Ghost imaging in the random paraxial regime

Garnier, Josselin

doi:10.3934/ipi.2016006

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…As indicated above, this experiment has some resemblance with other speckle intensity correlation imaging methods [6,13,14,15,17,20]. More precisely it is equivalent to (and motivated by) a recent experiment reported in [1] (see Figure 2.2): 1) A fluorescent object is placed behind a scattering medium.…”

Section: Fig 22 the Second Experimental Imaging Set-upmentioning

confidence: 55%

“…In the refocusing problem, phase conjugation or time reversal of waves lead to a sharp focusing at the original source point and this mechanism is the same as the one giving a stable sharp empirical covariance function for the speckle pattern in the above experiments in the situation with one point source only. The experiment we model in this paper moreover bears similarities with ghost imaging where also a bucket detector is used [6,15,20]. It is different from ghost imaging in that the covariance of the bucket measurements themselves are computed, for different incident angles, rather than with respect to the measurements of a reference multi-element sensor array that does not see the object.…”

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confidence: 99%

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Non-invasive imaging through random media

Garnier¹,

Sølna²

2018

Preprint

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When waves propagate through a strongly scattering medium the energy is transferred to the incoherent wave part by scattering. The wave intensity then forms a random speckle pattern seemingly without much useful information. However, a number of recent physical experiments show how one can extract useful information from this speckle pattern. Here we present the mathematical analysis that explains the quite stunning performance of such a scheme for speckle imaging. Our analysis identifies a scaling regime where the scheme works well. This regime is the white-noise paraxial regime, which leads to the Itô-Schrödinger model for the wave amplitude. The results presented in this paper conform with the sophisticated physical intuition that has motivated these schemes, but give a more detailed characterization of the performance. The analysis gives a description of (i) the information that can be extracted and with what resolution (ii) the statistical stability or signal-to-noise ratio with which the information can be extracted.

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Section: Fig 22 the Second Experimental Imaging Set-upmentioning

confidence: 55%

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confidence: 99%

Non-invasive imaging through random media

Garnier¹,

Sølna²

2018

Preprint

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“…Since then, Katz and co-workers [3] have suggested a compressive GI (CGI) scheme that combines compressive sensing with the GI [1][2][3][4][5][6][7][8][9][10][11][12][13]. This scheme reduces the requirements for iterative computations in the GI-based image reconstruction techniques and improves the reconstruction rate via compressive-sensing computations.…”

Section: Introductionmentioning

confidence: 99%

Optical encryption based on the algorithm of compressive ghost imaging and phase-shifting digital holography

Zhang¹,

Xiong²,

Zhang³

et al. 2018

Ukr. J. Phys. Opt.

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We present a compressive ghost-imaging encryption (GIE) scheme based on phase-shifting digital holography (PSDH). With our technique based on the PSDH, the optical information is recorded from each point of an object. Then each part of a hologram can reconstruct the original image, thus improving resolution of a reconstructed image. Using the characteristics of randomness of the PSDH, we improve security of the encryption scheme. In our simulations, a binary image is taken as a target and the mutual information, the PSDG degree and the peak signalto-noise ratio are calculated. The compressive GIE scheme based on the PSDH is compared with a pseudo-inverse algorithm based on PSDH and a common GIE scheme based on the PSDH. The simulation results demonstrate that our compressive scheme manifests better reconstruction quality, compressibility and security.

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“…In spite of the limited data (15) and the strong scattering, we show that it is possible to image the target using a ghost-like imaging modality. Ghost imaging was introduced in the optics literature [17][18][19][20] and was analyzed in the context of wave propagation in random media in [21]. The random source is realized in this context by a laser beam passed through a rotating glass diffuser [20], followed by a beam splitter that divides the beam in two parts: the first part illuminates the object of interest, which is typically a mask, and is then captured by a single pixel (bucket) detector.…”

Section: Introductionmentioning

confidence: 99%

A ghost imaging modality in a random waveguide

Borcea¹,

Garnier²

2018

Inverse Problems

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We study the imaging of a penetrable scatterer, aka target, in a waveguide with randomly perturbed boundary. The target is located between a partially coherent source which transmits the wave, and a detector which measures the spatially integrated energy flux of the wave. The imaging is impeded by random boundary scattering effects that accumulate as the wave propagates. We consider a very large distance (range) between the target and the detector, where that cumulative scattering is so strong that it distributes the energy evenly among the components (modes) of the wave. Conventional imaging is impossible in this equipartition regime. Nevertheless, we show that the target can be located with a ghost imaging modality. This forms an image using the cross-correlation of the measured energy flux, integrated over the aperture of the detector, with the time and space resolved energy flux in a reference waveguide, at the search range. We consider two reference waveguides: The waveguide with unperturbed boundary, in which we can calculate the energy flux, and the actual random waveguide, before the presence of the target, in which the energy flux should be measured. We analyze the ghost imaging modality from first principles and show that it can be efficient in a random waveguide geometry in which there is both strong modal dispersion and mode coupling induced by scattering, provided that the standard ghost imaging function is modified and integrated over a suitable time offset window in order to compensate for dispersion and diffusion. The analysis quantifies the resolution of the image in terms of the source and detector aperture, the range offset between the source and the target, and the duration of the measurements.

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Ghost imaging in the random paraxial regime

Cited by 5 publications

References 24 publications

Non-invasive imaging through random media

Non-invasive imaging through random media

Optical encryption based on the algorithm of compressive ghost imaging and phase-shifting digital holography

A ghost imaging modality in a random waveguide

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