Gerchberg—Saxton algorithm: experimental realisation and modification for the problem of formation of multimode laser beams

Ilina, I. V.; Cherezova, Tatyana Yu.; Kudryashov, Alexis

doi:10.1070/qe2009v039n06abeh013642

Cited by 24 publications

(12 citation statements)

References 4 publications

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“…The limitation on the achievable PCF size is determined by the smallest feature size that can be etched and the damage threshold of the material used since a large input beam would result in a small intense focal spot. Error tolerance calculation for the GPC LS used in the experiment indicate that the system can tolerate axial misalignments within 2% of the focal length of the lens used and lateral displacements within 20% of the PCF radius and still maintain above 80% of is peak operating efficiency [16].…”

Section: Creating Optimal Illumination With a Gpc Light Shaper Modulementioning

confidence: 99%

“…This creates an intense beam that matches the shape of the phase-only modulation element (SLM) in the diffractive setup. For the experiment, we combine elements of the GPC in a compact add-on module, called the GPC Light Shaper (LS) [16], that can be conveniently integrated to an existing holographic setup.…”

Section: Creating Optimal Illumination With a Gpc Light Shaper Modulementioning

confidence: 99%

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GPC-enhanced read-out of holograms

Villangca

Bañas

Palima

et al. 2015

Optics Communications

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Section: Creating Optimal Illumination With a Gpc Light Shaper Modulementioning

confidence: 99%

Section: Creating Optimal Illumination With a Gpc Light Shaper Modulementioning

confidence: 99%

GPC-enhanced read-out of holograms

Villangca

Bañas

Palima

et al. 2015

Optics Communications

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“…In Figure 2 we report on the effect on execution time of the problem parameters ||u|| 2 2 , cond(Σ) and ||Σ|| 2 F . To do so, we discretized the range N = [10,2000] in 50 log-uniform steps and ran 500 experiments for each value of N , sampling u and Σ at random as in Algorithm 4.2. All experiments were run with the fastest configuration found in the previous experiments, i.e.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…, Q [18]. Despite being a classic problem in the signal processing world [10,7,8], the field of phase retrieval has experienced an increase in interest in recent years, thanks to the development of algorithms relying on semi-definite programming [3,4,20,9], Wirtinger flow [2,5] or sparse reconstructions [14,17].…”

mentioning

confidence: 99%

A Proximal Operator for Multispectral Phase Retrieval Problems

Roig-Solvas¹,

Makowski²,

Brooks³

2019

SIAM J. Optim.

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Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval problem commonly refers to the task of recovering a target signal based on the magnitude of linear projections of that signal onto known vectors, usually under the presence of noise. A more general problem is the multispectral phase retrieval problem, where sums of these magnitudes are observed instead. In this paper we study the proximal operator for this problem, which appears in applications like X-ray solution scattering. We show that despite its non-convexity, all local minimizers are global minimizers, guaranteeing the optimality of simple descent techniques. An efficient linear time exact Newton method is proposed based on the structure of the problem's Hessian. Initialization criteria are discussed and the computational performance of the proposed algorithm is compared to that of traditional descent methods. The studied proximal operator can be used in a distributed and parallel scenarios using an ADMM scheme and allows for exploiting the spectral characteristics of the problem's measurement matrices, known in many physical sensing applications, in a way that is not possible with non-splitted optimization algorithms. The dependency of the proximal operator on the rank of these matrices, instead of their dimension, can greatly reduce the memory and computation requirements for problems of moderate to large size (N > 10 4 ) when these measurement matrices admit a low-rank representation. 2 for A t ∈ C M ×Kt and b t ∈ R + for t = 1, . . . , T , which can be seen as an instance of 1.1 where f t = (A t y) H (A t y) − b t 2 .

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“…Hence, the sequence can be iteratively developed until a convergent solution is found. The proof of convergence of such algorithms can be found elsewhere (Combettes and Trussell, 1990;Il'ina et al, 2009).…”

Section: Algorithmmentioning

confidence: 99%

Image processing techniques for high-resolution structure determination from badly ordered 2D crystals

Biyani

Scherer

Righetto

et al. 2017

Preprint

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Abstract2D electron crystallography can be used to study small membrane proteins in their native environment. Obtaining highly ordered 2D crystals is difficult and time-consuming.However, 2D crystals diffracting to only 10-12 Å can be prepared relatively conveniently in most cases. We have developed image-processing algorithms allowing to generate a high resolution 3D structure from cryo-electron crystallography images of badly ordered crystals.These include movie-mode unbending, refinement over sub-tiles of the images in order to locally refine the sample tilt geometry; implementation of different CTF correction schemes;and an iterative method to apply known constraints in the real and reciprocal space to approximate amplitudes and phases in the so-called missing cone regions. These algorithms applied to a dataset of the potassium channel MloK1 show significant resolution improvements to approximately 5Å.. CC-BY-NC 4.0 International license It is made available under a (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/113415 doi: bioRxiv preprint first posted online Mar. 3, 2017; Biyani et al., Image processing techniques for high-resolution 2D electron crystallography 3

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Gerchberg—Saxton algorithm: experimental realisation and modification for the problem of formation of multimode laser beams

Cited by 24 publications

References 4 publications

GPC-enhanced read-out of holograms

GPC-enhanced read-out of holograms

A Proximal Operator for Multispectral Phase Retrieval Problems

Image processing techniques for high-resolution structure determination from badly ordered 2D crystals

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