Optical coherenscopy based on phase-space tomography

Cámara, Alejandro; Rodrigo, José A.; Alieva, Tatiana

doi:10.1364/oe.21.013169

Cited by 19 publications

(13 citation statements)

References 38 publications

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“…It is based upon the measurement of the intensity distributions of the beam transformed by a fractional Fourier transform (FrFT) system, which has been demonstrated to be powerful for beam characterization [8,9].…”

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confidence: 99%

“…1(a). The vortex beams were generated by illuminating the hologram with a collimated coherent and partially coherent laser beam [9], correspondingly. In our case, the partially coherent illumination was obtained by collimation of the laser light scattered by a rotating ground glass diffuser.…”

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confidence: 99%

“…In our case, the partially coherent illumination was obtained by collimation of the laser light scattered by a rotating ground glass diffuser. This illumination beam has a DoC γr exp−πr 2 ∕2w 2 c , where w c 0.45 mm [9]. Therefore the resulting SMB is described by Γr 1 ; r 2 LG 4;1 r 1 ; wLG 4;1 r 2 ; w exp−πr 1 − r 2 2 ∕2w 2 c .…”

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Recovery of Schell-model partially coherent beams

Rodrigo

Alieva

2014

Opt. Lett.

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Partially coherent light is often preferable to its completely coherent counterpart in applications such as imaging, sensing, and free-space optical communications. To fully exploit its advantages, techniques able to retrieve information carried by the beam are required. Here, we develop and experimentally demonstrate a phase-space optics technique for complete spatial analysis of widely used Schell-model beams. It allows for fast information recovery and can be applied for quantitative phase imaging of objects under partially coherent illumination. The further development of imaging techniques requires a more realistic model of illumination as partially coherent light instead of its limiting cases: the coherent or incoherent light used so far. Moreover, partially coherent beams have important advantages with respect to completely coherent ones in other relevant applications such as lithography, plasma confinement, and free-space communication, to name a few. The description of partially coherent light is inherently complex, and its characterization is difficult even in the quasi-monochromatic scalar paraxial approximation. Indeed, a two-dimensional (2D) partially coherent beam is described by a complexvalued 4D function, that is, mutual intensity (MI) defined as Γr 1 ; r 2 hf r 1 f r 2 i, where: r 1;2 is the position vector in a plane transverse to the beam propagation direction and h·i stands for ensemble averaging. The coherent case corresponds to Γ c r 1 ; r 2 f r 1 f r 2 . Schell-model partially coherent beams (SMBs) [1], described by Γr 1 ; r 2 f r 1 f r 2 γr 1 − r 2 Γ c r 1 ; r 2 γr 1 − r 2 , where γr is an equal-time complex degree of spatial coherence (DoC), are often used in practical applications. This kind of beam is generated, for example, when a partially coherent plane wave characterized by γr propagates through an object described by a complex modulation function, f r, as sketched in Fig. 1(a). We recall that, according with the van Cittert Zernike theorem, a partially coherent plane wave can be created by collimating light emitted from an incoherent source with intensity distribution I inc r. Specifically, γr ∝ R I inc r 0 exp−i2πr 0 r∕λf cl dr 0 , where λ is the wavelength and f cl is the focal length of the collimating lens [2]. Moreover, the generalization of structurally stable and spiral coherent beams to the partially coherent case is also described by the Schell model [3,4]. In the last decades, special attention has been paid to coherent vortex beams that carry orbital angular momentum (OAM) useful for different applications such as optical tweezers and free-space communications [5]. On the other hand, the SMB vortex has been found more robust than its coherent counterpart to distortions caused by turbulent atmosphere [6,7]. We underline that the valuable information carried by the SMB is often encoded into f r, while γr in most, but not all, cases is known.In this Letter we propose and experimentally demonstrate an iterative MI retrieval technique for arbitrary SMBs with a priori known ...

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Recovery of Schell-model partially coherent beams

Rodrigo

Alieva

2014

Opt. Lett.

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“…Phase space tomography (PST) is a classic approach for solving the optical coherence retrieval problem, i.e., estimating the state of coherence of an optical field using only measurements of intensity [1][2][3][4][5][6][7]. The approach is grounded in the idea that the Fourier transform of intensity profiles captured under varying levels of defocus form slices of the ambiguity function, a phase space representation that quantifies an optical field's state of coherence [8,9].…”

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Apparent coherence loss in phase space tomography

et al. 2017

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A sensor pixel integrates optical intensity across its extent, and we explore the role that this integration plays in phase space tomography. The literature is inconsistent in its treatment of this integration-some approaches model this integration explicitly, some approaches are ambiguous about whether this integration is taken into account, and still some approaches assume pixel values to be point samples of the optical intensity. We show that making a point-sample assumption results in apodization of and thus systematic error in the recovered ambiguity function, leading to underestimating the overall degree of coherence. We explore the severity of this effect using a Gaussian Schell-model source and discuss when this effect, as opposed to noise, is the dominant source of error in the retrieved state of coherence.

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“…While this setup allows automatized video-rate measuring of any projection set suitable for the WD reconstruction (for example one which we have discussed above or the set P 0,γx,γy,0 (r) corresponding to the FrFT used in 23 ) there is a set which is more appropriate for practical application of the phase space tomography. This set, P 0,0,γ,α (r) , as it has been demonstrated in 32 allows simultaneous performing of the data acquisition and processing. Since every projection subset for a fixed angle α 0 is an independent entity, then the WD and the MI of the optical field at the points along the parallel lines which form angle α 0 with the axes y can be obtained from this subset.…”

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Synthesis and characterization of complex partially coherent beams

Alieva

Cámara

Rodrigo

2015

Photonic Instrumentation Engineering II

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Partially coherent light provides attractive benefits for different applications in microscopy, astronomy, telecommunications, optical lithography, etc. However, design and generation of partially coherent beams with desirable properties is challenging. Moreover, the experimental characterization of the spatial coherence is a difficult problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured and analyzed. We discuss the techniques for design and generation of partially coherent structurally stable beams and the recently developed phase-space tomography methods supported by simple experimental setups for practical quantitative characterization of partially coherent light spatial structure, including its local coherence properties.

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Optical coherenscopy based on phase-space tomography

Cited by 19 publications

References 38 publications

Recovery of Schell-model partially coherent beams

Recovery of Schell-model partially coherent beams

Apparent coherence loss in phase space tomography

Synthesis and characterization of complex partially coherent beams

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