The multiplate antenna

Schell, A.

doi:10.1109/tap.1966.1138741

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…In the scalar paraxial approximation the MI of a two-dimensional (2D) wavefield is described by a complex-valued 4D MI defined as Γ(r 1 , r 2 ) = f (r 1 ) f * (r 2 ) , where: r 1,2 = (x, y) 1,2 is a position vector in a plane transverse to the light propagation direction and · stands for ensemble averaging. Completely coherent beams are characterized by Γ c (r 1 , r 2 ) = f (r 1 ) f * (r 2 ) while Schell-model partially coherent beams (SMBs) [21] are described by Γ(r 1 , r 2 ) = f (r 1 ) f * (r 2 ) γ (r 1 − r 2 ) = Γ c (r 1 , r 2 )γ ( r), where γ ( r) is an equal-time complex degree of spatial coherence (DSC). The Schell model is widely used in different imaging applications, including microscopy.…”

Section: Introductionmentioning

confidence: 99%

Rapid quantitative phase imaging for partially coherent light microscopy

Rodrigo¹,

Alieva²

2014

Opt. Express

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Abstract:Partially coherent light provides promising advantages for imaging applications. In contrast to its completely coherent counterpart, it prevents image degradation due to speckle noise and decreases cross-talk among the imaged objects. These facts make attractive the partially coherent illumination for accurate quantitative imaging in microscopy. In this work, we present a non-interferometric technique and system for quantitative phase imaging with simultaneous determination of the spatial coherence properties of the sample illumination. Its performance is experimentally demonstrated in several examples underlining the benefits of partial coherence for practical imagining applications. The programmable optical setup comprises an electrically tunable lens and sCMOS camera that allows for high-speed measurement in the millisecond range.

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Section: Introductionmentioning

confidence: 99%

Rapid quantitative phase imaging for partially coherent light microscopy

Rodrigo¹,

Alieva²

2014

Opt. Express

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“…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.…”

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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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“…For our model we have a typical undulator source of 3 rd generation synchrotron facilities in mind; but the idea of the following considerations is common for classical light sources and can in principle be applied to bending magnets, x-ray tubes, and modern micro-focus lab sources as well. [11,22].…”

Section: Degree Of Coherencementioning

confidence: 99%

Wave optical simulations of x-ray nano-focusing optics

Osterhoff¹

2012

Göttingen Series in X-Ray Physics

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The multiplate antenna

Cited by 9 publications

References 10 publications

Rapid quantitative phase imaging for partially coherent light microscopy

Rapid quantitative phase imaging for partially coherent light microscopy

Recovery of Schell-model partially coherent beams

Wave optical simulations of x-ray nano-focusing optics

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