This paper examines the use of Constant Photocurrent (CPM) measurements on thin film semiconductors, employing steady (DC) and modulated (AC) sub-gap illumination, to determine the density of localised states (DOS) in the bandgap. AC and DC measurements often result in different apparent absorption spectra. It is demonstrated that it is possible not only to extract information from the respective 'absorption' spectra, on the DOS below the Fermi level - i.e. occupied states, but also on the density of unoccupied states above the Fermi level. The ability to discriminate between these two groups of states by using DC and AC modulated sub-gap light arises from the frequency dependence of the different excitation pathways by which free electrons can be produced. AC modulated excitation will reveal absorption associated with transitions from occupied states into the conduction band, while DC excitation will include transitions from the valence band into unoccupied defect states, followed by slow thermal emission to the conduction band. We examine the temperature dependence of the CPM spectra and present a simple analysis of the DC and AC absorption spectra which allows the two regions of the DOS, above and below the Fermi level, to be determined.