Semi-quantum mechanical explanation

The incoming beam has a polarisation perpendicular to the magnetic field in the precession regions. In the field one can consider the wave function of the neutron to be the superposition of the two eigen states, the up and the down state.

The blue-red rectangles represent the magnetic precession fields created with four electromagnets.  In the middle a magnetised foil works as a pi-flipper, which effectively flips the neutron polarisation. This yields opposite refraction of the neutron paths of the two eigen states.  In the second magnet the eigen states experience reversed refraction and continue along two parallel paths.  This separation is tuned by varying the magnetic field strength.  The separation, named the spin-echo length, can be between 20 nanometer and 20 micrometer.  The second two magnets focus the two spin states again.  Without a sample in the beam this will result in the initial polarisation.  However, if a sample is set in the beam, which is inhomogeneous over the length scale of the spin-echo length, then the beam will get depolarised.  SESANS measures thus the correlation in density between the two spin-states over the spin-echo length: the density correlation function.

Real-space neutron scattering methods
W.G. Bouwman, J. Plomp, V.O. de Haan, W.H. Kraan, A.A. van Well, K. Habicht, T. Keller, M.T. Rekveldt
Nuclear Instruments and Methods in Physics Research A 586 9–14 (2008)
http://dx.doi.org/10.1016/j.nima.2007.11.045