When imaging with ultrasonic phased arrays, what do we actually image? What quantitative information is contained in the image? Ad-hoc delay-and-sum methods such as the synthetic aperture focusing technique (SAFT) and the total focusing method (TFM) fail to answer these questions. We have shown that a new quantitative approach allows the formation of flaw images by explicitly inverting the Thompson-Gray measurement model. To examine the above questions, we have set up a software simulation test bed that considers a 2-D scalar scattering problem of a cylindrical inclusion with the method of separation of variables. It is shown that in SAFT types of imaging the only part of the flaw properly imaged is the front surface specular response of the flaw. Other responses (back surface reflections, creeping waves, etc.) are improperly imaged and form artifacts in the image. In the case of TFM-like imaging the quantity being properly imaged is an angular integration of the front surface reflectivity. The other, improperly imaged responses are also averaged, leading to a reduction in some of the artifacts present. Our results have strong implications for flaw sizing and flaw characterization with delay-and-sum images.