Geometrical optics approach to the intensity distribution in finite cylindrical media

Abstract

When irradiated unilaterally, certain cylindrical fungi act like a cylindrical lens. This behavior is the basis of phototropism (directed growth caused by asymmetrical illumination). A quantitative treatment of phototropism implies the description of light distribution at the inner boundary of finite nonscattering and weakly scattering homogeneous and radially stratified cylindrical media. This problem is solved using geometrical optics. First parameter representations for caustic and wavefronts within a homogeneous cylinder are derived. Then, the lens properties of the system are expressed by expansion coefficients. Geometrical optics fails at the caustic; there the field distribution is calculated with Airy functions. On the basis of intensity distributions, formulas for the absorption of light by oriented photoreceptors located at the wall of the system are derived. The theory is then applied to a special biological object.