Limits on the performance of near field phase aberration correction
Speed of sound inhomogeneities cause significant degradation of ultrasonic images. In some parts of the body inhomogeneities can be modeled as a thin time delay screen at the surface of the skin. Such aberrators may be compensated for by adjusting time delays used for transmit and receive focusing. This compensation is subject to error because of imperfect estimation of the required compensating time delays (time delay estimation error or TDEE) and because of integration of the aberrator across relatively large array elements (aberrator integration error or AIE). We present analytical expressions which predict the magnitude of AIE and TDEE. We also present expressions which describe the accumulation of errors for a number of array geometries. The derived expressions are utilized in examples which illustrate the tradeoffs inherent to the design of phase aberration correction algorithms and transducers. These examples indicate that two-dimensional arrays with as many as one thousand elements may be needed for accurate phase aberration correction.