Factored form descent: a practical algorithm for coherence retrieval

Zhang, Zhengyun; Chen, Zhi; Rehman, Shakil; Barbastathis, George

doi:10.1364/oe.21.005759

Cited by 8 publications

(9 citation statements)

References 21 publications

(29 reference statements)

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“…One is a simulation with realistic noise of two coherent Gaussian beams that are slightly decohered with respect to each other. Another is experimental data from [49] consisting of a Schell-model source imaged by a single positive lens. In both cases, the data consists of intensity profiles captured at 250 µm axial intervals by a single row of pixels in a 3.2 µm pitch camera with wavelength λ equal to 532 nm.…”

Section: Resultsmentioning

confidence: 99%

“…We use the experimental data from [49], wherein the intensity profile of a partially coherent beam is imaged at 201 positions along the optical axis. The partially coherent beam was generated by focusing an LED light source through a 532 nm bandpass filter onto a 100 µm slit located at the front focal plane of a 100 mm focal length cylindrical lens.…”

Section: Experimental Datamentioning

confidence: 99%

“…We note that the K m s are Hermitian, but we keep the conjugate transpose notation here to be consistent with later uses of inner products in the paper, which involve matrices which may or may not be Hermitian. In many situations, the K m s are low-rank; for example, rank-one operators were used in [44,49].…”

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confidence: 99%

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Coherence Retrieval Using Trace Regularization

Bao¹,

Barbastathis²,

Gao³

et al. 2018

SIAM J. Imaging Sci.

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The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from measurements through a process called coherence retrieval, otherwise known as phase-space tomography. As practical considerations often rule out the availability of a complete set of measurements, coherence retrieval is usually a challenging high-dimensional ill-posed inverse problem. In this paper, we propose a trace-regularized optimization model for coherence retrieval and a provably-convergent adaptive accelerated proximal gradient algorithm for solving the resulting problem. Applying our model and algorithm to both simulated and experimental data, we demonstrate an improvement in reconstruction quality over previous models as well as an increase in convergence speed compared to existing first-order methods.

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Section: Resultsmentioning

confidence: 99%

Section: Experimental Datamentioning

confidence: 99%

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Coherence Retrieval Using Trace Regularization

Bao¹,

Barbastathis²,

Gao³

et al. 2018

SIAM J. Imaging Sci.

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“…We therefore expect there to be significant difficulties especially when the incident WDF contains features smaller than the aperture WDF. Performing deconvolution to recover the WDF may benefit from techniques such as coded apertures [30,31] and compressed sensing [10,32].…”

Section: Discussionmentioning

confidence: 99%

Wigner function measurement using a lenslet array

et al. 2013

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Geometrical-optical arguments have traditionally been used to explain how a lenslet array measures the distribution of light jointly over space and spatial frequency. Here, we rigorously derive the connection between the intensity measured by a lenslet array and wave-optical representations of such light distributions for partially coherent optical beams by using the Wigner distribution function (WDF). It is shown that the action of the lenslet array is to sample a smoothed version of the beam's WDF (SWDF). We consider the effect of lenslet geometry and coherence properties of the beam on this measurement, and we derive an expression for cross-talk between lenslets that corrupts the measurement. Conditions for a high fidelity measurement of the SWDF and the discrepancies between the measured SWDF and the WDF are investigated for a Schell-model beam.

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“…It is based on factored form descent (FFD) [20], a coherence retrieval algorithm that computes the coherence modes of a partially coherent field given a linear operator description of a known optical system and measured intensity values through said optical system. We adapt FFD to the problem of coherent field retrieval by imposing a hard rank constraint; this is accomplished by modifying the merit function to allow only a single mode:…”

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confidence: 99%

Phase imaging using shifted wavefront sensor images

et al. 2014

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We propose a new approach to the complete retrieval of a coherent field (amplitude and phase) using the same hardware configuration as a Shack-Hartmann sensor but with two modifications: first, we add a transversally shifted measurement to resolve ambiguities in the measured phase; and second, we employ factored form descent (FFD), an inverse algorithm for coherence retrieval, with a hard rank constraint. We verified the proposed approach using both numerical simulations and experiments.

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Factored form descent: a practical algorithm for coherence retrieval

Cited by 8 publications

References 21 publications

Coherence Retrieval Using Trace Regularization

Coherence Retrieval Using Trace Regularization

Wigner function measurement using a lenslet array

Phase imaging using shifted wavefront sensor images

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