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Due to the historical reasons all the image capturing and projection systems work with a “flat-to-flat” configuration: the image is detected in a camera focal plane and then projected to a flat display or a flat screen. Recently, we entered a new era with two major technical levers – curved sensors and 3D/immersive imaging. This new combination allows us, on the one hand, to easily capture spherical images and, on another hand, to view spherical images without any intermediate plane picture. Indeed, the image used in an immersive projection system can be assimilated to a sphere where the user can move his head in different directions. Meanwhile, a camera based on curved sensor would be able to capture almost a perfect spherical scene. All the basic processes for editing and post-production can thus be done on a spherical data basis. In this work we consider design of lenses for capturing and projecting images on spherical surfaces. Due to the spherical symmetry reasons it is just natural to use monocentric lenses for these purposes. Such a design evolves from a simple ball lens, where the pupil center coincides with the center of symmetry, to a more realistic design with 4 components in 2 groups. We consider a lens with 12 mm focal length and F/1.77 aperture, covering the field of view up to 90 degrees. It works with an object located 3 m away from the camera and the spatial resolution reaches 57 lines/mm. The same design can be re-scaled and modified to serve as a projection system working with a curved screen. We consider a spherical screen with 12 m radius, which can be related to a planetarium cupola. We analyze image quality of such a system and show that the image distortion should be re-defined and the corrected value is lower than a conventional one by factor of 1.4. Also, we perform an end-to-end image simulation to demonstrate that the projected wide-angle scene is close enough to a one observed directly by a human eye.
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