Hemispherical projection lens for insect behavior analysis

Virtual reality projection systems have been used formerly to study if mammals, including humans, are able to act in or understand virtual environments.
Insects have been more difficult to study in such circumstances, one of the factors being their large, almost hemispherical field of view. Designing such a projection system that is capable of fulfilling the full field of vision of an insect is a challenging task.
Normally, when designing a photographic objective, one of the goals is to minimize field curvature in order to provide sharp image through the whole sensor surface. However, because the image surface in this case is a sphere, flat field is not desirable and the design task becomes an opposite of a typical camera lens. Introducing field curvature becomes mandatory.
We have designed and built a system with satisfactory image quality throughout the whole spherical surface with reasonable number of lenses as an add-on for common digital projectors.
The manufactured system is able to project an image to a solid angle of 11.95 steradians, and when compared to the whole sphere which is represented with a solid angle of 4π steradians, approximately 5 % of the total sphere area is not illuminated.