Michelson Interferometer - Broad Source

The intensity of the interference fringes for a Michelson interferometer having a source emitting with a Gaussian profile having a bandwidth of Δν is given by
 

where I₁ and I₂ are the intensities of the two beams, λ is the wavelength, c is the speed of light, and d is the path length difference between the two interferometer arms.  x and y are coordinates in the focal plane of a lens of focal length f.

The fringes as a function of path difference are shown below.  Note that the path difference is larger at the center of the fringe pattern than at the edge so the contrast of the center fringes wash out first as the path length difference between the two interferometer arms increases.
 

Thanks to
José Antonio Díaz Navas
Catedrático de Escuela Universitaria
Departamento de Óptica
Facultad de Ciencias
Avda. Severo Ochoa S/N
18071-Granada Spain
email: jadiaz@ugr.es
web: www.ugr.es/~jadiaz