Abstract: The present invention discloses a lithographic apparatus, a device manufacturing method, and a robotics system capable of specifying a trajectory to be followed by a substrate relative to a radiation beam comprising a position and/or an orientation as a function of time. The specified trajectory is characterized as a mathematical smooth function up to at least the third order which connects a first state and a second state, wherein both the first state and the second state comprise boundary values for at least the position and/or the orientation and for first and second derivatives of the position and/or orientation.

Abstract: The main mask pattern of a photomask is corrected by adding serifs of one type (inner or outer) to a pair of mutually adjacent corners in the pattern, and adding a serif of the opposite type (outer or inner) to the edge between the corners. When the photomask is used to create a resist pattern by photolithography in the fabrication of a semiconductor device, the serifs combine to produce an optical proximity correction that reduces corner rounding and increases edge straightness in the resist pattern.