Combined geometric and physical optics analysis of passive non-line-of-sight light-field measurement

We provide an analysis of retrievable non-line-of-sight (NLOS) information from hidden objects, whose passive blackbody radiation is reflected from a non-specular surface, such as a rough wall, and derive an optimized optical design procedure for capturing the NLOS light field. In particular, we investigate two NLOS imaging regimes. In the scattering-limited regime, the reflecting surface is rough compared to the blackbody radiation wavelength, and the scattering generally corrupts the NLOS information. The light field in this regime is modeled by the bidirectional reflectance distribution function using a geometric optics approximation. In the diffraction-limited regime, the reflecting surface is smooth compared to the radiation wavelength. This light field is modeled by the Wigner distribution function and carries with it all the diffraction properties of the imaging system that can degrade the NLOS information. By merging these two expressions, we are able to understand the measured NLOS light field for surfaces that range from highly scattering to highly specular, and for long and short radiation wavelengths. In particular, using the Fresnel number and its scattering-counterpart which we have newly proposed in this current paper, we can theoretically predict the optimal imaging lens focusing conditions for the best optical design to retrieve the NLOS information for a variety of surfaces and wavelengths. Moreover, our analysis provides an intuitive physical interpretation of the NLOS information degradation in the light field space under these various reflectance conditions and can be used to numerically simulate the measured light field. We note that those analyses are also applicable to a single NLOS image capture, since a conventional camera image is a slice of the light field. Once we measure the NLOS data with the best optical design, we can then use it for any desired applications, such as the NLOS imaging and object location estimation. Experiments are performed using long-wave infrared radiation and THz radiation from thermally elevated objects to explore the scattering-limited and diffraction-limited regimes respectively. We find that there is a notable shift in the ideal lens focusing conditions in these two cases, and that the measured shifts are accurately predicted by our model.