Аннотация:We consider phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using the method of known background scatterers. In particular, in dimension d ≥ 2, we show that |f1|2 at high energies uniquely determines v via explicit formulas, where f1 is the scattering amplitude for v + w1, w1 is an a priori known nonzero background scatterer, under the condition that supp v and supp w1 are sufficiently disjoint. If this condition is relaxed, then we give similar formulas for finding v from |f|2, |f1|2, where f is the scattering amplitude for v. In particular, we continue studies of Novikov (2016 J. Geom. Anal. 26 346–59) and Leshem et al (2016 Nat. Commun. 7 1–6).