Experimental observations of black holes are based on the theoretical discourse of geodesics, gravitational lensing or quasinormal modes. The latter is based on spacetime perturbations due to scalar, vector and tensor fields on a fixed background geometry, described in the framework of Teukolsky's equation. Since gravitational lensing in the high-frequency limit can be described by a ray-optical approach, the distortions of a black hole's background are sufficiently described for this case. However, observations in the low-frequency limit can also play an important role, as the EHT has shown. These require the solution of a wave equation. Several approaches rely on the approximation by eikonals or full numerical calculations, neglecting the full low-frequency regime. In this work, wave scattering is treated analytically using the Green's function method and solutions to the separate radial and angular Teukolsky equations in combination with a partial wave technique for a scalar and monochromatic perturbation. The results are applied to the analytical description of wave-optical imaging via Kirchhoff-Fresnel diffraction, leading, for example, to the formation of observable black hole shadows for a Kerr-de Sitter spacetime. A comparison with the ray-optical description is given, providing new insights into wave-optical effects and properties and complementing the ray-optical approach. An outlook is given to the Taub-NUT spacetime by this method and in which sense it is currently limited.