This chapter begins with a discussion of wave propagation and diffraction by considering a three-dimensional scalar wave field in a linear, homogeneous and isotropic medium. The use of spherical waves to solve diffraction problems has a long and rich history, which starts with Huygens' principle (Huygens 1690), whereas the use of plane waves is a much more recent practice. The most common approximation to the boundary values is the so-called physical-optics approximation, according to which the field or its normal derivative at the scatterer is determined by geometrical optics. This approximation implies that diffraction at the edge of the scattering body is neglected when determining the boundary values. According to the Debye approximation, the field in the focal region is a superposition of plane waves whose propagation vectors fall inside the geometrical cone formed by drawing straight lines from the focal point through the edge of the aperture.