Stüßer, N.; Hofmann, T.: On the form invariant volume transformation in phase space by focusing neutron guides: An analytic treatment. Nuclear Instruments & Methods in Physics Research A 727 (2013), p. 84-89
10.1016/j.nima.2013.06.026

Abstract:
Taperedguideswithsupermirrorcoatingarefrequentlyusedtofocusneutronbeamsonspecimens.The divergencedistributioninthefocusedbeamisofagreatimportanceforthequalityofneutron instrumentation. Usingananalyticapproachwederivethetaperingwhichisneededtoachieveaform invariantphasespacetransformationofarectangularphasevolume.Inadditionweconsidertheeffectof beam attenuationbythe finite reflectivityofsupermirrors.