An expansion of the incident Gaussian beam in terms of the cylindrical vector wave functions natural to an infinite cylinder of arbitrary orientation is presented. With such an expansion, the problem of interaction between a Gaussian beams and an infinite cylinder is studied in the framework of the generalized Lorenz-Mie theory. As an example, for the case of a tightly focused Gaussian beams propagating perpendicularly to the cylinder axis, the scattering characteristics are described in detail, and numerical results of the normalized differential scattering cross section are evaluated.

A new feedback optimization design method based on arithmetic sequence is proposed to design free-form optical systems for an extended LED source. Taken LED lens designed by this method as an example, we find that the design process is simple and high regional illuminance uniformity and high light output efficiency could be simultaneously achieved.

A preliminary investigation into aspects of the sewing machine is presented. A mechanical structure is proposed, whose difference with the traditional one is the rotation axe according to the direction of the next stitch. To get the perfect sewing tracks, the theoretical movement of the process is set up. The results of the samples showed that this architecture can meet most of typical geometrical figures, especially the irregular ones.