A method for the quantitative characterization of strained Si/SixGe1-x multilayers and interfaces by high-resolution transmission electron microscopy (HRTEM) in [110] and [100] projections is presented. The method relies on the functional relationship between the composition x and the first-order Fourier coefficients of the image intensity, which is quasi-linear and insensitive to strain over a range of imaging conditions for the electron energy of 400 keV considered. By application of a novel image-processing algorithm, which allows a precise measurement of image Fourier coefficients in geometrically distorted lattice images, local composition values x can be determined at near-atomic resolution with an accuracy of at Delta x +0.1, and interface sharpness can be detected at the atomic level. Applications of the method to the analysis of strained short-period SimGen superlattices are presented.