Identification of the dynamics of time-varying phase aberrations from time histories of the point-spread function

Abstract

To optimally compensate for time-varying phase aberrations with adaptive optics, a model of the dynamics of the aberrations is required to predict the phase aberration at the next time step. We model the time-varying behavior of a phase aberration, expressed in Zernike modes, by assuming that the temporal dynamics of the Zernike coefficients can be described by a vector-valued autoregressive (VAR) model. We propose an iterative method based on a convex heuristic for a rank-constrained optimization problem, to jointly estimate the parameters of the VAR model and the Zernike coefficients from a time series of measurements of the point-spread function (PSF) of the optical system. By assuming the phase aberration is small, the relation between aberration and PSF measurements can be approximated by a quadratic function. As such, our method is a blind identification method for linear dynamics in a stochastic Wiener system with a quadratic nonlinearity at the output and a phase retrieval method that uses a time-evolution-model constraint and a single image at every time step.

Low-rank optimization in system identification

“…However, because the problem is non-convex, such a method is typically prone to local minimas. In our experiments it has been shown that convergence to a good solution is difficult unless the initial guess is very close to the optimal solution [7]. Therefore, it is paramount to find an alternative strategy to solve this problem.…”

“…Finally, consider the RMP that spawned from replacing a bilinearity with a linear rank constraint in Equation (2.41): where λ ∈ R + is a regularization parameter [7].…”

High-contrast integral field spectrograph (HCIFS): multi-spectral wavefront control and reduced-dimensional system identification

“…Fourier optics approximation) always cause mismatches between the real system and the state-space model. Recently, data-driven approaches have been developed to achieve system identification using a telescope's point spread function (PSF) images [39] or real-time wavefront control data [40,41]. One of the experimentally verified approaches [40] uses an E-M algorithm to identify model parameters, which iteratively reconstructs the hidden electric field (E-step) and updates system's Jacobian matrix (M-step).…”

Phase retrieval of large-scale time-varying aberrations using a non-linear Kalman filtering framework

“…Moreover, by including the temporal and statistical models of the turbulence and sensors, KF is known to be robust against modeling errors and measurement noise, making it particularly suitable for dealing with dynamic aberrations and noisy measurements. Small-phase aberrations have also been assumed in other algorithms that aim to estimate temporal dynamic aberrations [15,16]. Possible applications include estimating NCPAs (which occur in various fields such as astronomy [17,18] and ophthalmology [19,20]), wind induced dynamic non-common path vibrations [21], or the low-wind effect [18].…”