We have been developing the ideal observer formalism for sonography, which is based on the best-possible diagnostic performance. The ideal performance was compared to that of trained human observers to estimate the visual efficiency for discriminating lesion features. We find that humans are generally less than 10% efficient at accessing visual information essential for breast cancer diagnosis. In seeking ways to improve this process, we must first establish a connection between standard ROC observer metrics and instrument properties used in system design. In radiography, that relationship is made through the lesion signal-to-noise ratio SNR I. SNR I 2, which describes task information, is simply related to contrast and spatial resolutions and noise power. Those relations break down for sonography due to the quadratic form of the ideal observer. Our goal in this paper is to establish a rigorous connection between ideal performance and engineering design metrics, which has directly applications for sonographic system design and optimization.