This paper describes a second-generation dual sine-grid surface encoder for 2-D position measurements. The surface encoder consisted of a 2-D grid with a 2-D sinusoidal pattern on its surface, and a 2-D angle sensor that detected the 2-D profile of the surface grid The 2-D angle sensor design of previously developed first-generation surface encoders was based on geometric optics. To improve the resolution of the surface encoder, we fabricated a 2-D sine-grid with a pitch of $10{mu}m$. We also established a new optical model for the second-generation surface encoder that utilizes diffraction and interference to generate its measured values. The 2-D sine-grid was fabricated on a workpiece by an ultra precision lathe with the assistance of a fast tool servo. We then performed a UV-casting process to imprint the sine-grid on a transparent plastic film and constructed an experimental setup to realize the second-generation surface encoder. We conducted tests that demonstrated the feasibility of the proposed surface encoder model.