...nes vs. distant scenes In Fig. 5 (left), l1 = l2 = ‖AB‖ (v+u) u ; the sensor convolves a stretched version of the template with a planar scene at a distance (v + u). This is the scenario explained in =-=[3]-=-. However, for distant scenes defined on the hemisphere, the solid angle are important. △ABP1 and △ABP2 have the same base but different sides, and so the two angular supports are unequal; ω1 = ω2. 5...

...nvolution in terms of light-fields: For a distant scene, spherical convolution on a planar sensor (a) integrates rays along a line curve in the light-field (b), suggesting quadratically curved optics =-=[1]-=-, such as lenslets. ω + 90 + θ1 + 90 − θ2 = 180 ω = θ2 − θ1 From the previous two equations, we can attempt to solve for θ1 and θ2. From Snell’s law and the solutions to these, we can obtain θ ′ 1 and...

...ircular design for wide-angle filtering that has perfect spherical filtering. 3 An imaging example of Snell’s window In Fig. 4 we shown an imaging example of Snell’s window (a miniaturized version of =-=[2]-=-) for an outdoor scene, showing that indeed our setup is able to provide 180 degree FOV and comparing it to a simple pinhole view of the same scene which has less FOV. 4 Lensless imaging for planar sc...