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We propose in this paper a globally numerical method to solve a phaselesscoefficient inverse problem: how to reconstruct the spatially distributedrefractive index of scatterers from the intensity (modulus square) of the fullcomplex valued wave field at an array of light detectors located on ameasurement board. The propagation of the wave field is governed by the 3DHelmholtz equation. Our method consists of two stages. On the first stage, weuse asymptotic analysis to obtain an upper estimate for the modulus of thescattered wave field. This estimate allows us to approximately reconstruct thewave field at the measurement board using an inversion formula. This reducesthe phaseless inverse scattering problem to the phased one. At the secondstage, we apply a recently developed globally convergent numerical method toreconstruct the desired refractive index from the total wave obtained at thefirst stage. Unlike the optimization approach, the two-stage method describedabove is global in the sense that it does not require a good initial guess ofthe true solution. We test our numerical method on both computationallysimulated and experimental data. Although experimental data are noisy, ourmethod produces quite accurate numerical results.

A numerical method to solve a phaseless coefficient inverse problem from a single measurement of experimental data