Abstract

The computer aided geometric design industry (CAGD) uses a flexible curve called NonUniform Rational B-Splines (NURBS). NURBS offer a numerically stable curve, local curve control, and geometric intuitive control points for manipulating the curve. This thesis investigates the advantages and disadvantages of using NURBS in optical design applications. NURBS curves offer a rational segmented polynomial curve with the flexibility of setting both the order of the B-spline segments and the locations of the knots, or joints, between the B- spline segments. The rational nature of the curve allows representations of spheres and conics. Changing the order of the B-spline segments makes it possible to use these curves to accurately correct higher order aberrations in optical systems. The local control offered by adjusting the knot locations between the B-spline segments allows the optical designer to reduce aberrations that are not naturally distributed across the aperture. A very⁷ brief explanation of NURBS curve mathematics is presented followed by a number of the optical performance comparisons between rotationally symmetric NURBS surfaces and standard optical surfaces.

© 2002 Optical Society of America