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Fast computation method for derivatives of multilayer stack reflectance

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Abstract

An analytical procedure for the calculation of the derivatives of the reflectance R of a dielectric multilayer stack is presented. Considered are the derivatives (∂R/∂nk)d, (∂R/∂nk)D, (∂R/∂dk)n, and (∂R/∂Dk)n, nk, dk, and Dk being the refractive index, the thickness, and the effective optical thickness of the kth layer, respectively. These calculations lead to a computational algorithm which, as compared with the method using finite difference approximation, reduces the computer time by a factor of f (the total number of layers).

© 1978 Optical Society of America

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