Fourier series approach to synthesis.
The specified reflectance of a multilayer optical filter is formulated as a Fourier series. The coefficients are related via sample relations to the necessary refractive indices of the layers. The method is approximate but has the advantage of simplicity and efficiency, which makes it a useful design tool. The method is also useful as a companion to the exact methods of synthesis since it can provide the starting values for these exact methods. A versatile design example is solved to demonstrate the utility of the method. It is also shown that once a set of refractive indices is found, an infinite set of solutions can be found by simple scaling of the refractive indices.