The 1-D point spread function (PSF) of MR images  is given by
where Nx is the number of samples in the frequency domain, and Ax represents the sampling interval in the spatial domain. Eq. (10.45) is well approximated
The 3-D PSF is given by m (x; Ax, Ay,Az) = m (x; Ax) ■ m (y; Ay) ■ m (z; Az), (10.48)
where Ax, Ay, and Az are sampling intervals along the x-axis, y-axis, and z-axis, respectively.
In actual MR imaging, the magnitude operator is applied to the complex number obtained at each voxel by FFT reconstruction, whose effects are not negligible . Thus, the MR image of the sheet structure with orientation and thickness t is given by f (x) = |s(x; t, re4) * m(x; Ax, Ay, Az)l (10.49)
where * denotes the convolution operation.
Was this article helpful?