  Purpose: Double diffusion encoding (DDE) MRI enables the estimation of
microscopic diffusion anisotropy, yielding valuable information on tissue
microstructure. A recent study proposed that the acquisition of rotationally
invariant DDE metrics, typically obtained using a spherical "5-design", could
be greatly simplified by assuming Gaussian diffusion, facilitating reduced
acquisition times that are more compatible with clinical settings. Here, we aim
to validate the new minimal acquisition scheme against the standard DDE
5-design, and to quantify the proposed method's noise robustness to facilitate
future clinical use. Methods: DDE MRI experiments were performed on both ex
vivo and in vivo rat brains at 9.4 T using the 5-design and the proposed
minimal design and taking into account the difference in the number of
acquisitions. The ensuing microscopic fractional anisotropy ({\mu}FA) maps were
compared over a range of b-values up to 5000 s/mm2. Noise robustness was
studied using analytical calculations and numerical simulations. Results: The
minimal protocol quantified {\mu}FA at an accuracy comparable to the estimates
obtained via the more theoretically robust DDE 5-design. {\mu}FA's sensitivity
to noise was found to strongly depend on compartment anisotropy and tensor
magnitude in a non-linear fashion. When {\mu}FA < 0.75 or when mean diffusivity
is particularly low, very high signal to noise ratio (SNR) is required for
precise quantification of {\mu}FA. Conclusion: Our work supports using DDE for
quantifying microscopic diffusion anisotropy in clinical settings but raises
hitherto overlooked precision issues when measuring {\mu}FA with DDE and
typical clinical SNR.
