  A numerical recipe is given for obtaining the density image of an initially
compact quantum mechanical wavefunction that has expanded by a large but finite
factor under free flight. The recipe given avoids the memory storage problems
that plague this type of calculation by reducing the problem to the sum of a
number of fast Fourier transforms carried out on the relatively small initial
lattice. The final expanded state is given exactly on a coarser magnified grid
with the same number of points as the initial state. An important application
of this technique is the simulation of measured time-of-flight images in
ultracold atom experiments, especially when the initial clouds contain
superfluid defects. It is shown that such a finite-time expansion, rather than
a far-field approximation is essential to correctly predict images of
defect-laden clouds, even for long flight times. Examples shown are: an
expanding quasicondensate with soliton defects and a matter-wave interferometer
in 3D.
