  We present a simple, frequency domain, preprocessing step to Kirchhoff
migration that allows the method to image scatterers when the wave field phase
information is lost at the receivers, and only intensities are measured. The
resulting imaging method does not require knowing the phases of the probing
field or manipulating the phase of the wave field at the receivers. In a regime
where the scattered field is small compared to the probing field, the problem
of recovering the full-waveform scattered field from intensity data can be
formulated as an embarrassingly simple least-squares problem. Although this
only recovers the projection (on a known subspace) of the full-waveform
scattered field, we show that, for high frequencies, this projection gives
Kirchhoff images asymptotically identical to the images obtained with full
waveform data. Our method can also be used when the source is modulated by a
Gaussian process and autocorrelations are measured at an array of receivers.
