The history of cartography has been marked by the endless search for the perfect form for the representation of the information on a spherical surface manifold into the flat planar format of the printed page or computer screen. Dozens of cartographic formats have been proposed over the centuries from ancient Greek times to the present. This is an issue not just for the mapping of the globe, but in all fields of science where spherical entities are found. The perceptual and representational advantages and drawbacks of many of these formats are considered, particularly in the tension between a unified representation, which is always distorted in some dimension, and a minimally distorted representation, which can only be obtained by segmentation into sectorial patches. The use of these same formats for the mapping of spherical manifolds are evaluated, from quantum physics through the mapping of the brain to the large-scale representation of the cosmos.
There are many test charts and software to determine the intrinsic geometric calibration of a camera including distortion. But all of these setups have a few problems in common. They are limited to finite object distances and require large test charts for calibrations at greater distances combined with powerful and uniform illumination. On production lines the workaround for this problem is often times the use of a relay lens which itself introduces geometric distortions and therefore inaccuracies that need to be compensated for. A solution to overcome these problems and limitations has originally been developed for space applications and has already become a common method for the calibration of satellite cameras. We have now turned the lab setup on an optical bench into a commercially available product that can be used for the calibration of a huge variety of cameras for different applications. This solution is based on a diffractive optical element (DOE) that gets illuminated by a plane wave generated with an expanded laser diode beam. In addition to the conventional methods the proposed one also provides the extrinsic orientation of the camera and therefore allows the adjustment of cameras to each other.