It is demonstrated that scattering by a rough surface can be described in terms of the coherent transfer function, which was first developed to describe the process of imaging. The two-dimensional (one transverse and one longitudinal) coherent transfer function for confocal imaging is presented for a high-angle theory. From this an effective transfer function for imaging of rough surfaces is developed, based on the Kirchhoff approximation. It is described how confocal imaging can be used to investigate various scattering mechanisms, and can be used for reconstruction of surface profiles in the Kirchhoff approximation. PACS numbers: 42.25.Fx, 42.30.-d There is much interest at present in the scattering of light by rough surfaces. This has been greatly brought about by the observation of the phenomenon of enhanced backscattering [I -61 For surfaces which are not too rough, scattering can be explained by the Kirchhoff ap proximation [7]. Because the general problem of scatter ing in three dimensions is quite complicated, many of the current papers consider the simpler case of a one dimensional rough surface (assumed constant in the y direction) illuminated by a plane wave incident in the x-z plane [81 Then for TE or TM polarization no depolari zation is introduced upon scattering. Enhanced back scattering results from multiple scattering and construc tive interference, but the full details are not completely understood. The inverse problem of reconstructing a surface profile from scattering data has also been considered [91 As in this case it is necessary to measure (or restore) the phase as well as the modulus of the scattered radiation; this is conveniently done using a microscope objective which en sures phase coherence over a range of illumination and scattering angles. Scattering data for various angles of il lumination and detection can then be selected by positioning masks in the back focal plane of the objective. Alternatively the surface can be illuminated simultane ously by a spectrum of plane waves, the relative phases of which can be altered by scanning the surface relative to the focused spot. In confocal imaging [10] a pinhole is placed in front of the detector onto which the scattered radiation is focused. In this case imaging of a thick structure can be described by a two-dimensional (one transverse and one longitudinal) coherent transfer func tion [Ill For TE or TM polarization, there is no depo larization on scattering. As there is one direction cosine each for the incident and scattered radiation, there is a one-to-one and onto mapping between these representa tions. Thus each pair of transverse and longitudinal spa tial frequencies corresponds to a particular pair of in cident and scattering directions (actually two pairs, cor responding to two reciprocal paths). Thus a 20 image of the surface contains the complete 'scattering data within the aperture of the objective lens. In two dimensions the image amplitude (Fig. I) in con focal reflection can be expressed in terms of the scattering function S(m2,m I)' where m ),m2 are the direction cosines in the x direction for the incident and scattered radiation [121, as u(x,z) = f_+oooo f-+: PI (ml)P2(m2)S(m2,ml)exp[ - ik{[m2 - mdx+ {(I - mi> 112+ (I -mf) 1/2}Zl1dml dm2. The pupil functions P)'P2 are zero outside of the pupil (I)