Hyper-hemispheric lens distortion model for 3D-imaging SPAD-array-based applications

Panoramic omnidirectional lenses have the typical draw-back effect to obscure the frontal view, producing the classic "donut-shape" image in the focal plane. We realized a panoramic lens in which the frontal field is make available to be imaged in the focal plane together with the panoramic field, producing a FoV of 360° in azimuth and 270° in elevation; it have then the capabilities of a fish eye plus those of a panoramic lens: we call it hyper-hemispheric lens. We built and test an all-spherical hyper-hemispheric lens. The all-spherical configuration suffer for the typical issues of all ultra wide angle lenses: there is a large distortion at high view angles. The fundamental origin of the optical problems resides on the fact that chief rays angles on the object side are not preserved passing through the optics preceding the aperture stop (fore-optics). This effect produce an image distortion on the focal plane, with the focal length changing along the elevation angles. Moreover, the entrance pupil is shifting at large angle, where the paraxial approximation is not more valid, and tracing the rays appropriately require some effort to the optical designer. It has to be noted here as the distortion is not a source-point-aberrations: it is present also in well corrected optical lenses. Image distortion may be partially corrected using aspheric surface. We describe here how we correct it for our original hyper-hemispheric lens by designing an aspheric surface within the optical train and optimized for a Single Photon Avalanche Diode (SPAD) array-based imaging applications.