  Difference imaging is a technique for obtaining precise relative photometry
of variable sources in crowded stellar fields and, as such, constitutes a
crucial part of the data reduction pipeline in surveys for microlensing events
or transiting extrasolar planets. The Optimal Image Subtraction (OIS) algorithm
permits the accurate differencing of images by determining convolution kernels
which, when applied to reference images of particularly good quality, provide
excellent matches to the point-spread functions (PSF) in other images of the
time series to be analysed. The convolution kernels are built as linear
combinations of a set of basis functions, conventionally bivariate Gaussians
modulated by polynomials. The kernel parameters must be supplied by the user
and should ideally be matched to the PSF, pixel-sampling, and S/N of the data
to be analysed. We have studied the outcome of the reduction as a function of
the kernel parameters using our implementation of OIS within the TRIPP package.
  From the analysis of noise-free PSF simulations as well as test images from
the ISIS OIS package, we derive qualitative and quantitative relations between
the kernel parameters and the success of the subtraction as a function of the
PSF sizes and sampling in reference and data images and compare the results to
those of implementations in the literature. On this basis, we provide
recommended parameters for data sets with different S/N and sampling.
