3D imaging in volumetric scattering media using phase-space measurements.

We demonstrate the use of phase-space imaging for 3D localization of multiple point sources inside scattering material. The effect of scattering is to spread angular (spatial frequency) information, which can be measured by phase space imaging. We derive a multi-slice forward model for homogenous volumetric scattering, then develop a reconstruction algorithm that exploits sparsity in order to further constrain the problem. By using 4D measurements for 3D reconstruction, the dimensionality mismatch provides significant robustness to multiple scattering, with either static or dynamic diffusers. Experimentally, our high-resolution 4D phase-space data is collected by a spectrogram setup, with results successfully recovering the 3D positions of multiple LEDs embedded in turbid scattering media.

[1]  J. M. Cowley,et al.  The scattering of electrons by atoms and crystals. I. A new theoretical approach , 1957 .

[2]  Joseph W. Goodman,et al.  WAVEFRONT‐RECONSTRUCTION IMAGING THROUGH RANDOM MEDIA , 1966 .

[3]  Jack D. Gaskill.  Imaging Through a Randomly Inhomogeneous Medium by Wavefront Reconstruction , 1968 .

[4]  H. Kogelnik,et al.  Holographic Imaging Through a Random Medium , 1968 .

[5]  Mj Martin Bastiaans.  The Wigner distribution function applied to optical signals and systems , 1978 .

[6]  A. Lohmann,et al.  The wigner distribution function and its optical production , 1980 .

[7]  R. Alfano,et al.  Ballistic 2-D Imaging Through Scattering Walls Using an Ultrafast Optical Kerr Gate , 1991, Science.

[8]  J. Fujimoto,et al.  Optical Coherence Tomography , 1991 .

[9]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[10]  J. E. Thomas,et al.  Measurement of smoothed Wigner phase-space distributions for small-angle scattering in a turbid medium. , 1998, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Path Integral Methods and Applications , 2000, quant-ph/0004090.

[12]  Joseph Rosen,et al.  Seeing through biological tissues using the fly eye principle. , 2003, Optics express.

[13]  Marc Levoy,et al.  Synthetic aperture confocal imaging , 2004, SIGGRAPH 2004.

[14]  P. Hanrahan,et al.  Light Field Photography with a Hand-held Plenoptic Camera , 2005 .

[15]  Marc Levoy,et al.  Light Fields and Computational Imaging , 2006, Computer.

[16]  A. Mosk,et al.  Focusing coherent light through opaque strongly scattering media. , 2007, Optics letters.

[17]  R. Nowak,et al.  Statistical detection and imaging of objects hidden in turbid media using ballistic photons. , 2007, Applied optics.

[18]  K. Fujita.  [Two-photon laser scanning fluorescence microscopy]. , 2007, Tanpakushitsu kakusan koso. Protein, nucleic acid, enzyme.

[19]  B. Javidi,et al.  Three-dimensional visualization of objects in scattering medium by use of computational integral imaging. , 2008, Optics express.

[20]  Chia-Kai Liang,et al.  Programmable aperture photography: multiplexed light field acquisition , 2008, SIGGRAPH 2008.

[21]  Stephen J. Wright,et al.  Sparse Reconstruction by Separable Approximation , 2008, IEEE Transactions on Signal Processing.

[22]  M. Levoy,et al.  Wigner distributions and how they relate to the light field , 2009, 2009 IEEE International Conference on Computational Photography (ICCP).

[23]  Francisco E. Robles,et al.  Dual window method for processing spectroscopic optical coherence tomography signals with simultaneously high spectral and temporal resolution. , 2009, Optics express.

[24]  Shree K. Nayar,et al.  Programmable Aperture Camera Using LCoS , 2010, IPSJ Trans. Comput. Vis. Appl..

[25]  S. Popoff,et al.  Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. , 2009, Physical review letters.

[26]  Douglas Lanman,et al.  Descattering Transmission via Angular Filtering , 2010, ECCV.

[27]  Changhuei Yang,et al.  Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation , 2010, Optics express.

[28]  Eric Betzig,et al.  Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues , 2010, Nature Methods.

[29]  Ivo M Vellekoop,et al.  Turbidity suppression from the ballistic to the diffusive regime in biological tissues using optical phase conjugation. , 2010, Journal of biomedical optics.

[30]  Demetri Psaltis,et al.  Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle. , 2010, Optics express.

[31]  Adam Wax,et al.  Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry. , 2010, Optics letters.

[32]  Thomas Deselaers,et al.  ClassCut for Unsupervised Class Segmentation , 2010, ECCV.

[33]  Francisco E. Robles,et al.  Molecular imaging true-colour spectroscopic optical coherence tomography. , 2011, Nature photonics.

[34]  Laura Waller,et al.  Instability-driven recovery of diffused images. , 2011, Optics letters.

[35]  Miguel A. Alonso,et al.  Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles , 2011 .

[36]  Benjamin Recht,et al.  Atomic norm denoising with applications to line spectral estimation , 2011, Allerton.

[37]  J. Rodenburg,et al.  Ptychographic transmission microscopy in three dimensions using a multi-slice approach. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[38]  O. Katz,et al.  Looking around corners and through thin turbid layers in real time with scattered incoherent light , 2012, Nature Photonics.

[39]  Yaron Silberberg,et al.  Spatiotemporal focusing through a thin scattering layer. , 2012, Optics express.

[40]  W. Choi,et al.  Maximal energy transport through disordered media with the implementation of transmission eigenchannels , 2012, Nature Photonics.

[41]  L. Waller,et al.  Phase-space measurement and coherence synthesis of optical beams , 2012, Nature Photonics.

[42]  Gongguo Tang,et al.  Sparse recovery over continuous dictionaries-just discretize , 2013, 2013 Asilomar Conference on Signals, Systems and Computers.

[43]  G. Pedrini,et al.  Looking through a diffuser and around an opaque surface: a holographic approach. , 2014, Optics express.

[44]  M. Fink,et al.  Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations , 2014, Nature Photonics.

[45]  M. Alonso,et al.  Using shadows to measure spatial coherence. , 2014, Optics letters.

[46]  S. Popoff,et al.  Image transmission through a scattering medium: Inverse problem and sparsity-based imaging , 2014, 2014 13th Workshop on Information Optics (WIO).

[47]  David Abookasis,et al.  Feasibility study of hidden flow imaging based on laser speckle technique using multiperspectives contrast images , 2014 .

[48]  Kannan Ramchandran,et al.  Multiplexed coded illumination for Fourier Ptychography with an LED array microscope. , 2014, Biomedical optics express.

[49]  Jason W Fleischer,et al.  Phase-space measurement for depth-resolved memory-effect imaging. , 2014, Optics express.

[50]  L. Tian,et al.  3D intensity and phase imaging from light field measurements in an LED array microscope , 2015 .