A method for generating smooth freeform optical surfaces from B-spline is proposed. In this method, the unit tangent vectors of feature data points are employed as constraints. Based on design methods of freeform surface, both feature data points and unit tangent vectors are obtained, and control points and knot vectors of the freeform surface are computed by the interpolation theory. The freeform surfaces are constructed with the control points and knot vectors to ensure the desired normal at each feature data point. Freeform surfaces are constructed by this method and compared with the traditional method. The results show that beams are controlled well by this method with a maximum uniformity more than 99%, and better results can be obtained with fewer feature data points for this method.
© 2011 Optical Society of America
Original Manuscript: May 9, 2011
Revised Manuscript: July 22, 2011
Manuscript Accepted: July 22, 2011
Published: August 25, 2011
Rengmao Wu, Zhenrong Zheng, Haifeng Li, and Xu Liu, "Constructing optical freeform surfaces using unit tangent vectors of feature data points," J. Opt. Soc. Am. A 28, 1880-1888 (2011)