I am generally interested in the mathematical modelling of optical systems such as vertebrate (fish) eye lenses, with focus on optics as well as information processing. Specifically, my present activities include the following.
Such lenses typically are of the gradient type, with an approximate rotational symmetry. It is characterized by its index gradient, n(r), where r is the distance to the center. The gradient is only partly measurable from the externally accessible properties of the lens. This implies that a pair of lenses with distinct index gradients can possess identical refractive properties, as measured from the outside. I investigate the relations between such lenses, and the existence of a most economical lens with given refractive properties.
It is easy to grow a homogeneous lens by adding cell layers with a fixed index. For a gradient lens growing with its bearer things are more difficult, if continuous functionality is desired: The entire index gradient has to be scaled up, and the refracting index of existing layers has to be continually modified. I study a set of models for the mechanisms involved.