Materials-analysis measurements that employ neutron-absorption techniq
ues may benefit from cold neutrons that may be focused using a lens co
nsisting of polycapillary fibers. An expression is derived for the int
ensity gain and the size of the beam along the beam path, including th
at at the focus, and a criterion is developed for the depth of focus.
The gain in intensity at the focus depends not only on the design para
meters of the lens but also on the divergence and wavelength of the in
cident beam. This analysis is applied to the two neutron lenses that h
ave previously been tested.