INSIGHT relies on a standard Michelson interferometer. This is used to measure the spatially-resolved first order autocorrelation function of the beam at each point of the detector (standard Fourier-transform spectroscopy), from which one can deduce the frequency-resolved spatial intensity profile of the beam. This measurement is performed for multiple planes at and around best focus (here, around the image plane of the best focus). These data are then injected into an iterative phase-retrieval algorithm of the Gerchberg-Saxton type, to determine the spatial phase profile of the beam at each frequency.
“Spatio-spectral metrology at focus of ultrashort lasers: a phase retrieval approach”, A. Borot and F. Quéré, Optics Express (2018) 26 p.26444