An improved envelope method (EM) is presented in this paper that allows the determination of the refractive index (n(f)) and absorption coefficient (alpha) of non-uniformly thick, absorbing films on a slightly absorbing substrate from a single transmission measurement. The limitation of the previous version of the EM [R. Swanepoel, J. Phys. E: Sci. Inst. 17 (1984) 896] only permitted the evaluation of samples that exhibited a transparent region in the near infrared (NIR). As an initial test of the improved EM, n(f) and alpha(f) of a 0.5-mum thick epitaxially grown silicon-on-sapphire (SOS) film were determined over the range of 1.1-3.2 eV, with increased absorption being observed at the silicon: sapphire interface. Subsequently, sputtered amorphous silicon (a-Si) films, which exhibit absorption throughout the visible-NIR spectrum, were successfully characterised and a definite trend towards lower absorption coefficients for films deposited at higher temperatures was observed. After the a-Si films were subjected to solid phase crystallisation (SPC), increased sub-bandgap absorption was attributed to higher defect levels in the films, which also resulted in amorphous features remaining in the Raman spectra. (C) 2004 Elsevier B.V. All rights reserved.