Measurement of the dispersion relation in a crystal: Inelastic neutron scattering Is the analyzer in the thees axes spectrometer just another monochromator? 
If we can measure the energy of the neutrons after scattering with a detector, why do we need the analyzer?
 A: I will expand on my comment to more fully answer the question. 
A reactor is a fine source of neutrons, but they come out at a spread of energies particularly since 'moderating' within the reactor, and 'thermalizing' outside of the reactor both involve multiple scattering events which, even if perfectly elastic, result in a distribution of neutron energies. The collimator is basically a long flight tube that means that the neutrons that make it down the tube are all flying in the same direction (but with different energies).  
Now the neutrons hit the monochromator.  This directs all neutrons with a certain energy towards the sample.  To a reasonable level, the result is a beam of neutrons with a single energy, and thus a single momentum.  Upon hitting the sample ('Probe' above), these neutrons scatter through both elastic and inelastic events. The angle $\theta$ selects the change in momentum for the scattering event (since the incident momentum is fixed by the selected energy, anything deflected in that direction has had the same change in momentum). If all scattering events were elastic, the scattered energy would also all be the same.  But wait - we are looking for inelastic scattering events as well.  These will have the same change in momentum, but a different energy.
To measure the energy spectrum (for a given momentum change), the analyzer (another monochromator) is scanned.  For many experiments that would show a large elastically scattered peak, and then a variety of inelastic peaks of interest to the experimenter.  Varying the incident neutron energy, the scattered momentum, and the energy distribution at that momentum allows you to map out the inelastic events in detail. 
Without the detector, how do you measure anything? Angle α sets the energy and momentum of the neutrons being sent to the material to be probed. Angle θ chooses the scattered neutron momentum. Finally, angle β picks off those neutrons with the desired momentum and energy to measure. You need to energy analyze the scattered neutrons to separate the elastic from the inelastic scattering events. And you then need to actually detect them, and plot up how many you detect at different settings of the spectrometer to get the dispersion relation
