The concept of polarimetry in active remote sensing is extended to passive remote sensing. The potential use of the third and fourth Stokes parameters U and V, which play an important role in polarimetric active remote sensing, is demonstrated for passive remote sensing. It is shown that, by the use of the reciprocity principle, the polarimetric parameters of passive remote sensing can be obtained through the solution of the associated direct scattering problem. These ideas are applied to study polarimetric passive remote sensing of periodic surfaces. The solution of the direct scattering problem is obtained by an integral equation formulation which involves evaluation of periodic Green's functions and normal derivative of those on the surface. Rapid evaluation of the slowly convergent series associated with these functions is observed to be critical for the feasibility of the method. New formulas, which are rapidly convergent, are derived for the calculation of these series. The study has shown that the brightness temperature of the Stokes parameter U can be significant in passive remote sensing. Values as high as 50 K are observed for certain configurations.