Phase diversity experimental results: deconvolution of ν Scorpii

A theoretical description of Phase Diversity is done in some detail to lay the foundations for the experimental effort. The Phase Diversity algorithm is formulated in the context of nonlinear programming where a metric is developed and then minimized. This development will show how the Zernike coefficients can be solved for directly using nonlinear optimization techniques. Computer simulations are used to validate the algorithms and techniques. The results of the computer simulations are shown. Once the confidence of the algorithms and techniques are established in the computer simulations, they are used on actual laboratory data. Detailed discussion of the laboratory implementation will be described and the laboratory results will be shown.

The phase diversity (PD) algorithm is an image-based co-phasing error detection method for segmented mirror synthetic aperture optical systems. Particle swarm optimization (PSO) is suitable for PD for its fast convergence speed and simple structure. However, with the increase of the numbers of subapertures, optimization of cost function formed by the PD algorithm becomes a high-dimension non-linear optimization problem, which would lead PSO to result in a premature solution. Regarding the problem above, this paper presented a modified PSO in the PD algorithm to co-phase the segmented primary mirror, which overcame drawbacks of the traditional PSO, such as premature convergence and deactivation of particles, and enhanced the dig ability of the algorithm. Vast simulation results show that the modified PSO in the PD algorithm can effectively restore the segmented primary mirror, reducing the peak-to-valley (PV) value to 0.0012λ and the root mean square error to 0.0007λ, and raising the Strehl ratio to over 0.999. A comparison was also conducted to show that the modified PSO has advantages over two existing algorithms in higher accuracy and faster convergence speed.

There is high demand for deploying real-time or near real-time implementation of image reconstruction techniques for intelligence, surveillance, and reconnaissance (ISR) systems, as well as biomedical systems, and border applications. While many image restoration techniques have been implemented, their computational complexity makes them unsuitable for real-time systems. This work presents massively parallelized algorithms for two and three-dimensional image reconstruction of objects using deconvolution and bispectrum techniques. Speckle imaging (SI) techniques are more preferred for phase reconstruction because of its high restoration quality at the lower values of signal-to-noise ratio (SNR), especially for smaller targets, and its shift-invariant property which makes it insensitive to random motion of an object. This work proposes, a novel strategy for parallelization of recursive bispectrum algorithm. Furthermore, parallel bispectrum speckle imaging technique is used as an initial step for parallelized multi-frame blind deconvolution (MFBD) image restoration algorithm in order to speed-up the reconstruction process for anisoplanatic, long horizontal path imaging. The parallel hybrid Bispectrum- MFBD (B-MFBD) technique, through massive parallelization, provides significantly large improvement to both bispectrum SI and MFBD parts of the hybrid algorithm. The work also investigates phase diversity (PD) technique as the special case of MFBD algorithm, where the object is observed with a stack of intentionally defocused images. The known defocused information between phases is used to estimate the object and aberration function. The multi-plane PD was implemented for wide field fluorescence microscopy imaging of three-dimensional objects. The PD algorithm was subsequently used to generate 3D point cloud data for the image from its single view.

We propose an adaptive optics system for a lightweight remote sensing sensor. The phase diversity (PD) technique, in which known wavefronts (Phase Diversity) are applied to the optics and the inherent aberrations are estimated using the acquired images without a priori information, is a key to realizing the system. For the reduction of computing cost and the enhancement of the estimation accuracy of aberration, a spatial light modulator (SLM) is adopted not only for wavefront compensator but also for PD generator. The SLM produces arbitrary "aberration modes" that are each represented by a Zernike polynomial. Therefore, optimal phase diversities are applied to the optical system and particular modes are effectively obtained, which makes it possible to overcome the conventional PD generated by defocusing that describes only quadratic form and lacks information of a particular mode. In order to solve the complex inverse problem of phase diversity with low computing cost, a general regression neural network (GRNN) is used. Moreover, principal component analysis compresses the input data for GRNN by extracting information from collected images in Fourier space, and reduces computation cost considerably. The performance is validated by numerical simulation, and the result of experiment using SLM is described.

The well known phase diversity technique has long been used as a premier passive imaging method to mitigate the degrading effects of atmospheric turbulence on incoherent optical imagery. Typically, an iterative, slow method is applied that uses the Zernike basis set and 2-D Fourier transforms in the reconstruction process. In this paper, we demonstrate a direct method for estimating the un-aberrated object brightness from phase or phase difference estimates that 1) does not require the use of the Zernike basis set or the intermediate determination of the generalized pupil function, 2) directly determines the optical transfer function without the requirement for an iterative sequence of 2-D Fourier Transforms, 3) provides a more accurate result than the Zernike-based approaches since there are no Zernike series truncation errors, 4) lends itself to fast and parallel implementation, and 5) can use stochastic search methods to rapidly determine simultaneous phases or phase differences required to determine the correct optical transfer function estimate. As such, this new implementation of phase diversity provides potentially faster, more accurate results than previous approaches yet still retains inherent compatibility with the traditional Zernike-based methods. The theoretical underpinnings of this new method along with demonstrative computer simulation results are presented.

Exoplanet direct imaging with a ground-based telescope needs a very high performance adaptive optics (AO) system, so-called eXtreme AO (XAO), a coronagraph device, and a smart imaging process. One limitation of AO system in operation remains the Non Common Path Aberrations (NCPA). To achieve the ultimate XAO performance, these aberrations have to be measured with a dedicated wavefront sensor placed in the imaging camera focal plane, and then pre-compensated using the AO closed loop process. In any events, the pre-compensation should minimize the aberrations at the coronagraph focal plane mask. An efficient way for the NCPA measurement is the phase diversity technique. A pixel-wise approach is well-suited to estimate NCPA on large pupils and subsequent projection on the deformable mirror with Cartesian geometry. However it calls for a careful regularization for optimal results. The weight of the regularization is written in close-form for un-supervised tuning. The accuracy of NCPA pre-compensation is below 8 nm for a wide range of conditions. Point-by-point phase estimation improves the accuracy of the Phase Diversity method. The algorithm is validated in simulation and experimentally. It will be implemented in SAXO, the XAO system of the second generation VLT instrument: SPHERE.

Wavefront sensorless adaptive optics system for extended objects based on linear phase diversity technique

The High Performance CO2 Lidar Surveillance Sensor system (HI-CLASS) is a state-of- the-art coherent ladar system which will provide precision tracking and high resolution imaging at the Air Force Maui Optical Station (AMOS). System development is occurring in 3 phases representing increasing hardware/software complexity and system capability. The recently-completed Phase 1 HI-CLASS system employs a compact, pulsed, coherent CO2 oscillator, a heterodyne receiver, and signal recorder coupled to the AMOS 0.6 m Laser Beam Director to demonstrate target (satellite) acquisition and tracking, illumination, return signal detection, signal recording, and off-line processing for range and range rate extraction and range-amplitude imaging. This paper will discuss the Phase 1 HI-CLASS hardware configuration, test objectives, and test results to date employing cooperative, retro-equipped satellites and describe the Phase 2 hardware currently undergoing initial testing.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Within the last decade, the declassification of adaptive optics techniques and systems developed for defense purposes opened new opportunities to the astronomical community. Since the military resolution requirements are not qualitatively different from the astronomical ones, astronomers may profit from the quite sizable investments already made. On the other hand, the astronomical observations are much more demanding than the military ones with respect to the required accuracy, stability and sensitivity. In 1994, after contacts made during an adaptive optics meeting in Munich, we started a joint project to observe the ejected matter from the luminous blue variable (LBV) P-Cygni with the AMOS compensated imaging system (CIS). In this paper we describe the problems encountered and the experience gained in more than two years of operations with CIS. The satisfactory results obtained so far prompted us to plan a more ambitious program. We aim to profit from the acquired know-how for preparing a proposal of astronomical observations designed in such a way of taking the utmost advantage of the capabilities of the new USAF AEOS adaptive optics system.

We compare the performance of four metrics for use in a phase diversity algorithm. Three of the metrics utilize a regularization based on the signal-to-noise ratio.

The phase diversity technique is studied as a wave-front sensor to be implemented with widely extended sources. The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images (in focus and out of focus) by use of a maximum-likelihood approach. The propagation of the photon noise in the images on the estimated phase is derived from a theoretical analysis. The covariance matrix of the phase estimator is calculated, and the optimal distance between the observation planes that minimizes the noise propagation is determined. The phase error is inversely proportional to the number of photons in the images. The noise variance on the Zernike polynomials increases with the order of the polynomial. These results are confirmed with both numerical and experimental validations. The influence of the spectral bandwidth on the phase estimator is also studied with simulations.

The misalignment between recorded in-focus and out-of-focus images using the Phase Diversity (PD) algorithm leads to a dramatic decline in wavefront detection accuracy and image recovery quality for segmented active optics systems. This paper demonstrates the theoretical relationship between the image misalignment and tip-tilt terms in Zernike polynomials of the wavefront phase for the first time, and an efficient two-step alignment correction algorithm is proposed to eliminate these misalignment effects. This algorithm processes a spatial 2-D cross-correlation of the misaligned images, revising the offset to 1 or 2 pixels and narrowing the search range for alignment. Then, it eliminates the need for subpixel fine alignment to achieve adaptive correction by adding additional tip-tilt terms to the Optical Transfer Function (OTF) of the out-of-focus channel. The experimental results demonstrate the feasibility and validity of the proposed correction algorithm to improve the measurement accuracy during the co-phasing of segmented mirrors. With this alignment correction, the reconstructed wavefront is more accurate, and the recovered image is of higher quality.

The technique of Phase Diversity (PD) is widely adopted to measure the wavefront error caused by atmosphere turbulence and system error. PD solves the Zernike coefficients of the wavefront by utilizing two images obtained with different defocus value. In this paper, we propose a method to restore the image and estimate the wavefront error of an imaging system. And we use present white noises to verify the robustness of the algorithm. We design an experiment system and implement it in our laboratory. The proposed algorithm is validated by computer simulations and experimental results. To use a broadband white object in experimental system a reasonable simplification for the system model is done. Our results show that the robustness against Gaussian white noises of the method is better then the case when the variance value is 0.03. The proposed method can be used as a wavefront sensor and restore the degradative images by photoelectric image system.

We validate by simulations an extension of the phase diversity technique that uses long exposure adaptive optics corrected images for sensing quasi-static aberrations during the scientific observation, in particul ar for high-contrast imaging. The principle of the method is th at, for a su ciently long exposure time, the residual turbulence is averaged into a convolutive component of the image and that phase diversity estimates the sole static aberrations of interest. The advantages of such a pro cedure, compared to the processing of short- exposure image pairs, are that the separation between static aberrat ions and turbulence-induced ones is performed by the long-exposure itself and not numerically, that only one image pair must be processed, that the estimation benefits from the high SNR of long-exposure images, and that only the static aberrations of interest are to be estimated. Long-exposure phase diversity can also be used as a phasing sensor for a segmented aperture telescope. Thus, it may be particularly useful for future planet finder projects such as EPICS on the European ELT.

Context.The performance of high-contrast imaging instruments is limited by wavefront errors, in particular by non-common path aberrations (NCPAs). Focal-plane wavefront sensing (FPWFS) is appropriate to handle NCPAs because it measures the aberration where it matters the most, that is to say at the science focal plane. Phase retrieval from focal-plane images results, nonetheless, in a sign ambiguity for even modes of the pupil-plane phase.Aims.The phase diversity methods currently used to solve the sign ambiguity tend to reduce the science duty cycle, that is, the fraction of observing time dedicated to science. In this work, we explore how we can combine the phase diversity provided by a vortex coronagraph with modern deep learning techniques to perform efficient FPWFS without losing observing time.Methods.We applied the state-of-the-art convolutional neural network EfficientNet-B4 to infer phase aberrations from simulated focal-plane images. The two cases of scalar and vector vortex coronagraphs (SVC and VVC) were considered using a single post-coronagraphic point spread function (PSF) or two PSFs obtained by splitting the circular polarization states, respectively.Results.The sign ambiguity has been properly lifted in both cases even at low signal-to-noise ratios (S/Ns). Using either the SVC or the VVC, we have reached a very similar performance compared to using phase diversity with a defocused PSF, except for high levels of aberrations where the SVC slightly underperforms compared to the other approaches. The models finally show great robustness when trained on data with a wide range of wavefront errors and noise levels.Conclusions.The proposed FPWFS technique provides a 100% science duty cycle for instruments using a vortex coronagraph and does not require any additional hardware in the case of the SVC.