In practical images, ideal step edges are actually transformed into exponential ramp edges, due to the general low pass filtering nature of imaging systems. This paper discusses the application of a newly developed expansion matching method for optimal ramp edge detection. Expansion matching optimizes a novel matching criterion called discriminative signal to noise ratio (DSNR). The DSNR criterion represents the desirable qualities of a sharp matching response with good localization and minimal off-center response. These requirements are consistent with the three criteria of signal-to-noise ratio, localization, and multiple response suppression used by Canny (1986) and others for optimal edge detection. We compare the optimal ramp edge detector based on DSNR with the ramp edge detector derived from Canny's criteria. We show that our ramp edge detector performs better than the ramp detector obtained from Canny's criteria in terms of DSNR and is relatively easier to derive for various amounts of noise and slopes.