Inverse source problem for three-dimensional partially coherent sources and fields

The inverse source problem for arbitrary, three-dimensional, wide-sense stationary, spatially and temporally partially coherent sources is formulated. The formulation is based on an extension of the Porter–Bojarski inverse source integral equation (ISIE) for deterministic fields and is developed in the space–frequency domain. The known data are assumed to be the cross-spectral density of the field generated by the source, along with its normal derivative, elevated on a surface enclosing the support volume of the source, whereas the unknown is the cross-spectral density of the source itself. The solution of the partially coherent ISIE is shown to be nonunique, the nonuniqueness being intimately related to the nonuniqueness of the corresponding deterministic equation. Special cases of source coherence are shown to lead to unique inversions; however, the results do not completely parallel the deterministic case. An exact solution for the radiating portion of the source cross-spectral density is presented in the form of an eigenfunction expansion, and this is compared with the space-frequency expansion developed by Wolf [ J. Opt. Soc. Am.72, 343 ( 1982)] for arbitrary source cross-spectral densities.

[1]  Robert P. Porter.  Diffraction-Limited Scalar Image Formation with Holograms of Arbitrary Shape , 1970 .

[2]  N. Bojarski,et al.  A survey of the near-field far-field inverse scattering inverse source integral equation , 1982 .

[3]  A Nonradiating Linear Combination of Quasihomogeneous Current Correlations , 1978 .

[4]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[5]  D. McGuire.  Source coherence and far-field intensity patterns , 1979 .

[6]  W. H. Carter,et al.  Correlation Theory of Wavefields Generated by Fluctuating, Three-dimensional, Primary, Scalar Sources: I. General Theory , 1981 .

[7]  Recently Developed Formulations of the Inverse Problem in Acoustics and Electromagnetics , 1974 .

[8]  L. Mandel,et al.  Spectral coherence and the concept of cross-spectral purity , 1976 .

[9]  A. J. Devaney,et al.  Radiating and nonradiating classical current distributions and the fields they generate , 1973 .

[10]  R. P. Porter,et al.  Generalized holography and computational solutions to inverse source problems , 1982 .

[11]  The scalar theory of nonradiating partially coherent sources , 1979 .

[12]  R. P. Porter,et al.  Holography and the inverse source problem , 1982 .

[13]  A. Devaney,et al.  Comments on "Nonuniqueness in inverse source and scattering problems" , 1982 .

[14]  B. Hoenders.  The Uniqueness of Inverse Problems , 1978 .

[15]  Jack K. Cohen,et al.  Nonuniqueness in the inverse source problem in acoustics and electromagnetics , 1975 .

[16]  E. Wolf.  New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources , 1982 .

[17]  E. Wolf.  New spectral representation of random sources and of the partially coherent fields that they generate , 1981 .

[18]  Anthony J. Devaney,et al.  Inverse problem for random sources (A) , 1978 .

[19]  H. P. Baltes,et al.  Radiant intensity and spatial coherence for finite planar sources , 1977 .

[20]  W. H. Carter,et al.  Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources , 1978 .

[21]  W. H. Carter,et al.  Correlation Theory of Wavefields Generated by Fluctuating, Three-dimensional, Scalar Sources , 1981 .

[22]  On the existence of non-radiating frequencies in the radiation from a stochastic current distribution , 1980 .