The interaction of light from a relatively medium power CW laser with a nonlinear medium, such as nematic liquid crystals, has been used to devise an interferometer for measuring aberrations of the incident beam. The reorientation of anisotropic molecules of the medium contributes to the induced refractive index change An that is usually a strong nonlinear function of |E|2. The associated self-focussing and diffraction effects produce a spherical beam which is used as the reference wave. The operation of this common-path interferometer can be described by taking analogy with a point-diffraction interferometer.
C. P. Grover,
"Laser Interferometer For Optical Testing Using Nonlinear Optical Effect", Proc. SPIE 0952, Laser Technologies in Industry, (16 January 1988); doi: 10.1117/12.968911; https://doi.org/10.1117/12.968911