Digital Holography and Phase Retrieval

Duadi, Hamootal; Margalit, Ofer; Micó, Vicente; Rodrigo, José A.; Alieva, Tatiana; Garcı́a, Javier; Zalevsky, Zeev

doi:10.5772/13993

Cited by 10 publications

(13 citation statements)

References 44 publications

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“…Since then, a variety of methods have been proposed to carry out these multiple measurements; depending on the particular application, these may include the use of various gratings and/or of masks, the rotation of the axial position of the sample, and the use of defocusing implemented in a spatial light modulator, see [22] for details and references. Other approaches include ptychography, an exciting field of research, where one records several diffraction patterns from overlapping areas of the sample, see [60,63] and references therein.…”

Section: Phaselift -A Novel Methodologymentioning

confidence: 99%

“…While holographic techniques have been successfully applied in certain areas of optical imaging, they are generally difficult to implement in practice [22]. Hence, the development of algorithms for signal recovery from magnitude measurements is still a very active field of research.…”

Section: Main Approaches To Phase Retrievalmentioning

confidence: 99%

“…Roughly speaking, the idea is to let the signal of interest x interfere with a known reference beam y. One typically measures |x + y| 2 and |x − iy| 2 and precise knowledge of y allows, in principle, to recover the amplitude and phase of x. Holographic techniques are hard to implement [22] in practice. Instead, we propose using a modulated version of the signal itself as a reference beam which in some cases may be easier to implement.…”

Section: Theorymentioning

confidence: 99%

See 2 more Smart Citations

Phase Retrieval via Matrix Completion

Candès

Eldar²,

Strohmer

et al. 2013

SIAM J. Imaging Sci.

665

850

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This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach, called PhaseLift, combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover.

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Section: Phaselift -A Novel Methodologymentioning

confidence: 99%

Section: Main Approaches To Phase Retrievalmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

See 1 more Smart Citation

Phase Retrieval via Matrix Completion

Candès

Eldar²,

Strohmer

et al. 2013

SIAM J. Imaging Sci.

665

850

View full text Add to dashboard Cite

show abstract

“…A common theme among these alternatives is the use of interference to extract more information about the desired signal. For example, holography interferes the signal of interest x ∈ C M with a known reference signal y ∈ C M , taking measurements of the form |F (x + ωy)| 2 , where ω ∈ C has unit modulus and F denotes the Fourier transform [19]; three such measurements (i.e., 3M scalar measurements) suffice for injectivity [50]. Alternatively, spectral phase interferometry for direct electric-field reconstruction (SPIDER) interferes the signal of interest x ∈ C M with time-and frequency-shifted versions of itself Sx ∈ C M , taking measurements of the form |F (x + Sx)| 2 [29]; while popular in practice for ultrashort pulse measurement, SPIDER fails to accurately resolve the relative phase of well-separated frequency components [31].…”

mentioning

confidence: 99%

Phase Retrieval with Polarization

Alexeev¹,

Bandeira²,

Fickus³

et al. 2014

SIAM J. Imaging Sci.

134

180

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In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a novel measurement design which is inspired by interferometry and exploits certain properties of expander graphs. We also give an efficient phase retrieval procedure, and use recent results in spectral graph theory to produce a stable performance guarantee which rivals the guarantee for PhaseLift in Voroninski, PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, preprint, arXiv:1109.4499, 2011]. We use numerical simulations to illustrate the performance of our phase retrieval procedure, and we compare reconstruction error and runtime with a common alternating-projections-type procedure.

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“…Holographic techniques are among the more popular methods that have been proposed to measure the phase of the optical wave. While holographic techniques have been successfully applied in certain areas of optical imaging, they are generally difficult to implement in practice [18]. In our case, for remotely diagnosing, the possibility of using a concrete reference field is excluded.…”

Section: Introductionmentioning

confidence: 99%