Programmable two-dimensional optical fractional Fourier processor

Rodrigo, José A.; Alieva, Tatiana; Calvo, M. L.

doi:10.1364/oe.17.004976

Cited by 60 publications

(29 citation statements)

References 15 publications

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“…A video rate measurement of these intensity distributions can be performed using the programmable FrFT setup reported in [10], which is sketched in Fig. 1(b).…”

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confidence: 99%

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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“…A video rate measurement of these intensity distributions can be performed using the programmable FrFT setup reported in [10], which is sketched in Fig. 1(b).…”

mentioning

confidence: 99%

Recovery of Schell-model partially coherent beams

Rodrigo

Alieva

2014

Opt. Lett.

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“…[33] which comprises two generalized lenses implemented by two spatial light modulators (SLMs) and a digital camera. The distance z between every two consecutive elements is fixed.…”

Section: Coherenscope Setupmentioning

confidence: 99%

Optical coherenscopy based on phase-space tomography

Cámara¹,

Rodrigo²,

Alieva³

2013

Opt. Express

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Abstract:Partially coherent light provides attractive benefits in imaging, beam shaping, free-space communications, random medium monitoring, among other applications. However, 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. In addition, real-world applications usually require quantitative characterization of the local spatial coherence of a beam in the absence of a priori information, together with fast acquisition and processing of the experimental data. Here we propose and experimentally demonstrate a technique that solves this problem. It comprises an optical setup developed for automatized video-rate measurement and a method -phase-space tomographic coherenscopy-allowing parallel data acquisition, processing, and analysis. This technique significantly simplifies the spatial coherence analysis and opens up new perspectives for the development of tools exploiting the degrees of freedom hidden into light coherence.

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“…The experimental verification of the proposed techniques is performed using the optical setup that allows an automated implementation of the sFrFT for the running parameter α that is described in [44]. The setup consists of two SLMs and a digital camera located at fixed positions.…”

Section: Introductionmentioning

confidence: 99%

Partially coherent stable and spiral beams

et al. 2013

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Stable and spiral coherent beams, which do not change the form of their intensity distribution apart from possible scaling and rotation during propagation and therefore possess self-healing properties, are widely applied in science and technology. On the other hand, it has been found that partially coherent light often provides better output than coherent light. Here we consider two methods for the design and experimental generation of partially coherent stable and spiral beams.

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Programmable two-dimensional optical fractional Fourier processor

Cited by 60 publications

References 15 publications

Recovery of Schell-model partially coherent beams

Recovery of Schell-model partially coherent beams

Optical coherenscopy based on phase-space tomography

Partially coherent stable and spiral beams

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