Nonlinear spline wavefront reconstruction from Shack–Hartmann intensity measurements through small aberration approximations

Brunner, Elisabeth; Visser, Coen C. de; Verhaegen, Michel

doi:10.1364/josaa.34.001535

Cited by 5 publications

(6 citation statements)

References 18 publications

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“…(13) in a distributed manner without approximation errors, future work should investigate the formulation of the distributed DM projection problem, e.g., as a sharing optimization problem with ADMM [19]. Coupling constraints on local command vectors u i can be employed to achieve consensus between actuators that are shared by neighboring partitions or whose influence functions reach neighboring partitions [17].…”

Section: A Distributed Projection Problemmentioning

confidence: 99%

“…The SH sensor is an array of lenslets that creates a focal spot pattern from which approximations of the local spatial WF gradients in each subaperture are derived [1,15]. Whereas the limited amount of processed data, i.e., two slope measurements per subaperture, restricts the slope-based D-SABRE method to linear B-spline polynomials, two approaches have been introduced that can extend the method to higher degree polynomials: (1) by exploiting the integrative nature of the SH sensor, a more advanced sensor model has been implemented that utilizes first-and second-order moment measurements of the focal spots [16]; and (2) by combining the standard D-SABRE with an additional correction step in which the pixel information in the focal spots is directly worked with, using an algorithm based on small aberration approximations of the focal spot models [17]. Employing a cubic B-spline representation of the phase, both approaches can achieve WF estimates that are superior to the linear D-SABRE WF estimates if applied to a given SH array.…”

Section: Introductionmentioning

confidence: 99%

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GPU implementation for spline-based wavefront reconstruction

et al. 2018

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This paper presents an adaptation of the distributed-spline-based aberration reconstruction method for Shack-Hartmann (SH) slope measurements to extremely large-scale adaptive optics systems and the execution on graphics processing units (GPUs). The introduction of a hierarchical multi-level scheme for the elimination of piston offsets between the locally computed wavefront (WF) estimates solves the piston error propagation observed for a large number of partitions with the original version. To obtain a fully distributed method for WF correction, the projection of the phase estimates is locally approximated and applied in a distributed fashion, providing stable results for low and medium actuator coupling. An implementation of the method with the parallel computing platform CUDA exploits the inherently distributed nature of the algorithm. With a standard off-the-shelf GPU, the computation of the adaptive optics correction updates is accomplished in under 1 ms for the benchmark case of a 200×200 SH array.

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Section: A Distributed Projection Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

GPU implementation for spline-based wavefront reconstruction

et al. 2018

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“…9,10 The SHWFS operates on two fundamental procedures: wavefront slope calculation and wavefront reconstruction algorithms. The previous research on reconstruction algorithms primarily focused on spatial domain analysis [11][12][13][14] to evaluate the performance of the reconstructors. Departing from conventional metrics, the spatial frequency response provides comprehensive insights into assessing distinct wavefront reconstructors.…”

Section: Introductionmentioning

confidence: 99%

A frequency-response-optimized Shack–Hartmann zonal wavefront reconstructor based on Fan’s model

Fan,

Duan,

et al. 2024

Review of Scientific Instruments

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This paper introduces an optimized method for zonal wavefront reconstruction utilizing Fan’s model, specifically tailored to enhance the frequency response. Analysis of the system frequency response demonstrates a 27% increase in bandwidth compared to the Southwell model. Examination of reconstruction errors at various frequency points reveals consistently smaller values when compared to the Southwell model. Validation through numerical simulations and real experiments underscores the superior performance of the proposed reconstructor, particularly noticeable at higher response levels within the mid- and high-frequency domains.

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“…A reason is that the use of double exposure procedures for such a measurement process would inevitably generate unwanted noise to the obtained data. Fortunately, under certain circumstances the phase can be estimated from only one PSF image; see, for example, [3,5,7]. In this paper, we investigate the phase retrieval problem, given a single PSF image, with a priori information that the phase is sparse.…”

mentioning

confidence: 99%

“…The Frobenius norm and the maximum norm are denoted by \| \cdot \| and \| \cdot \| \infty , respectively. Mathematical operations including the multiplication, the division, the modulus, the argument, 3 the exponential, the square, the square root, and the equality are understood elementwise in this paper. The distance function associated to a set \Omega \subset \BbbC n\times n is defined by dist(\cdot , \Omega ) : \BbbC n\times n \rightar \BbbR + : x \mapsto \rightar inf w\in \Omega \| x -w\| , and the set-valued mapping P \Omega : \BbbC n\times n \rightri \Omega : x \mapsto \rightar \{ w \in \Omega | \| x -w\| = dist(x, \Omega ) \} is the corresponding projector.…”

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confidence: 99%

Phase Retrieval with Sparse Phase Constraint

Thao¹,

Lüke²,

Soloviev³

et al. 2020

SIAM Journal on Mathematics of Data Science

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In this paper, we propose and investigate the phase retrieval problem with the a priori constraint that the phase is sparse (SPR), which encompasses a number of practical applications, for instance, in characterizing phase-only objects such as microlenses, in phase-contrast microscopy, in optical path difference microscopy, and in Fourier ptychography, where the phase object occupies a small portion of the whole field. The considered problem is strictly more general than the sparse signal recovery problem, which assumes the sparsity of the signal because the sparsity of the signal trivially implies the sparsity of the phase, but the converse is not true. As a result, existing solution algorithms in the literature of sparse signal recovery cannot be applied to SPR and there is an appeal for developing new solution methods for it. In this paper, we propose a new regularization scheme which efficiently captures the sparsity constraint of SPR. The idea behind the proposed approach is to perform a metric projection of the current estimated signal onto the set of all the signals whose phase satisfies the sparsity constraint. The main challenge here is that the latter set is not convex and its associated projector in general does not admit a closed form. One novelty of our analysis is to establish an explicit form of that projector when restricted to those points which are relevant to the solutions of SPR. Note that this result is fundamentally different from the widely known calculation form for projections onto intensity constraint sets. Based on this new result, we propose an efficient solution method, named the sparsity regularization on phase (SROP) algorithm, for the SPR problem in the challenging setting where only one point-spread-function image is given, and we analyze its convergence. The algorithm is the combination of the Gerchberg--Saxton (GS) algorithm with the projection step described above. In view of the GS algorithm being equivalent to the alternating projection for an associated two-set feasibility, the SROP algorithm is shown to be the cyclic projection for an associated three-set feasibility, one of the sets being analyzed in this paper for the first time. Analyzing regularity properties of the involved sets, we obtain convergence results for the SROP algorithm based on our recent convergence theory for the cyclic projection method. Numerical results show clear effectiveness and efficiency of the proposed solution approach for the SPR problem.

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Nonlinear spline wavefront reconstruction from Shack–Hartmann intensity measurements through small aberration approximations

Cited by 5 publications

References 18 publications

GPU implementation for spline-based wavefront reconstruction

GPU implementation for spline-based wavefront reconstruction

A frequency-response-optimized Shack–Hartmann zonal wavefront reconstructor based on Fan’s model

Phase Retrieval with Sparse Phase Constraint

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