The methods and techniques for the slitless spectroscopy software aXe, which was designed to reduce data from the various slitless spectroscopy modes of Hubble Space Telescope instruments, are described. aXe can treat slitless spectra from different
instruments such as ACS, NICMOS and WFC3 through the use of a configuration file which contains all the instrument dependent parameters. The basis of the spectral extraction within aXe are the position, morphology and photometry of the objects on a companion direct image. Several aspects of slitless spectroscopy, such as the overlap of spectra, an extraction dependent on object shape and the provision of flat-field cubes, motivate a dedicated software package, and the solutions offered within aXe are discussed in detail. The effect of the mutual contamination of spectra can be quantitatively assessed in aXe, using spectral and morphological information from the companion direct image(s). A new method named aXedrizzle for 2D rebinning and co-adding spectral data, taken with small shifts or dithers, is described. The extraction of slitless spectra with optimal weighting is outlined and the correction of spectra for detector fringing for the ACS CCDs is presented. Auxiliary software for simulating slitless data and for visualizing the results of an aXe extraction is outlined.
