Phase retrieval using nonlinear diversity

Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O.; Kutz, J. Nathan; Fleischer, Jason W.

doi:10.1364/ao.52.000d92

Cited by 31 publications

(11 citation statements)

References 34 publications

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“…Barsi, Wan, and Fleischer [5] and Barsi and Fleischer [4] demonstrated that the use of a defocusing nonlinear medium can improve the imaging resolution beyond Abbe's diffraction limit. Subsequently, the same group harnessed medium nonlinearity to the well-known Gerchberg-Saxton algorithm for phase retrieval, i.e., the retrieval of complex phase using only intensity measurement [38,39]. The authors noted that "...…”

Section: Imaging and Reversibility In Nonlinear Opticsmentioning

confidence: 99%

“…Whether the NLS is physically irreversible is of practical importance. Indeed, in the last decade there have been algorithmic and experimental attempts at holography [5,4,26,27,43], phase retrieval [38,39], and pulse reconstruction [8,53] in focusing Kerr media, all of which rely on the time-reversal symmetry of the NLS. This study, therefore, reveals some of the fundamental limitations that any such reversal technique would face, and highlights the importance of accurately capturing the radiation for reversal experiments to succeed.…”

Section: Introductionmentioning

confidence: 99%

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Loss of physical reversibility in reversible systems

Sagiv

Ditkowski

Goodman

et al. 2020

Physica D: Nonlinear Phenomena

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A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear Schrödinger equation and the φ 4 equation can become "physically irreversible". By this, we mean that realistically-small experimental errors in measuring the output can lead to dramatic differences between the recovered input and the original one. The loss of reversibility reveals a natural "arrow of time", reminiscent of the thermodynamic one, which is the direction in which the radiation is emitted outward. Our results are relevant to imaging and reversal applications in nonlinear optics.Hence, if y(t f ) = 0 at some time t f > 0, then y(0) cannot be uniquely determined.

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Section: Imaging and Reversibility In Nonlinear Opticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Loss of physical reversibility in reversible systems

Sagiv

Ditkowski

Goodman

et al. 2020

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Similar to other phase retrieval techniques [4][5][6][7][8][9][10][11][12][13][14], the recovery process of FP consists of alternating enforcement of the known sample information in the spatial domain, and a fixed constraint in the Fourier domain. In particular, the recovery process of FP shares its roots with ptychography [15][16][17][18][19][20][21][22][23][24][25][26][27], a lensless imaging approach that applies translational diversity (i.e., shifting the sample laterally) to recover its complex image.…”

Section: Introductionmentioning

confidence: 99%

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging

et al. 2014

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Abstract:We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging. The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object. The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process. We demonstrate two applications of the reported scheme. In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects. The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object. We also demonstrate a reconstruction resolution better than the detector pixel limit (i.e., pixel super-resolution). In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging. By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field. This platform's maximum achievable resolution is ultimately determined by the camera's traveling range, not the aperture size of the lens. The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy.

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“…18 This alignment also provides a strong foundation for other methods of phase retrieval, e.g. for initial conditions in nonlinear methods 19 or to remove ambiguities in reconstruction, 20 and does not suffer from possible artifacts present in coherent methods, e.g. speckle and sensitivity to interference jitter.…”

mentioning

confidence: 96%

Flow-scanning optical tomography

et al. 2014

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We present a 3D tomography technique for in vivo observation of microscopic samples. The method combines flow in a microfluidic channel, illumination through a slit aperture, and a Fourier lens for simultaneous acquisition of multiple perspective angles in the phase-space domain. The technique is non-invasive and naturally robust to parasitic sample motion. 3D absorption is retrieved using standard back-projection algorithms, here a limited-domain inverse radon transform. Simultaneously, 3D differential phase contrast images are obtained by computational refocusing and comparison of complementary illumination angles. We implement the technique on a modified glass slide which can be mounted directly on existing optical microscopes. We demonstrate both amplitude and phase tomography on live, freely swimming C. elegans nematodes.

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Phase retrieval using nonlinear diversity

Cited by 31 publications

References 34 publications

Loss of physical reversibility in reversible systems

Loss of physical reversibility in reversible systems

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging

Flow-scanning optical tomography

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