Phase Diversity Method Research Articles

Advanced Phase Diversity Method for telescope static aberration compensation

Accurate calibration is essential for high-performance Adaptive Optics (AO) systems in astronomy. This paper presents a novel methodology for AO systems calibration that preserves the optical path integrity while achieving high-quality results. By eliminating the need for optical modifications, this approach simplifies system complexity and accounts for all static aberrations. The main novelty of this proposal is an advanced Phase Diversity (PD) method for estimating static optical aberrations. Unlike conventional PD techniques, this approach uses the AO system’s deformable mirror to introduce different diversities, eliminating the need for additional calibration hardware. Furthermore, the optimizer Adam is introduced for the first time in this field to estimate the optical aberrations. To evaluate the performance of this new methodology, a set of experiments under varying operating conditions and optimization parameters has been conducted. Results demonstrated that the presented methodology is capable of providing diffraction-limited corrected images with a Strehl Ratio (SR) exceeding 0.80 within 2 min. Furthermore, employing a Manhattan distance-based error function effectively balanced estimation speed and accuracy. The method demonstrated effectiveness across a wide range of aberration magnitudes, achieving an error of 3 nm in the best scenarios. This proposal represents an advancement in the identification and correction of static aberrations in telescope optical systems, directly improving the acquisition of high-quality references for AO sensing.

Exploring Wavefront Detection in Imaging Systems with Rectangular Apertures Using Phase Diversity.

The attainment of a substantial aperture in the rotating synthetic aperture imaging system involves the rotation of a slender rectangular primary mirror. This constitutes a pivotal avenue of exploration in space telescope research. Due to the considerable aspect ratio of the primary mirror, environmental disturbances can significantly impact its surface shape. Active optical technology can rectify surface shape irregularities through the detection of wavefront information. The Phase Diversity (PD) method utilizes images captured by the imaging system to compute wavefront information. In this study, the PD method is applied to rotating synthetic and other rectangular aperture imaging systems, employing Legendre polynomials to model the wavefront. The study delved into the ramifications stemming from the aperture aspect ratio and aberration size.

Sequential phase diversity for wavefront correction using a deformable mirror with modeling errors.

The phase diversity (PD) method is effective for scene-based wavefront sensing and control (WFSC) in spaceborne high-resolution imagers for Earth observation. The simplest way of performing the PD WFSC is offering a diversity wavefront by directly actuating a corrective device, such as a deformable mirror. However, this strategy faces a challenge in constructing a numerical model of the provided diversity wavefront because some corrective actuators' properties prevent us from precisely determining their deflection behaviors. To avoid this modeling issue, we propose the sequential PD (SPD) method to compensate for static aberration using a corrective device with modeling errors. The SPD WFSC repeats the PD WFSC to gradually correct the aberration, where the estimated corrective wavefront is regarded as the known diversity in the subsequent PD WFSC. The numerical simulation validated that the proposed idea improved the correction performance when a corrective device had a linear modeling error. Additionally, a demonstration experiment succeeded in aberration removal using a face-sheet deformable mirror with inter-actuator coupling and non-linear responses. An additional simulation demonstrated that the proposed method effectively corrected the discontinuous wavefront aberration in multi-aperture imaging systems. The SPD WFSC can potentially bring us optical remote sensing systems with unprecedentedly high resolution.

Piston Detection of Optical Sparse Aperture Systems Based on an Improved Phase Diversity Method

The piston error has a significant effect on the imaging resolution of the optical sparse aperture system. In this paper, an improved phase diversity method based on particle swarm optimization and the sequential quadratic programming algorithm is proposed, which can overcome the drawbacks of the traditional phase diversity method and particle swarm optimization, such as the instability that results from polychromatic light conditions and premature convergence. The method introduces factor β in the stage of calculating the objective function, and combines the advantages of a heuristic algorithm and a nonlinear programming algorithm in the optimization stage, thus enhancing the accuracy and stability of piston detection. Simulations based on a dual-aperture optical sparse aperture system verified that the root mean square error obtained by the method can be guaranteed to be within 0.001λ (wavelength), which satisfies the requirement of practical imaging. An experimental test was also conducted to demonstrate the performance of the method, and the test results showed that the quality of the image after piston detection and correction improved significantly compared to images with the co-phase error.

Fast High-Resolution Phase Diversity Wavefront Sensing with L-BFGS Algorithm

The presence of manufacture error in large mirrors introduces high-order aberrations, which can severely influence the intensity distribution of point spread function. Therefore, high-resolution phase diversity wavefront sensing is usually needed. However, high-resolution phase diversity wavefront sensing is restricted with the problem of low efficiency and stagnation. This paper proposes a fast high-resolution phase diversity method with limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm, which can accurately detect aberrations in the presence of high-order aberrations. An analytical gradient of the objective function for phase-diversity is integrated into the framework of the L-BFGS nonlinear optimization algorithm. L-BFGS algorithm is specifically suitable for high-resolution wavefront sensing where a large phase matrix is optimized. The performance of phase diversity with L-BFGS is compared to other iterative method through simulations and a real experiment. This work contributes to fast high-resolution image-based wavefront sensing with a high robustness.

Cophasing detection of the segmented diffractive optical elements with the phase diversity method

The diffractive optical elements (DOEs) have the advantages of lightweight, low-cost, loose surface-figure tolerances and convenient folding, which provides a direction for next-generation large (>20 m) space telescopes. However, the cophasing of the DOEs limits its application in telescopes and decreases the optical system performance. The phase diversity method is studied and introduced to solve the cophasing detection of the two segmented DOEs. An improved experimental system is set up using the phase diversity method, and the experiment results show that the piston error and tilt error of the two mirrors are 0.03λ and 0.05 μrad, respectively, which meet the actual needs of the cophasing errors.

A deep learning approach for focal-plane wavefront sensing using vortex phase diversity

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.

Iterative framework for a high accuracy aberration estimation with one-shot wavefront sensing

Deep neural networks have contributed to the progress of image-based wavefront sensing adaptive optics (AO) with the non-iterative regression of aberration. However, algorithms relying on the one-shot point spread function (PSF) typically yield less accuracy. Thus, this paper proposes an iterative closed-loop framework for wavefront aberration estimation outperforming the non-iterative baseline methods with the same computation. Specifically, we simulate the defocus PSF concerning the estimation of the Zernike coefficients and input it into the backbone network with the ground-truth defocus PSF. The difference between the ground-truth and estimated Zernike coefficients is used as a new label for training the model. The prediction updates the estimation, and the accuracy refined through iterations. The experimental results demonstrate that the iterative framework improves the accuracy of the existing networks. Furthermore, we challenge our scheme with the multi-shot phase diversity method trained with baseline networks, highlighting that the framework improves the one-shot accuracy to the multi-shot level without noise.

A machine-learning approach to correcting atmospheric seeing in solar flare observations

ABSTRACT Current post-processing techniques for the correction of atmospheric seeing in solar observations – such as Speckle interferometry and Phase Diversity methods – have limitations when it comes to their reconstructive capabilities of solar flare observations. This, combined with the sporadic nature of flares meaning observers cannot wait until seeing conditions are optimal before taking measurements, means that many ground-based solar flare observations are marred with bad seeing. To combat this, we propose a method for dedicated flare seeing correction based on training a deep neural network to learn to correct artificial seeing from flare observations taken during good seeing conditions. This model uses transfer learning, a novel technique in solar physics, to help learn these corrections. Transfer learning is when another network already trained on similar data is used to influence the learning of the new network. Once trained, the model has been applied to two flare data sets: one from AR12157 on 2014 September 6 and one from AR12673 on 2017 September 6. The results show good corrections to images with bad seeing with a relative error assigned to the estimate based on the performance of the model. Further discussion takes place of improvements to the robustness of the error on these estimates.

Phase diversity method based on an improved particle swarm algorithm used in co-phasing error detection.

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.

Experimental research on phase diversity method for correcting vortex beam distortion wavefront

The orbital angular momentum (OAM) of the vortex beam has infinite dimension and are orthogonal to each other. OAM multiplexing technology is one of the key technologies to improve the channel capacity of wireless optical communication system. When the vortex beams propagate in atmospheric turbulence, it will cause wavefront distortion. The phase diversity (PD) method is used to obtain the phase information by inversely extracting the intensity information of the focal plane and the defocus plane, and realize the correction of the vortex beam distortion wavefront. The simulation and experimental results show that the relative powers of the single-mode and multi-mode multiplexed vortex beams can be effectively improved using the PD method to correct the distortion wavefront. The crosstalk between modes is reduced, and the correction effect increases with the decrease of topological charge.

An MDPSK homodyne receiver with adaptive phase-diversity

ABSTRACT We propose an adaptive phase-diversity method for optical M-ary differential phase-shift keying (MDPSK) homodyne receivers, to achieve coherent optical communication. This method involves eliminating the random fluctuations in the phase differences between the signal light and local oscillator and the in-plane and quadrature signal (IQ) imbalance compensation. For the former, a phase-diversity method, which can theoretically eliminate all phase-related noise, is proposed. The gain and phase imbalances between the I and Q channels can be compensated completely by using automatic phase- and gain-control systems. The core idea is the adaptability of the receiver to the local phase shift of the local oscillator. The performance of the receiver is not sensitive to environmental factors such as temperature and vibrations. Our simulation results show that the imbalances between the IQ channels can be completely compensated over a wide imbalance range, and the baseband signals can be accurately recovered using the proposed scheme.

Multi-plane phase retrieval methods to recover free- aberrations object complex field via SLM

This paper explains two iterative phase recovery methods where the goal of each one is different. The Phase Diversity method is used to recover the wavefront aberrations in optical incoherent imaging systems when an extended object is illuminated. The purpose of the Multi-plane Phase Retrieval method is recovering the object complex field seen from the image plane, therefore the object has to be illuminated with coherent light. Both methods are simultaneously used to pick out the aberrations and free aberrations object phase. The use of both methods is proposed as a methodology for the integration of optical instruments.

Detecting wavefront amplitude and phase using linear phase diversity.

We propose a simplified phase diversity method based on the first-order Taylor expansion of the optical transfer function (OTF) as the light intensity on the pupil plane is not uniform but presents Gaussian distribution. By extending the Zernike polynomial term to the complex field, we regard the distribution of the light intensity as the imaginary part of the phase, which can be solved together with the phase aberration (the real part of the phase). The approximation of the OTF using the first-order Taylor expansion can simplify the relationship between the phase and OTF to linear relation, so that the aberration can be quickly solved. We present an experiment that validates the advantage of our method. The result shows that the modified method has a higher accuracy with less time compared to the traditional phase diversity algorithm, and can acquire the distribution of the light on the pupil plane.

Field diversity phase retrieval method for wavefront sensing in monolithic mirror space telescopes.

To guarantee the uniqueness of the solution for the wavefront phase, a series of intensity images with known phase diversities is usually needed in the current phase retrieval wavefront sensing methods. However, to obtain these intensity images with deliberately added diversity phases, some additional instruments (e.g., beam splitters) or operations (e.g., adjustment of the focus) are usually needed, which can pose a challenge for wavefront sensing in space telescopes. This paper proposes a new concept for retrieving the wavefront phase of monolithic mirror space telescopes with perturbations, where the intensity measurements with phase diversities are directly obtained from different field positions of one image, without the need for any additional instruments or operations. To realize this new concept, we present a modified phase diversity method to account for the unknown phase diversities between these intensity measurements based on an in-depth understanding of the net aberration fields induced by misalignments and figure errors. Relevant simulations for different cases are performed to demonstrate the feasibility and accuracy of the proposed method. Since in this method the phase diversities between different intensity measurements are mainly induced by the diversities in the field position, we call it the field diversity phase retrieval method. This work can present great facility for wavefront sensing in monolithic mirror space telescopes.

An analytic expression for coronagraphic imaging through turbulence. Application to on-sky coronagraphic phase diversity

Abstract The ultimate performance of coronagraphic high-contrast exoplanet imaging systems such as SPHERE or GPI is limited by quasi-static aberrations. These aberrations produce speckles that can be mistaken for planets in the image. In order to design instruments, correct quasi-static aberrations or analyse data, the expression of the point spread function of a coronagraphic instrument in the presence of residual turbulence is most useful. Here, we derive an analytic expression for this point spread function that is an extension to coronagraphic imaging of Roddier's expression for imaging through turbulence. We give a physical interpretation of its structure, we validate it by numerical simulations and we show that it is computationally efficient. Finally, we incorporate this imaging model into a coronagraphic phase diversity method (COFFEE) and validate by simulations that it allows wave-front reconstruction in the presence of residual turbulence. The preliminary results, which give a sub-nanometric precision in the case of a SPHERE-like system, strongly suggest that quasi-static aberrations could be calibrated during observations by this method.

Phase-diversity method using phase-shifting interference algorithms for digital coherent receivers

We describe phase-diversity optical coherent receivers (CRx) using the phase-shifting-interference (PSI) framework. The goals of the analysis are several-fold. First, we show that coherent detection can be realized with optical hybrids that have an arbitrary number of branches and phase shifts using a closed-form solution of the inphase-quadrature mapping. Second, we show that CRx with 2×4 90° hybrids using balanced detection (BD) and CRx with 2×3 120° hybrid using single-ended detection (SED) perform optimally compared to alternative configurations. A proof-of-concept WDM colorless 10×132-Gb/s PDM-QPSK transmission experiment is conducted. We demonstrate that an example of arbitrary phase diversity CRx with a 2×3 90° hybrid SED operates with a 0.3dB signal-to-noise-ratio (SNR) penalty relative to conventional CRx at 6400km and 4480km for bit-error-rates below the threshold of 2×10−2 and the threshold of 3.8×10−3 respectively. The sensitivity degradation of the 2×3 90° hybrid SED with respect to the 2×4 90° hybrid BD in the shot noise limited regime at a distance of 4480km is 3dB, which matches well with the predicted penalty from the PSI analytical model. To the best of our knowledge, this paper is the first attempt to model a CRx using the PSI model.

Redundancy computation analysis and implementation of phase diversity based on GPU

Phase diversity method is not only used as an image restoration technique, but also as a wavefront sensor. However, its computations have been perceived as being too burdensome to achieve its real-time applications on a desktop computer platform. In this paper, the implementation of the phase diversity algorithm based on graphic processing unit (GPU) is presented. The redundancy computations for the pupil function, point spread function, and optical transfer function are analyzed. Two kinds of implementation methods based on GPU are compared: one is the general method which is accomplished by GPU library CUFFT without precision loss (method-1) and the other one performed by our own custom FFT with little damage of precision considering the redundant calculations (method-2). The results show the cost and gradient functions can be speeded up by method-2 in contrast with the method-1 and the overhead of global memory access by kernel fusion can be reduced. For the image of 256 x 256 with the sampling factor of 3, the results reveal that method-2 achieves speedup of 1.83x compared with method-1 when the central 128 x 128 pixels of the point spread function are used.

Extracting DEM from airborne X-band data based on PolInSAR

Abstract. Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR) is a new trend of SAR remote sensing technology which combined polarized multichannel information and Interferometric information. It is of great significance for extracting DEM in some regions with low precision of DEM such as vegetation coverage area and building concentrated area. In this paper we describe our experiments with high-resolution X-band full Polarimetric SAR data acquired by a dual-baseline interferometric airborne SAR system over an area of Danling in southern China. Pauli algorithm is used to generate the double polarimetric interferometry data, Singular Value Decomposition (SVD), Numerical Radius (NR) and Phase diversity (PD) methods are used to generate the full polarimetric interferometry data. Then we can make use of the polarimetric interferometric information to extract DEM with processing of pre filtering , image registration, image resampling, coherence optimization, multilook processing, flat-earth removal, interferogram filtering, phase unwrapping, parameter calibration, height derivation and geo-coding. The processing system named SARPlore has been exploited based on VC++ led by Chinese Academy of Surveying and Mapping. Finally compared optimization results with the single polarimetric interferometry, it has been observed that optimization ways can reduce the interferometric noise and the phase unwrapping residuals, and improve the precision of DEM. The result of full polarimetric interferometry is better than double polarimetric interferometry. Meanwhile, in different terrain, the result of full polarimetric interferometry will have a different degree of increase.

利用相位差异法检测镜面面形

利用相位差异法检测镜面面形