Figure 1

(a) Real and (b) imaginary parts of the diffusion-weighted normalized signal (dots) for the equilateral triangle with a diffusion gradient applied along the $y$ direction (${\delta }_1=1-{\delta }_2$, $L=5\mu \mathrm{m}$, free diffusion constant $D=1\mu {\mathrm{m}}^2/\mathrm{ms}$ and $T=100\mathrm{ms}$, $DT/L^2=4$). The solid line is the Fourier transform of the pore space function; the dashed line is the signal calculated in the Gaussian phase approximation. A slow transition from diffusion Gaussian phase approximation to imaging type behavior (solid line) can be observed. The measured signal for short ${\delta }_2$ does not coincide exactly with the Fourier transform for large $q$ values; however, this is the case for longer diffusion times (data not shown).Reuse & Permissions

Figure 2

Fourier transform of the diffusion-weighted signal for an equilateral triangular domain. Current standard techniques are depicted in (a) and (b). Temporally elongated magnetic field gradients (a) yield an approximately Gaussian-shaped curve that describes the displacement probability of the centers of mass of the two trajectories that a particle moves along during the first and second gradient [see Eq. (4)]. Temporally narrow gradients (b) yield the squared magnitude of the Fourier-transformed pore space function. Since the phase information is lost, the inverse transformation cannot be performed properly and the triangular structure is lost. (c) This diffusion experiment with temporally asymmetric gradients is essentially a disguised NMR imaging experiment and thus reveals the exact shape of the domain. (d) Using temporally moderately asymmetric gradient profiles yields a mixture contrast of (a) and (c). The profile (d) is advantageous since the hardware requirements are less demanding than for (c), while much of the structural information is still observable. Parameters: $L=10\mu \mathrm{m}$, $D=1\mu {\mathrm{m}}^2/\mathrm{ms}$, $T=100\mathrm{ms}$, maximal $q\mathrm{\text{value}}=40\mu {\mathrm{m}}^{-1}$, increment of $q\mathrm{\text{values}}=0.5\mu {\mathrm{m}}^{-1}$. (a) ${\delta }_1={\delta }_2=1/2$. (b) ${\delta }_1={\delta }_2=1/100$. (c) ${\delta }_1=99/100$, ${\delta }_2=1/100$. (d) ${\delta }_1=4/5$, ${\delta }_2=1/5$.Reuse & Permissions