From a recently proposed technique, used to determine the modal weights of beams made up of incoherent superpositions of Hermite-Gaussian (PIG) modes, we derive the analytical expression of a family of functions which are biorthogonal to the squared HG functions. The knowledge of such functions enables the reconstruction of the modal content of these beams by means of the scalar-product with the intensity profile across a transverse plane.
Borghi, R., Piquero, G., Santarsiero, M. (2001). Use of biorthogonal functions for the modal decomposition of multimode beams. OPTICS COMMUNICATIONS, 194, 235-242.