In a pulsed ultrasound beam, echoes detected from a flat, circular piston of arbitrary size depend on the time‐space characteristics of the entire pulse‐echo measurement system, being a function of as many parameters as it takes to accurately define the system. In the limiting case of a target that is small relative to the spatial extent of an interrogating plane wave, an echo pattern is known to be a relatively simple function of the dimensionless productk0b, wherek0is the wave number andbis the radius of the target. In a companion paper preceding this one [F. E. Barber, J. Acoust. Soc. Am.90, 8–17 (1991)], the author has described the scanning acoustic microprobe, a pulse‐echo system in which the time‐space properties of the interrogating waves are specified completely byk0and a single additional parameters0, which is the characteristic radius of a spherically symmetric, Gaussian‐distributed scattering volume. In this system, the reflection pattern of a flat, circular piston of any arbitrary size is thus a function of two dimensionless parameters, namelyk0bandb/s0. In this paper, this functional relationship is derived, a physical system is described, and analytical and experimental results are reported. It is shown that the diameter, orientation, and impedance mismatch properties of this simple target can be measured unambiguously over a range of target sizes from about a wavelength (2π/k0) to a beam diameter (about 3s0). For a typical ultrasound system, this is about a 5–1 range; i.e., a range extending to target sizes about five times smaller than can be detected in a simpleB‐mode imaging system. Theoretical and experimental results are described and discussed in detail. The implications of such a system for quantitative analysis of more complex target structures and constituents are explored. The methods lead naturally to a new technique for imaging that will display fine‐scale features not seen by any other method.