  Inelastic neutron scattering at high momentum transfers (i.e. $Q\ge20$ {\AA})
or DINS provides direct observation of the momentum distribution of light
atoms, making it a powerful probe for studying single-particle motions in
liquids and solids. The quantitative analysis of DINS data requires an accurate
knowledge of the instrument resolution function $R_{i}({Q},E)$ at each $Q$ and
energy transfer $E$, where the label $i$ indicates whether the resolution was
experimentally observed $i={obs}$ or simulated $i=sim$. Here, we describe two
independent methods for determining the total resolution function
$R_{i}({Q},E)$ of the ARCS neutron instrument at the Spallation Neutron Source,
Oak Ridge National Laboratory. The first method uses experimental data from an
archetypical system (liquid $^4$He) studied with DINS, which are then
numerically deconvoluted using its previously determined intrinsic scattering
function to yield $R_{obs}({Q},E)$. The second approach uses accurate Monte
Carlo simulations of the ARCS spectrometer, which account for all instrument
contributions, coupled to a representative scattering kernel to reproduce the
experimentally observed response $S({Q},E)$. Using a delta function as
scattering kernel, the simulation yields a resolution function $R_{sim}({Q},E)$
with comparable lineshape and features as $R_{obs}({Q},E)$, but somewhat
narrower due to the ideal nature of the model. Using each of these two
$R_{i}({Q},E)$ separately, we extract characteristic parameters of liquid
$^4$He such as the intrinsic linewidth $\alpha_2$ (which sets the atomic
kinetic energy $\langle K\rangle\sim\alpha_2$) in the normal liquid and the
Bose-Einstein condensate parameter $n_0$ in the superfluid phase. The extracted
$\alpha_2$ values agree well with previous measurements, independently of which
$R_i(Q,y)$ is used to analyze the data.
