Method and apparatus for combining and generating trajectories

A method for generating a trajectory to drive a stage, comprising:

• receiving first input parameters for a first trajectory and second input parameters for a second trajectory;
• converting the first input parameters of the first trajectory into a first derivative-jerk and the second input parameters of the second trajectory into a second derivative-jerk;
• combining the first derivative-jerk and the second derivative-jerk together into a third derivative-jerk corresponding to a modified version of the first trajectory and the second trajectory;
• and
• determining a combined trajectory associated with the third derivative-jerk by integrating the third derivative-jerk one or more times.

An exposure apparatus that exposes a substrate during processing, comprising:

• an energy emission system that forms an image on a substrate;
• a substrate stage that supports the substrate and moves the substrate along one or more axes relative to the energy emission system;
• an actuator operatively connected to the substrate stage that moves the substrate stage in response to controller signals corresponding to a trajectory;
• a controller operatively connected to the actuator that generates the trajectory by receiving first input parameters for a first trajectory and second input parameters for a second trajectory, converting the first input parameters of the first trajectory into a first derivative-jerk and the second input parameters of the second trajectory into a second derivative-jerk, and combining the first derivative-jerk and the second derivative-jerk together into a third derivative-jerk that modifies the first trajectory and the second trajectory.

An apparatus for generating a trajectory used in precision lithography, comprising:

• means for receiving first input parameters for a first trajectory and second input parameters for a second trajectory;
• means for converting the first input parameters of the first trajectory into a first derivative-jerk and the second input parameters of the second trajectory into a second derivative-jerk;
• means for arranging the first derivative-jerk to overlap the second derivative jerk by a time interval and reduce the time period for performing the first trajectory and second trajectory;
• and
• means for combining the first derivative-jerk and the second derivative-jerk together into a third derivative-jerk using a smaller time interval than required separately by the first derivative-jerk and the second derivative-jerk.