources. The wavefront is sent through a modified Mach-Zehnder interferometer. A small, central part of the wavefront is used as referen…
An adaptive optics system with a single deformable mirror is being implemented on the THEMIS 90cm solar telescope. This system is designed to operate in the visible and is required to be as robust as possible in order to deliver the best possible correction in any atmospheric conditions, even if wavefronts are sensed on some low-contrast solar granulation. In extreme conditions, the images given by the subapertures of the Shack-Hartmann wavefront sensor get randomly blurred in space, in the set of subapertures, and the distribution of blurred images is rapidly changing in time, some of them po…
The Multiconjugate Adaptive optics Demonstrator (MAD) has successfully demonstrated on sky both Star Oriented (SO) and Layer Oriented (LO) multiconjugate adaptive optics techniques. While SO has been realized using 3 Shack-Hartmann wavefront sensors (WFS), we designed a multi-pyramid WFS for the LO. The MAD bench accommodates both WFSs and a selecting mirror allows choosing which sensor to use. In the LO approach up to 8 pyramids can be placed on as many reference stars and their light is co-added optically on two different CCDs conjugated at ground and to an high layer. In this paper we discu…
Commonly used wavefront sensors, the Shack Hartmann wavefront sensor and the pyramid wavefront sensor, for example, have large dynamic range or high sensitivity, trading one regime for the other. A new type of wavefront sensor is being developed and is currently undergoing testing at the University of Arizona's Center for Astronomical Adaptive Optics. This sensor builds on linear optical differentiation theory by using linear, spatially varying halfwave plates in an intermediate focal plane. These filters, along with the polarizing beam splitters, divide the beam into four pupil images, simila…
The basic outline of a pupil plane WaveFront Sensor is reviewed taking into account that the source to be sensed could be different from an unresolved source, i.e. it is extended, and that it could deploy also in a 3D fashion, enough to exceed the field's depth of the observing telescope. Under these conditions it is pointed out that the features of the reference are not invariant for different position on the pupil and it is shown that the INGOT WFS is the equivalent of the Pyramid for a Laser Guide Star. Under these conditions one can imagine to use a Dark WFS approach to improve the SNR of …
The new class of large telescopes, as the future ELT, are designed to work with Laser Guide Star (LGS) tuned to a resonance of atmosphere sodium atoms. This wavefront sensing technique presents complex issues for an application to big telescopes due to many reasons mainly linked to the finite distance of the LGS, the launching angle, Tip-tilt indetermination and focus anisoplanatism. The implementation of a laboratory Prototype for LGS wavefront sensor (WFS) at the beginning of the phase study of MAORY, the Multi-conjugate Adaptive Optics RelaY for the ELT first light, has been indispensable t…
The nonlinear curvature wavefront sensor (nlCWFS) has been shown to be a promising alternative to existing wavefront sensor designs. Theoretical studies indicate that the inherent sensitivity of this device could offer up to a factor of 10 times improvement compared to the widely-used Shack-Hartmann wavefront sensor (SHWFS). The nominal nlCWFS design assumes the use of four detector measurement planes in a symmetric configuration centered around an optical system pupil plane. However, the exact arrangement of these planes can potentially be optimized to improve aberration sensitivity, and mini…
Laser Guide Star (LGS) Shack-Hartmann (SH) wavefront sensors for next generation Extremely Large Telescopes (ELTs) require low-noise, large format (about 1Mpx), fast detectors to match the need for a large number of subapertures and a good sampling of the very elongated spots. One path envisaged to fulfill this need has been the adoption of CMOS detectors with a rolling shutter read-out scheme, that allows low read-out noise and fast readout time at the cost of image distortion due to the detector rows exposed in different moments. In this work we analyze the impact of the rolling shutter read…
The performance of adaptive optics systems is partially dependant on the algorithms used within the real-time control system to compute wavefront slope measurements. We demonstrate use of a matched filter algorithm for the processing of elongated laser guide star (LGS) Shack-Hartmann images, using the CANARY adaptive optics instrument on the 4.2m William Herschel Telescope and the European Southern Observatory Wendelstein LGS Unit placed 40m away. This algorithm has been selected for use with the forthcoming Thirty Meter Telescope, but until now had not been demonstrated on-sky. From the resul…
Ground-based high contrast imaging (HCI) and extreme adaptive optics (AO) technologies have advanced to the point of enabling direct detections of gas-giant exoplanets orbiting beyond the snow lines around nearby young star systems. However, leftover wavefront errors using current HCI and AO technologies, realized as "speckles" in the coronagraphic science image, still limit HCI instrument sensitivities to detecting and characterizing lower-mass, closer-in, and/or older/colder exoplanetary systems. Improving the performance of AO wavefront sensors (WFSs) and control techniques is critical to i…
Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this, however identification and tracking of relevant turbulent parameters (such as wind speeds) is required for such parametric techniques. This can complicate practical implementations and introduce stability issues when encountering variable conditions. Here we present a nonlinear wavefront predictor using a Long Short-Term Memory (LSTM) artificial neural network (ANN) that assumes no prior knowledge of the atmosphere …
The use of laser guide stars in astronomical adaptive optics results in elongated Shack-Hartmann wavefront sensor image patterns. Image correlation techniques can be used to determine local wavefront slope by correlating each sub-aperture image with its expected elongated shape, or reference image. Here, we present a technique which allows the correlation reference images to be updated while the adaptive optics loop is closed. We show that this can be done without affecting the resulting point spread functions. On-sky demonstration is reported. We compare different techniques for obtaining the…
This paper describes the data preprocessing and reduction methods together with SLODAR analysis and wind profiling techniques for GeMS: the Gemini MCAO System. The wavefront gradient measurements of the five GeMS's Shack-Hartmann sensors, each one pointing to a laser guide star, are combined with the DM commands sent to three deformable mirrors optically conjugated at 0, 4.5 and 9 km in order to reconstruct pseudo-open loop slopes. These pseudo-open loop slopes are then used to reconstruct atmospheric turbulence profiles, based on the SLODAR and wind-profiling methods. We introduce the SLODAR …
The Low Wind Effect (LWE) refers to a phenomenon that occurs when the wind speed inside a telescope dome drops below $3$m/s creating a temperature gradient near the telescope spider. This produces phase discontinuities in the pupil plane that are not detected by traditional Adaptive Optics (AO) systems such as the pyramid wavefront sensor or the Shack-Hartmann. Considering the pupil as divided in 4 quadrants by regular spiders, the phase discontinuities correspond to piston, tip and tilt aberrations in each quadrant of the pupil. Uncorrected, it strongly decreases the ability of high contrast …
