Interferensfringe

Interferensfringe, commonly referred to as an interference fringe, is the pattern of alternating bright and dark bands that appears when two or more coherent light waves overlap with a fixed phase relationship. The pattern results from constructive interference (bright bands) and destructive interference (dark bands) between the overlapping wavefronts. For two beams of equal amplitude, the intensity can be written as I = 2I0 [1 + cos(delta)], where delta is the phase difference between the beams and delta = (2π/λ) Δ, with Δ being the optical path difference and λ the wavelength.

Fringe geometry depends on the experimental arrangement. In a simple two-slit setup, the linear fringe spacing on a screen is approximately y = λL/d, where L is the distance to the screen and d the slit separation. More complex geometries yield curved fringes: circular fringes arise in Newton’s rings (an air film between a lens and a flat plate), while parallel or curved fringes can appear in various interferometers such as Young’s setup, the Mach–Zehnder, or the Michelson interferometer.

Fringe visibility, or contrast, is defined as V = (Imax − Imin)/(Imax + Imin) and depends on the coherence and relative intensities of the interfering beams. Temporal coherence (related to spectral bandwidth) limits the maximum observable path difference, beyond which fringes fade. Applications of interferensfringe include precise metrology of optical path lengths, thickness measurements, surface topography, refractive-index determination, and wavefront analysis. In practice, monitoring fringe shifts enables measurements of tiny displacements, refractive changes, or thickness variations with high precision.