Displacement devices and methods and apparatus for detecting and estimating motion associated with same

An apparatus for estimating a position of a movable stage, the apparatus comprising:

• a stator comprising an array of sensors arranged relative to one another to provide a plurality of stator-Y oriented sensor columns and a plurality of stator-X oriented sensor rows;
• each stator-Y oriented sensor column comprising a plurality of sensors generally aligned with one another in a stator-Y direction and at least one pair of sensors in each stator-Y oriented sensor column spaced apart from one another in the stator-Y direction by a pitch Py;
• and
• a movable stage comprising a first Y-magnet array comprising a plurality of first magnetization segments, each first magnetization segment having a stage-Y direction length, Lyy, and a magnetization direction;
• a controller connected to receive information based on an output from each of the sensors and configured to use the information to determine a stator-X direction position of the movable stage;
• wherein the stage-Y direction length Lyy of each first magnetization segment conforms generally with Lyy=NyyPy, where Nyy is a positive integer.

A method for estimating a position of a movable stage, the method comprising:

• providing a stator comprising an array of sensors arranged relative to one another to provide a plurality of stator-Y oriented sensor columns and a plurality of stator-X oriented sensor rows;
• each stator-Y oriented sensor column comprising a plurality of sensors generally aligned with one another in a stator-Y direction and at least one pair of sensors in each stator-Y oriented sensor column spaced apart from one another in the stator-Y direction by a pitch Py;
• and
• each stator-X oriented sensor row comprising a plurality of sensors generally aligned with one another in a stator-X direction, the stator-X direction non parallel with the stator-Y direction, and at least one pair of sensors in each stator-X oriented sensor row spaced apart from one another in the stator-X direction by a pitch Px;
• providing a first movable stage comprising a first Y-magnet array comprising a plurality of first magnetization segments, the magnetization directions of the plurality of first magnetization segments exhibiting a first magnetic spatial period λx over a first stage-X direction width, Wyx1, of the first Y-magnet array;
• providing a second movable stage comprising a second Y-magnet array comprising a plurality of second magnetization segments, the magnetization directions of the plurality of second magnetization segments exhibiting a second magnetic spatial period λx over a second stage-X direction width, Wyx2, of the second Y-magnet array;
• obtaining information based on an output from each of the sensors and determining a stator-X direction position of the first movable stage and a stator-X direction position of the second movable stage based on the information.