Systems and methods for absolute positioning using repeated quasi-random pattern

A method for determining a high resolution absolute position of a two-dimensional detector array along a two-dimensional absolute scale, wherein the two-dimensional absolute scale includes a two-dimensional integrated scale pattern extending along first and second measuring axes, the two-dimensional integrated scale pattern comprising:

• a plurality of quasi-random pattern portions, each quasi-random pattern extending along the first and second measuring axes and having first and second dimensions, and each quasi-random pattern portion comprising at least a portion of at least one quasi-random pattern;
• and
• a plurality of code groups distributed within the two-dimensional integrated scale pattern and spaced apart along a first direction by substantially the first dimension and spaced apart along a second direction by substantially the second dimension, each code group comprising a plurality of code elements defining at least one code word, the at least one code word usable to identify a measurement value of a local datum along each of the first and second measuring axes;
• the method comprising:
• detecting an image of a portion of the two-dimensional integrated scale pattern corresponding to a current position using the detector array;
• determining an absolute measurement value of a local datum along each of the first and second measuring axes based on at least one code group included in the detected image;
• determining a measurement value of an offset of the detector array relative to the local datum along each of the first and second measuring axes based on at least one of a) the location of the local datum in the detected image, and b) the location of the at least a portion of at least one quasi-random pattern in the detected image;
• and
• combining the absolute measurement value of the local datum along each of the first and second measuring axes and the measurement value of the offset of the detector array relative to the local datum along each of the first and second measuring axes to determine a high resolution absolute position of the detector array along the first and second measuring axes of the two-dimensional absolute scale.