Temporal response of a random medium from speckle intensity frequency correlations.

We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diffusion regime are in excellent agreement with the intensity temporal response measured directly with an ultrafast pulse laser and a streak camera. Our speckle correlation measurements also demonstrate sensitivity to inhomogeneous samples, highlighting the potential application for imaging within a scattering medium.

[1]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[2]  First-order probability density function of the integrated speckle , 1991 .

[3]  H. Gamo.  Triple Correlator of Photoelectric Fluctuations as a Spectroscopic Tool , 1963 .

[4]  Ping Sheng,et al.  Scattering And Localization Of Classical Waves In Random Media , 1990 .

[5]  D. Delpy,et al.  Enhanced time-resolved imaging with a diffusion model of photon transport. , 1994, Optics letters.

[6]  L. O. Svaasand,et al.  Boundary conditions for the diffusion equation in radiative transfer. , 1994, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  First-order probability density functions of speckle measured with a finite aperture , 1974 .

[8]  C A Thompson,et al.  Diffusive media characterization with laser speckle. , 1997, Applied optics.

[9]  Feng,et al.  Correlations and fluctuations of coherent wave transmission through disordered media. , 1988, Physical review letters.

[10]  Shapiro,et al.  Fluctuations in transmission of waves through disordered slabs. , 1989, Physical review. B, Condensed matter.

[11]  J. Duderstadt,et al.  Nuclear reactor analysis , 1976 .

[12]  Jack D. Gaskill,et al.  Linear systems, fourier transforms, and optics , 1978, Wiley series in pure and applied optics.

[13]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[14]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[15]  Andrew M. Weiner,et al.  Imaging in scattering media by use of laser speckle , 1997 .

[16]  D. Delpy,et al.  Optical Imaging in Medicine , 1998, CLEO/Europe Conference on Lasers and Electro-Optics.

[17]  D. Middleton.  An Introduction to Statistical Communication Theory , 1960 .

[18]  A W Lohmann,et al.  Phase and amplitude recovery from bispectra. , 1984, Applied optics.

[19]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[20]  Toshimitsu Asakura,et al.  Effect of the point spread function on the average contrast of image speckle patterns , 1977 .

[21]  G. Parry.  Some Effects of Temporal Coherence on the First Order Statistics of Speckle , 1974 .

[22]  R. Wooding.  The multivariate distribution of complex normal variables , 1956 .

[23]  J. Marron,et al.  Unwrapping algorithm for least-squares phase recovery from the modulo 2π bispectrum phase , 1990 .

[24]  G. Maret,et al.  Observation of long-range correlations in temporal intensity fluctuations of light , 1997 .

[25]  Charles A. Bouman,et al.  Optical diffusion tomography by iterative- coordinate-descent optimization in a Bayesian framework , 1999 .

[26]  Azriel Z. Genack,et al.  Fluctuations, Correlation and Average Transport of Electromagnetic Radiation in Random Media , 1990 .

[27]  Kevin J Webb,et al.  Three-dimensional Bayesian optical diffusion tomography with experimental data. , 2002, Optics letters.

[28]  J. Klauder,et al.  Recovery of Laser Intensity from Correlation Data , 1969 .

[29]  Charles L. Matson.  Weighted least-squares phase reconstruction from the bispectrum , 1990, Optics & Photonics.

[30]  A. Genack,et al.  Relationship between Optical Intensity, Fluctuations and Pulse Propagation in Random Media , 1990 .

[31]  Thomas L. Grettenberg.  Representation theorem for complex normal processes (Corresp.) , 1965, IEEE Trans. Inf. Theory.

[32]  R. H. Brown,et al.  A New type of interferometer for use in radio astronomy , 1954 .

[33]  M. V. Rossum,et al.  Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion , 1998, cond-mat/9804141.

[34]  Irving S. Reed,et al.  On a moment theorem for complex Gaussian processes , 1962, IRE Trans. Inf. Theory.

[35]  A. Lohmann,et al.  Triple correlations , 1984, Proceedings of the IEEE.

[36]  Genack.  Optical transmission in disordered media. , 1987, Physical review letters.

[37]  V. Tuchin.  Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis , 2000 .

[38]  B. Wilson,et al.  Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties. , 1989, Applied optics.

[39]  SHECHAO FENG,et al.  Mesoscopic Conductors and Correlations in Laser Speckle Patterns , 1991, Science.

[40]  Clark,et al.  Effects of finite laser coherence in quasielastic multiple scattering. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[41]  A. Lohmann,et al.  Speckle masking in astronomy: triple correlation theory and applications. , 1983, Applied optics.

[42]  J. Goodman.  Statistical Optics , 1985 .

[43]  A M Weiner,et al.  Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source. , 2000, Optics letters.

[44]  Temporal response of a random medium from third-order laser speckle frequency correlations. , 2002, Physical review letters.

[45]  Marc A. Berger,et al.  An Introduction to Probability and Stochastic Processes , 1992 .

[46]  S R Arridge,et al.  Optical imaging in medicine: I. Experimental techniques , 1997, Physics in medicine and biology.

[48]  R. Smith,et al.  Linear Systems, Fourier Transforms and Optics , 1979 .

[49]  Robert R. Alfano,et al.  Time-resolved fluorescence and photon migration studies in biomedical and model random media , 1997 .

[50]  J. Goodman.  Statistical Properties of Laser Speckle Patterns , 1963 .

[51]  Li,et al.  Correlation in laser speckle. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[52]  Christopher A. Haniff,et al.  Erratum: Least-squares Fourier phase estimation from the modulo 2pi bispectrum phase phase [J. Opt. Soc. Am. A 8, 134-140 (1991)] , 1991 .