Wellenbild

Wellenbild is a German term used in physics and engineering to describe the spatial and temporal distribution of a wave. It covers how a wave's amplitude and phase vary across space and time and can refer to both the underlying wave field and the observable image produced by the wave at a given plane or detector.

The term is used in multiple disciplines. In optics it denotes the complex optical field, typically written as E(x,y,z,t); in acoustics the corresponding pressure field p(x,y,z,t); in quantum mechanics the wave function ψ(x,t). Wellenbild is related to but distinct from Wellenfront (surfaces of equal phase) and Wellenfeld (the complete wave field). In practice, the Wellenbild may be considered in near-field or far-field form, and is often recorded as an intensity pattern on a detector.

Mathematically, a monochromatic scalar Wellenbild can be represented as a complex field E(x,y,z) with amplitude A(x,y,z) and phase φ(x,y,z); the intensity is I = |E|^2. In optics, the two-dimensional Wellenbild in a detection plane determines the diffraction and interference patterns.

Applications include optical imaging and holography, interferometry, ultrasound and seismic imaging, and quantum-state reconstruction, where the measured Wellenbild provides information about the object, medium, or state under study. The concept serves as a bridge between wave theory and measurable signals in experimental setups.