  When simulating sky images, one often takes a galaxy image $F(x)$ defined by
a set of pixelized samples and an interpolation kernel, and then wants to
produce a new sampled image representing this galaxy as it would appear with a
different point-spread function, a rotation, shearing, or magnification, and/or
a different pixel scale. These operations are sometimes only possible, or most
efficiently executed, as resamplings of the Fourier transform $\tilde F(u)$ of
the image onto a $u$-space grid that differs from the one produced by a
discrete Fourier transform (DFT) of the samples. In some applications it is
essential that the resampled image be accurate to better than 1 part in $10^3$,
so in this paper we first use standard Fourier techniques to show that
Fourier-domain interpolation with a wrapped sinc function yields the exact
value of $\tilde F(u)$ in terms of the input samples and kernel. This operation
scales with image dimension as $N^4$ and can be prohibitively slow, so we next
investigate the errors accrued from approximating the sinc function with a
compact kernel. We show that these approximations produce a multiplicative
error plus a pair of ghost images (in each dimension) in the simulated image.
Standard Lanczos or cubic interpolators, when applied in Fourier domain,
produce unacceptable artifacts. We find that errors $<1$ part in $10^3$ can be
obtained by (1) 4-fold zero-padding of the original image before executing the
$x\rightarrow u$ DFT, followed by (2) resampling to the desired $u$ grid using
a 6-point, piecewise-quintic interpolant that we design expressly to minimize
the ghosts, then (3) executing the DFT back to $x$ domain.
