This paper describes a metric that can be used to characterize the resolution of arbitrary broadband coherent imaging systems. The metric is particularly suited to medical ultrasound because it characterizes scanner performance using the contrast obtained by imaging anechoic cysts of various sizes that are embedded in a speckle-generating background, accounting for the effect of electronic noise. We present the theoretical derivation of the metric and provide simulation examples that demonstrate its utility. We use the metric to compare a low-cost, handheld, C-scan system under development in our laboratory to conventional ultrasound scanners. We also present the results of simulations that were designed to evaluate and optimize various parameters in our system, including the f/# and apodization windows. We investigate the impact of electronic noise on our system and quantify the tradeoffs associated with quantization in the analog to digital converter. Results indicate that an f/1 receive aperture combined with 10-bit precision and a signal-to-noise ratio (SNR) of 0 dB per channel would result in adequate image quality.