Uniqueness of the inverse source problem for quasi-homogeneous, partially coherent sources

LaHaie, Ivan J.

doi:10.1364/josaa.3.001073

Cited by 14 publications

(10 citation statements)

References 9 publications

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“…Uniqueness can be restored when referring to incoherent (i.e., delta correlated sources) or quasi-homogeneous sources [28,33,39]. In the case of incoherent sources, namely, the case of interest in the present paper, Γ j s (x , x ) = I(x )δ(x − x ), so that Eq.…”

Section: Formulation Of the Problemmentioning

confidence: 97%

“…where, again with an abuse of notation, Γ e (x 1 , x 2 ) = Γ e (x 1 , x 2 , 0), defines the inverse source problem for partially coherent sources and fields [23,28,33,39], and, in particular, that of deducing second order statistics of the source from second order statistics of the radiated field on the segment (−a, a) of the z = d axis. As known, not only in the case of coherent sources, but also when partially coherent radiators are involved, this problem has a nonunique solution [40].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Experimental Field Reconstruction of Incoherent Sources

Capozzoli¹,

Curcio²,

Liseno³

2013

PIER B

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Abstract-The problem of characterizing random sources from near-field measurements and of devising the random field sampling procedure is tackled by a stochastic approach. The presented technique is an extension of that introduced in [22] and successfully adopted to experimentally characterize deterministic (CW and multi-frequency) radiators and fields. Under the assumption that the source is wide sense stationary, quasi-monochromatic and incoherent, its intensity is reconstructed by time-domain field measurements aimed at extracting information from the mutual coherence of the acquired near-field. The linear relation between the field coherence and the source intensity is inverted by using the Singular Value Decomposition (SVD) approach, properly representing the source intensity distribution by exploiting the a priori information (e.g., its size and shape) on the radiator. The sampling of the radiated random field is devised by a singular value optimization procedure of the relevant finite dimensional linear operator. Experimental results using a slotted reverberation chamber as incoherent source assess the performance of the approach.

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Section: Formulation Of the Problemmentioning

confidence: 97%

Section: Formulation Of the Problemmentioning

confidence: 99%

Experimental Field Reconstruction of Incoherent Sources

Capozzoli¹,

Curcio²,

Liseno³

2013

PIER B

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“…where, again with an abuse of notation, Γ e (x 1 , x 2 ) = Γ e (x 1 , x 2 , 0), defines the inverse source problem for partially coherent sources and fields [2], [8], [11], [14], and, in particular, that of deducing second order statistics of the source from second order statistics of the radiated field on D I . In this paper, we consider the case of incoherent (i.e., delta correlated sources), for which Γ j (x , x ) = I(x )δ(x − x ), I being the intensity of the source [2], [8], [11], [14], so that eq.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In this paper, we consider the case of incoherent (i.e., delta correlated sources), for which Γ j (x , x ) = I(x )δ(x − x ), I being the intensity of the source [2], [8], [11], [14], so that eq. (5) particularizes as (6) is an expression of the van Cittert-Zernike theorem [10].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Field sampling of incoherent sources

Capozzoli

Curcio

Esposito

et al. 2011

2011 IEEE International Symposium on Antennas and Propagation (APSURSI)

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The problem of characterizing random sources from near-field measurements performed on a domain DI and of devising the random field sampling procedure is tackled by a stochastic approach. The presented technique is an extension of that introduced in [A. Capozzoli, et al., Field sampling and field reconstruction: a new perspective, Radio Sci., vol. 45, 2010] and successfully adopted to experimentally characterize deterministic (CW) radiators and fields. Under the assumption that the source is wide sense stationary, quasi-monochromatic and incoherent, its intensity is reconstructed by time-domain field measurements aimed at extracting information from the mutual coherence of the field on DI. The linear relation between the field coherence on DI and the source intensity is inverted by using the Singular Value Decomposition (SVD) approach, properly representing the source intensity distribution by exploiting the a priori information (e.g., its size and shape) on the radiator. The sampling of the radiated random field is devised by a singular value optimization procedure of the relevant linear operator. Numerical results sketch the performance of the approach

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“…LaHaie has investigated the inverse source problem for arbitrary, three-dimensional, wide-sense stationary, spatially and temporally partially coherent sources and fields [2]. And later, LaHaie has also investigated the inverse problem of partially coherent sources which can be stated as determining the mutual coherent function of a localized random source from measurements of the mutual coherence function of the field generated by the source [3]. Recently, two kinds of the fast Fourier transform algorithm have been used to study of inverse Collins formula [4].…”

Section: Introductionmentioning

confidence: 99%