Inverse problems in astronomical adaptive optics

Ellerbroek, Brent L.; Vogel, Curtis R.

doi:10.1088/0266-5611/25/6/063001

Cited by 74 publications

(64 citation statements)

References 58 publications

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“…In order to dramatically increase numerical efficiency and robustness, we computed gradients of J OLS using an adjoint, or costate, method. 2,8 This required only two solutions of partial differential equations of the form (4) per gradient evaluation. Had we instead used the standard brute-force finite difference gradient approximation, based on…”

Section: Parameter Estimationmentioning

confidence: 99%

Modeling, parameter estimation, and open-loop control of MEMS deformable mirrors

Vogel

Tyler

2010

SPIE Proceedings

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We present a model for MEMS deformable mirrors (DMs) that couples a 2-dimensional, linear 4th order partial differential equation for the DM facesheet with linear spring models for the actuators. We estimate the parameters in this model using the method of output least squares, and we demonstrate the effectiveness of this approach with data from a 140-actuator MEMS test mirror produced at Boston University. A scheme for robust, computationally efficient open-loop control, which is based on this model, is also presented.

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Section: Parameter Estimationmentioning

confidence: 99%

Modeling, parameter estimation, and open-loop control of MEMS deformable mirrors

Vogel

Tyler

2010

SPIE Proceedings

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“…These sensors measure the average gradient of the wavefrontˆover a finite number of subapertures j k (see, e.g., [1,4,6] for details; we also recommend the overview [2]). The reconstruction of the wavefront from these measurements can be mathematically treated as solution of the following operator equation The union of all subapertures is denoted by D OE0; 1 2 .…”

Section: Introductionmentioning

confidence: 99%

On the Shack–Hartmann based wavefront reconstruction: Stability and convergence rates of finite-dimensional approximations

Neubauer

2012

Journal of Inverse and Ill-Posed Problems

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We study the problem of reconstructing a wavefront from measurements by Shack-Hartmann-type sensors. Mathematically, this leads to the problem of reconstructing a function from a discrete set of averages of the gradient.We investigate this problem in finite-dimensional subspaces of a scale of Hilbert spaces and show that the best approximate solutions are well-posed with respect to the L 2 -norm. Moreover, we present convergence rates with respect to different norms of the scale.

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“…This challenge has led to many studies in the past decade of new advanced algorithms for wavefront reconstruction and control on extremely large telescopes (ELTs) [4][5][6][7]. For the SCAO of the E-ELT, the Fourier transform reconstructor (FTR) [6] and the fractal iterative method (FRiM) [7] have been studied, and their performance in terms of AO correction quality has been demonstrated to be as good or better than a classical computation based on an MVM [8].…”

Section: Introductionmentioning

confidence: 99%

Computational performance comparison of wavefront reconstruction algorithms for the European Extremely Large Telescope on multi-CPU architecture

Fedrigo

Béchet

et al. 2012

Appl. Opt.

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The European Southern Observatory (ESO) is studying the next generation giant telescope, called the European Extremely Large Telescope (E-ELT). With a 42 m diameter primary mirror, it is a significant step from currently existing telescopes. Therefore, the E-ELT with its instruments poses new challenges in terms of cost and computational complexity for the control system, including its adaptive optics (AO). Since the conventional matrix-vector multiplication (MVM) method successfully used so far for AO wavefront reconstruction cannot be efficiently scaled to the size of the AO systems on the E-ELT, faster algorithms are needed. Among those recently developed wavefront reconstruction algorithms, three are studied in this paper from the point of view of design, implementation, and absolute speed on three multicore multi-CPU platforms. We focus on a single-conjugate AO system for the E-ELT. The algorithms are the MVM, the Fourier transform reconstructor (FTR), and the fractal iterative method (FRiM). This study enhances the scaling of these algorithms with an increasing number of CPUs involved in the computation. We discuss implementation strategies, depending on various CPU architecture constraints, and we present the first quantitative execution times so far at the E-ELT scale. MVM suffers from a large computational burden, making the current computing platform undersized to reach timings short enough for AO wavefront reconstruction. In our study, the FTR provides currently the fastest reconstruction. FRiM is a recently developed algorithm, and several strategies are investigated and presented here in order to implement it for real-time AO wavefront reconstruction, and to optimize its execution time. The difficulty to parallelize the algorithm in such architecture is enhanced. We also show that FRiM can provide interesting scalability using a sparse matrix approach.

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Inverse problems in astronomical adaptive optics

Cited by 74 publications

References 58 publications

Modeling, parameter estimation, and open-loop control of MEMS deformable mirrors

Modeling, parameter estimation, and open-loop control of MEMS deformable mirrors

On the Shack–Hartmann based wavefront reconstruction: Stability and convergence rates of finite-dimensional approximations

Computational performance comparison of wavefront reconstruction algorithms for the European Extremely Large Telescope on multi-CPU architecture

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