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.



Relaxation of mask design for single-shot phase imaging with a coded aperture

R. Egami, R. Horisaki, L. Tian, J. Tanida
Appl. Opt. 55, 1830-1837 (2016).

We present a method of relaxing the conditions of mask design in single-shot phase imaging with a coded aperture (SPICA), for extending the applications of SPICA. SPICA, based on compressive sensing, enables the acquisition of wide, high-resolution optical complex fields in a single exposure without the need for reference light. In our previous work on SPICA, a coded aperture (CA) was implemented with only amplitude modulation, resulting in a low transmission factor and low light efficiency because of the need for an independent phase retrieval process in the reconstruction. We attempt to alleviate these limitations by adapting a reconstruction algorithm to directly associate the phase-retrieval process with a sparsity-based reconstruction. With this approach, it is possible to realize SPICA with an amplitude-modulation-based CA having a high transmission factor, a phase-modulation-based CA, and a complex-amplitude (amplitude and phase)-modulation-based CA. We verified the effectiveness of these relaxed CA designs numerically and experimentally.

Empirical concentration bounds for compressive holographic bubble imaging based on a Mie scattering model
W. Chen, Lei Tian, S. Rehman, Z. Zhang, H. P. Lee, G. Barbastathis
Opt. Express 23, (2015).

We use compressive in–line holography to image air bubbles in water and investigate the effect of bubble concentration on reconstruction performance by simulation. Our forward model treats bubbles as finite spheres and uses Mie scattering to compute the scattered field in a physically rigorous manner. Although no simple analytical bounds on maximum concentration can be derived within the classical compressed sensing framework due to the complexity of the forward model, the receiver operating characteristic (ROC) curves in our simulation provide an empirical concentration bound for accurate bubble detection by compressive holography at different noise levels, resulting in a maximum tolerable concentration much higher than the traditional back-propagation method.

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.


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.


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.