Flux profile at focal area of concentrating solar dishes

We analytically, experimentally and computationally explore the solar radiation flux distribution in the interior region of a spherical mirror and compare it to that of a paraboloidal one with the same aperture area. Our investigation has been performed in the framework of geometrical optics. It is shown that despite one can assign a quasi focus, at half the radius, to a spherical mirror, the light concentration occurs as well on an extended line region which starts at half-radius on the optical axis. In contrast to a paraboloidal concentrator, a spherical mirror can concentrate the radiation parallel to its optical axis both in a point-focus and in a line-focus manner. The envelope of the reflected rays is also obtained. It is shown that the flux distribution has an axial symmetry. The radial dependence of the flux on a flat circular receiver is obtained. The flux longitudinal dependence is shown to exhibit three distinctive regions in the interval [0, R] (R is mirror radius). We obtain the radiational (optical) concentration ratio characteristics and find the optimal location of the flat receiver of a given size at which the concentration ratio is maximised. In contrast to a parabolic mirror, it is shown that this location depends on the receiver size. Our findings offers that in spherical mirrors one can alternatively use a line receiver and gains a considerable thermal energy harvest. Our results are supported by Monte Carlo ray tracing performed by Zemax optical software. Experimental validation has been performed in lab with a silver-coated lens as the spherical mirror.

Robust Pose Estimation and Calibration of Catadioptric Cameras With Spherical Mirrors

Catadioptric cameras broaden the field of view and reveal otherwise occluded object parts. They differ geometrically from central-perspective cameras because of light reflection from the mirror surface. To handle these effects, we present new pose-estimation and reconstruction models for imaging through spherical mirrors. We derive a closed-form equivalent to the collinearity principle via which three methods are established to estimate the system parameters: a resection-based one, a trilateration-based one that introduces novel constraints that enhance accuracy, and a direct and linear transform-based one. The estimated system parameters exhibit improved accuracy compared to the state of the art, and analysis shows intrinsic robustness to the presence of a high fraction of outliers. We then show that 3D point reconstruction can be performed at accurate levels. Thus, we provide an in-depth look into the geometrical modeling of spherical catadioptric systems and practical enhancements of accuracies and requirements to reach them.