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  • Received: Mar. 8, 2019

    Accepted: May. 20, 2019

    Posted: Jun. 19, 2019

    Published Online: Jun. 19, 2019

    The Author Email: Tian Lei (

    DOI: 10.1117/1.AP.1.3.036003

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    Waleed Tahir, Ulugbek S. Kamilov, Lei Tian. Holographic particle localization under multiple scattering[J]. Advanced Photonics, 2019, 1(3): 036003

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Advanced Photonics, Vol. 1, Issue 3, 036003 (2019)

Holographic particle localization under multiple scattering

Waleed Tahir1, Ulugbek S. Kamilov2,3, and Lei Tian1,*

Author Affiliations

  • 1Boston University, Department of Electrical and Computer Engineering, Boston, Massachusetts, United States
  • 2Washington University in St. Louis, Department of Electrical and Systems Engineering, St. Louis, Missouri, United States
  • 3Washington University in St. Louis, Department of Computer Science and Engineering, St. Louis, Missouri, United States


We introduce a computational framework that incorporates multiple scattering for large-scale three-dimensional (3-D) particle localization using single-shot in-line holography. Traditional holographic techniques rely on single-scattering models that become inaccurate under high particle densities and large refractive index contrasts. Existing multiple scattering solvers become computationally prohibitive for large-scale problems, which comprise millions of voxels within the scattering volume. Our approach overcomes the computational bottleneck by slicewise computation of multiple scattering under an efficient recursive framework. In the forward model, each recursion estimates the next higher-order multiple scattered field among the object slices. In the inverse model, each order of scattering is recursively estimated by a nonlinear optimization procedure. This nonlinear inverse model is further supplemented by a sparsity promoting procedure that is particularly effective in localizing 3-D distributed particles. We show that our multiple-scattering model leads to significant improvement in the quality of 3-D localization compared to traditional methods based on single scattering approximation. Our experiments demonstrate robust inverse multiple scattering, allowing reconstruction of 100 million voxels from a single 1-megapixel hologram with a sparsity prior. The performance bound of our approach is quantified in simulation and validated experimentally. Our work promises utilization of multiple scattering for versatile large-scale applications.


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