We present a promising approach to the extremely fast sensing and correction of small wavefront errors in adaptive optics systems. As our algorithm's computational complexity is roughly proportional to the number of actuators, it is particularly suitable to systems with 10,000 to 100,000 actuators. Our approach is based on sequential phase diversity and simple relations between the point-spread function and the wavefront error in the case of small aberrations. The particular choice of phase diversity, introduced by the deformable mirror itself, minimizes the wavefront error as well as the computational complexity. The method is well suited for high contrast astronomical imaging of point sources such as the direct detection and characterization of exoplanets around stars, and it works even in the presence of a coronagraph that suppresses the diffraction pattern. The accompanying paper in these proceedings by Korkiakoski et al. describes the performance of the algorithm using numerical simulations and laboratory tests.
We investigate the potential of phase-diversity (PD) and Gerchberg-Saxton (GS) algorithms in the calibration of
active instruments. A set of images is recorded with the focal-plane scientific camera, each image having a known
and unique defocus. The phase-retrieval algorithms are used, with those images, to estimate the non-common
path aberration that needs to be compensated by correct alignment of the instrument. We demonstrate by
numerical simulations that such algorithms, in particular GS, are sufficient detection methods to fully correct
wavefronts with an rms error at least up to 6 rad — but this requires several iterative correction stages.
Phase-diversity methods allow to estimate both the wavefront disturbance as well as the object that is being imaged and that is extended in space. Hence, in principle, phase-diversity methods can be used for wavefront sensing as well, without the need to spill part of the observed light to wavefront sensing with a dedicated wavefront sensor.
However, the use of phase-diversity in real-time applications is prevented by its high computational complexity, determined by the number of parameters quantifying the wavefront and the object.
To reduce the computational complexity, metrics have been proposed that are independent of the object, that allow to only estimate the wavefront, but still yield a nonlinear inverse problem.
To further reduce the computational complexity of the wavefront estimation methods we consider linear approximations of these metrics, that allow to update the estimate of the wavefront by solving a linear least squares problem.
We study the estimation error w.r.t. the presence of noise and the spectral content of the extended object, and compare metrics presented in literature.
We show experimental results demonstrating the feasibility of an extremely fast sequential phase-diversity (SPD)
algorithm for point sources. The algorithm can be implemented on a typical adaptive optics (AO) system to
improve the wavefront reconstruction beyond the capabilities of a wavefront sensor by using the information
from the imaging camera. The algorithm is based on a small-phase approximation enabling fast numerical
implementation, and it finds the optimal wavefront correction by iteratively updating the deformable mirror.
Our experiments were made at an AO-setup with a 37 actuator membrane mirror, and the results show that
the algorithm finds an optimal image quality in 5–10 iterations, when the initial wavefront errors are typical
non-common path aberrations having a magnitude of 1–1.5 rad rms. The results are in excellent agreement with
corresponding numerical simulations.
We propose a new approach for the joint estimation of aberration parameters and unknown object from diversity
images with applications in imaging systems with extended objects as astronomical ground-based observations
or solar telescopes. The motivation behind our idea is to decrease the computational complexity of the conventional
phase diversity (PD) algorithm and avoid the convergence to local minima due to the use of nonlinear
estimation algorithms. Our approach is able to give a good starting point for an iterative algorithm or it can
be used as a new wavefront estimation method. When the wavefront aberrations are small, the wavefront can be approximated with a linear term which leads to a quadratic point-spread function (PSF) in the aberration parameters. The presented approach involves recording two or more diversity images and, based on the before mentioned approximation estimates the aberration parameters and the object by solving a system of bilinear equations, which is obtained by subtracting from each diversity image the focal plane image. Moreover, using the quadratic PSFs gives improved performance to the conventional PD algorithm through the fact that the gradients of the PSFs have simple analytical formulas.
KEYWORDS: Point spread functions, Wavefronts, Data transmission, Turbulence, Computer simulations, Zernike polynomials, Chemical elements, Tolerancing, Computing systems, Control systems
In this paper we give a new wavefront estimation technique that overcomes the main disadvantages of the phase
diversity (PD) algorithms, namely the large computational complexity and the fact that the solutions can get
stuck in a local minima. Our approach gives a good starting point for an iterative algorithm based on solving a
linear system, but it can also be used as a new wavefront estimation method. The method is based on the Born
approximation of the wavefront for small phase aberrations which leads to a quadratic point-spread function
(PSF), and it requires two diversity images. First we take the differences between the focal plane image and each
of the two diversity images, and then we eliminate the constant object, element-wise, from the two equations.
The result is an overdetermined set of linear equations for which we give three solutions using linear least squares
(LS), truncated total least squares (TTLS) and bounded data uncertainty (BDU). The last two approaches are
suited when considering measurements affected by noise. Simulation results show that the estimation is faster than conventional PD algorithms.
Wavefront sensorless adaptive optics methodologies are considered in many applications where the deployment
of a dedicated wavefront sensor is inconvenient, such as in fluorescence microscopy. In these methodologies,
aberration correction is achieved by sequentially changing the settings of the adaptive optical element until
a predetermined imaging quality metric is optimised. Reducing the time required for this optimisation is a
challenge. In this paper, a two stage data driven optimisation procedure is presented and validated in a laboratory
environment. In the first stage, known aberrations are introduced by a deformable mirror and the corresponding
intensities are measured by a photodiode masked by a pinhole. A generic quadratic metric is fitted to this
collection of aberrations and intensity measurements. In the second stage, this quadratic metric is used in order
to estimate and correct for optical aberrations. A closed form expression for the optimisation of the quadratic
metric is derived by solving a linear system of equations. This requires a minimum of N +1 pairs of deformable
mirror settings and intensity measurements, where N is the number of modes of the aberrations.
We have implemented a coherence-gated wavefront sensor on a two-photon excitation microscope. We used the backscattered near-infrared light from the sample to interfere with an optically flat reference beam. By applying a known waverfront tilt in the reference beam, a fringe pattern emerged on the camera. The deformmation of the wavefront due to the turbid media under study warps the fring pattern, similar to frequency modulation. Through Fourier transform analysis of the modulated fringe pattern we were able to determine the wave fornt aberrations induced by synthetic and biological samples. By defocussing the microscope objective and measuring the wavefront deformation we established that the errors are reproduceible to within λ/227 for the defocus mode.
KEYWORDS: Autoregressive models, Turbulence, Wavefronts, Wave propagation, Signal to noise ratio, Adaptive optics, Filtering (signal processing), Systems modeling, Wavefront distortions, Control systems
In recent years various researchers have proposed an optimal control approach for the rejection of
turbulence-induced wavefront distortions in an AO system. The essential element in the design
of an optimal controller is the choice for the turbulence model, which predicts the turbulence to
compensate for the inherent delay in the AO control loop. In this paper various models as proposed
in literature are considered; ranging from first order temporal models to high-order full spatialtemporal
models. The various models are analyzed and the resulting 1-step ahead predictors are
derived. The performance of the predictors are compared for a von Kármán type of turbulence
with frozen flow propagation in and time-varying propagation directions.
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