  We propose in this paper a globally numerical method to solve a phaseless
coefficient inverse problem: how to reconstruct the spatially distributed
refractive index of scatterers from the intensity (modulus square) of the full
complex valued wave field at an array of light detectors located on a
measurement board. The propagation of the wave field is governed by the 3D
Helmholtz equation. Our method consists of two stages. On the first stage, we
use asymptotic analysis to obtain an upper estimate for the modulus of the
scattered wave field. This estimate allows us to approximately reconstruct the
wave field at the measurement board using an inversion formula. This reduces
the phaseless inverse scattering problem to the phased one. At the second
stage, we apply a recently developed globally convergent numerical method to
reconstruct the desired refractive index from the total wave obtained at the
first stage. Unlike the optimization approach, the two-stage method described
above is global in the sense that it does not require a good initial guess of
the true solution. We test our numerical method on both computationally
simulated and experimental data. Although experimental data are noisy, our
method produces quite accurate numerical results.
