FAST COMPUTATION OF 2ND-ORDER DERIVATIVES OF REFLECTANCE, TRANSMITTANCE AND CORRESPONDING PHASE-SHIFTS IN THIN-FILM SYSTEMS

A new fast algorithm for the computation of the second-order derivativ es is described. The method is applicable to the evaluation of the sec ond-order derivatives of reflectance, transmittance and corresponding phase shifts for the light impinging on the substrate from both sides and with respect to any parameters of the system. The time needed for the computation of the whole Hessian matrix is roughly linearly depend ent on the number of layers. The precise and fast computation of Hessi an matrix enables one to use the optimization methods of quadratic rat e of convergence such as modified Newton method and speed up the optim ization routines for thin film systems.