How do you measure neutron energy? I think you can detect a neutron event with a scintillator (neutron to photon), photomultiplier tube (photon to electric signal) system, but how would a fusion neutron's energy (2.45 MeV) be typically measured?
 A: I'm going to answer for fairly energetic neutrons.
There are a several of parameters that you have to know and they are dependent on the details of your device to the point that you have to measure them; that is to say that you calibrate each device.
The parameters are 


*

*the fraction of the energy that gets transferred to fast charged particles (usually protons, but if helium is involved sometimes alphas).

*the quenching factor that applies to the light generation from those fast particle

*the acceptance and response of the PMTs as a function of the light energy 
Actually these factors are multiplicative so you only have to know the product, but the usual method of calibration extract all three of these (you'll note that #3 is already a product and you may or may not bother to tease that one apart).
So, working backwards
(3) You calibrate with know energy photons or electrons (or muons). This is easiest if you have a stopping detector; without one you either need a really good Monte Carlo or to stick a well calibrated calorimeter behind your device during testing.
For in situ calibration it is often possible to use cosmic muons for this step, but in that case you do need to calculate the energy loss.
(2) You calibrate with known energy protons and/or alphas or if your detector has the resolutions you look very carefully and the end of heavy particle tracks (for that you do not need to know the incident energy very well). Stopping is not a big problem here unless your device is very thin.
(1) You use a combination of high quality Monte Carlo and the best known-energy neutron source you can get. (There are some really great neutron sources, but time on them can be hard to get and because the MCs are so good these days it is often enough to uses a CoTS neutron generator of known isotope source.)

If you have a bunch of devices of uniform design and constructed from the same batch of input materials (or you trust the uniformity of the supply for some reason), then numbers 1 and 2 should be pretty constant and aside from doing a little cross-checking it is only #3 that you have to adjust for all devices, and gain-matching was on the schedule anyway. No loss.
A: There are many ways to measure the energy of neutrons, here a few:


*

*Use a chopper and measure the time of flight for length L between two chopper blades. E= 1/2 m v^2 <=> E = 1/2 m L^2/t^2

*Place a well known single crystal in a neutron diffractometer and apply Bragg's law 

*Evaluate the pulse form of an 3He detector tube.

*Measure how far the neutrons fall down in the gravity field of the earth in a known distance.

