  An experimental protocol is developed to directly measure the new material
functions revealed by medium amplitude parallel superposition (MAPS) rheology.
This experimental protocol measures the medium amplitude response of a material
to a simple shear deformation composed of three sine waves at different
frequencies. Imposing this deformation and measuring the mechanical response
reveals a rich data set consisting of up to 19 measurements of the third order
complex modulus at distinct three-frequency coordinates. We discuss how the
choice of the input frequencies influences the features of the MAPS domain
studied by the experiment. A polynomial interpolation method for reducing the
bias of measured values from spectral leakage and variance due to noise is
discussed, including a derivation of the optimal range of amplitudes for the
input signal. This leads to the conclusion that conducting the experiment in a
stress-controlled fashion possesses a distinct advantage to the
strain-controlled mode. The experimental protocol is demonstrated through
measurements of the MAPS response of a model complex fluid: a surfactant
solution of wormlike micelles. The resulting data set is indeed large and
feature-rich, while still being acquired in a time comparable to similar medium
amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data
represents measurements of an intrinsic material function by studying its
internal consistency, its compatibility with low-frequency predictions for
Coleman-Noll simple fluids, and its agreement with data obtained via MAOS
amplitude sweeps. Finally, the data is compared to predictions from the
corotational Maxwell model to demonstrate the power of MAPS rheology in
determining whether a constitutive model is consistent with a material's
time-dependent response.
