Polarized light for horizontal incidence and reflection by plane-parallel atmospheres

We show that the intensity vector of light reflected by a plane-parallel atmosphere is discontinuous if the directions of incidence and reflection are both horizontal. An exact expression describing the discontinuity is presented. This expression shows that the discontinuity is only due to first order scattering at the top of the atmosphere and occurs for all four Stokes parameters, as well as for the polarized intensity. No discontinuity exists, however, for the degrees of linear and circular polarization. The exact expression may be applied, for example, to clarify the results of photo-polarimetric observations of regions near the intensity poles of a planet. Another application concerns the possibility of obtaining values for the albedo of single scattering and scattering matrix elements as functions of the scattering angle at the top of a cloud deck or aerosol layer from observations for nearly horizontal directions of incidence and reflection.