Digital Holographic Imaging

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

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.

Compressive holographic video
Zihao Wang, Leonidas Spinoulas, Kuan He, Lei Tian, Oliver Cossairt, Aggelos K. Katsaggelos, and Huaijin Chen
Opt. Express 25, 250-262 (2017).

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate 10× temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.

dhv

Compressive holographic two-dimensional localization with 1/302 subpixel accuracy
Y. Liu, Lei Tian, C. Hsieh, G. Barbastathis
Optics Express 22, 9774-9782 (2014).

We propose the use of compressive holography for two–dimensional (2D) subpixel motion localization. Our approach is based on computational implementation of edge–extraction using a Fourier–plane spiral phase mask, followed by compressive reconstruction of the edge of the object. Using this technique and relatively low–cost computer and piezo motion stage to establish ground truth for the motion, we demonstrated localization within 1/30th of a camera pixel in each linear dimension.

subpixel2D

Scanning-free compressive holography for object localization with subpixel accuracy
Y. Liu, Lei Tian, J. W. Lee, H. Y. H. Huang, M. S. Triantafyllou, G. Barbastathis
Optics Letters 37, 3357-3359 (2012).

We propose quantitative localization measurement of a known object with subpixel accuracy using compressive holography. We analyze the theoretical optimal solution in the compressive sampling framework and experimentally demonstrate localization accuracy of 1/45 pixel, in good agreement with the analysis.

subpixel1D

Quantitative measurement of size and three-dimensional position of fast moving bubbles in air-water mixture flows using digital holography
Lei Tian, N. Loomis, J. Dominguez-Caballero, G. Barbastathis
Applied Optics 49, 1549 (2010).

We present a digital in-line holographic imaging system for measuring the size and three-dimensional position of fast-moving bubbles in air–water mixture flows. The captured holograms are numerically processed by performing a two-dimensional projection followed by local depth estimation to quickly and efficiently obtain the size and position information of multiple bubbles simultaneously. Statistical analysis on measured bubble size distributions shows that they follow lognormal or gamma distributions.

BUBBLE