The circular intensity of differential scattering (CIDS) for structures composed of an arbitrary collection of point polarizable groups has been obtained in analytical form using the second Born approximation, both for oriented and rotationally averaged structures. It is found that: (i) A CIDS signal is present in the forward direction parallel to the light beam. This forward CIDS does not appear in CIDS patterns calculated using the first Born approximation alone; (ii) the magnitude and shape of CIDS patterns for oriented periodic structures depend only on the properties of one unit cell of the structures and are independent of the overall size; (iii) CIDS can exist for scatterers made up of a collection of spherically symmetric point polarizable groups. In the first Born approximation anisotropic polarizable groups are required for the CIDS to be different from zero. In the second Born approximation the anisotropy necessary for CIDS is generated by the interaction between the scattering groups; (iv) the CIDS is largest when the chiral dimensions of the scatterer are of the order of the wavelength of light. © 1984 American Institute of Physics.