We explore the use of plenoptic data for performing passive non-line-of-sight imaging using light scattered from interior hallways at visible, long-wave infrared, and terahertz frequencies. The use of longer wavelength radiation in the LWIR and THz bands can increase the retrievable NLOS image information in comparison to visible radiation. However, significant scattering effects at LWIR wavelengths and diffraction effects at the millimeter wavelengths of THz radiation present unique optical design challenges. In this paper, by assuming a general imaging system for light field capture, we provide a theoretical framework to describe measured NLOS information including scattering and diffraction effects. Our analysis combines a ray-based light field description of the plenoptic space with a Wigner distribution function formalism to provide an intuitive physical understanding of the limits of NLOS imaging. Further, based on the analysis, we provide a simple strategy to design optical measurement systems in the LWIR and THz wavelength ranges.
A full description of light propagation in the ray regime is provided by the plenoptic function, where both the location and angle of each ray is known. In this paper, we investigate the utility of plenoptic data for extracting information from a scene where the light from objects in the scene is viewable only after scattering from a diffuse surface. The detected light is mathematically described as a light field that varies as a function of both space and propagation angle. The relationship between the object light field and the scattered light field is cast in terms of a system of Fredholm integral equations of the first kind, where the bidirectional reflectance distribution function (BRDF) of the scattering surface is incorporated into the kernel of the integral equations. The object information from the original scene is retrieved by solving the resulting system of integral equations.
We apply our mathematics to BRDFs containing the superposition of a quasi shift-invariant specular component and a diffuse component. This permits the use of efficient Fourier methods to solve the integral equations. These analytical solutions are verified via numerical simulation. In addition, we show experimental results from a light-field measurement studio equipped with a high-dynamic range scientific camera connected to a high-precision motorized stage. This studio is capable of measuring light fields with high accuracy. Experimental results of reconstructed light-fields will be reported.
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