Phaseless inverse scattering with background information

Abstract We consider phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using method of known background scatterers. In particular, in dimension d ⩾ 2, we show that | f 1 2 at high energies uniquely determines via explicit formulas, where is amplitude + w , an a priori nonzero scatterer, under condition supp and are sufficiently disjoint. If this relaxed, then give similar formulas finding from . continue studies Novikov (2016 J. Geom. Anal. 26 346–59) Leshem et al Nat. Commun. 7 1–6).