A Theory for the Christiansen Filter

Multiple scattering theory is applied to investigate the filter shape and bandwidth of the Christiansen filter which consists of a suspension of particles in a liquid such that the refractive index vs wavelength curves of the particles and the liquid intersect at a particular wavelength. It is shown that the filter shape is approximately gaussian, and that the fractional bandwidth depends inversely on the rate of change with wavelength of the difference in refractive index of the particles and the liquid and inversely on the square root of the product of the particle concentration, the average particle radius, and the length of the Christiansen cell. Initial agreement with reported experiments is encouraging.