The reflectance <i>R</i> of a multilayer stack is changed as either the thickness <i>t</i> or refractive index <i>n</i> of any of the films in the stack is altered. An efficient method of computing the first partial derivatives ∂<i>R</i>/∂<i>t</i> and ∂<i>R</i>/∂<i>n</i> is presented. An example is cited in which these derivatives are employed in a relaxation process which is utilized to improve the design of a multilayer containing absorbing films, which is used as a reflection filter in the vacuum-ultraviolet spectral region.
PHILIP W. BAUMEISTER, "Methods of Altering the Characteristics of a Multilayer Stack," J. Opt. Soc. Am. 52, 1149-1152 (1962)