Various algorithms have been proposed for determining the near-surface dielectric function epsilon(o) of depositing materials from kinetic complex reflectometric or ellipsometric data, even under conditions where the underlying sample structure is unknown. These capabilities are essential for sample-driven closed-loop feedback control of epitaxy, since they allow compositional fluctuations to be detected over nominally vanishingly small thicknesses without the instability inherent in conventional Fresnel analysis. The accuracy of earlier derivative approaches was improved significantly with the development of virtual-interface (V-I) theory, which is based on exact equations instead of exponential-spiral approximations that are valid only for optically thick films. I summarize previous relevant work, assess the accuracy of these derivative methods analytically for the complex normal-incidence reflectance, develop new algorithms by combining earlier approaches, develop a geometric construction that allows relative sensitivities, accuracies, and applicabilities of these algorithms for determining the composition of ternary alloys to be conveniently assessed, and propose a new hybrid V-I-Fresnel method that retains the stability of the V-I approach yet is exact. For ellipsometry the virtual-substrate approximation still represents the best combination of simplicity, speed, and acceptable accuracy.