Optical testing involving interferometric fringes is often adequate to obtain a quantitative estimate of a critical parameter such as "asphericity," i.e., the deviation of a surface from a perfect sphere at a specific radial distance. We propose a two-stage neural network solution that can provide such a quantitative output. The first stage is a self-organizing map network that efficiently performs fringe thinning by detecting fringe maxima even in the case of noisy low-contrast images. The second stage is a back-propagation-trained neural network that "learns" to interpret the thinned fringes represented by polynomial coefficients. Fringe patterns from a sample set of optical components, with known parameters that cover a wide range, are used for training. Experimental results were obtained in the case of fringe patterns from a Talbot interferometer for testing aspheric glass molds used in ophthalmic lens making. On test molds with asphericity values close to 0.050 mm, the difference between values obtained from the neural network and by contact measurement was less than 0.002 mm.