Wave extrapolation methods are commonly used to evaluate the farfield radiation pattern of a complex source from nearfield measurements. The nearfield data are usually collected with transducer arrays or matrices. This standard procedure poses problems of signal conditioning, calibration, and recording that may be avoided by performing a synthetic detection of the nearfield. This alternate procedure, which borrows its principle from the field of synthetic aperture radar (SAR), is explored and illustrated in this article. The problem of radial wave extrapolation in a layered configuration is also analyzed. Acoustic wave radiation from a uniform stream to a region at rest is specifically considered. Exact and approximate wave extrapolators are derived. Comparisons between experimental measurements and wave extrapolation results indicate that the combination of synthetic nearfield detection and radial wave extrapolation is reliable and that extrapolation in layered situations may be carried out with little additional effort.