System and method for roll alignment of a multi-nozzle extruder in three-dimensional object printers using cross-process measurements

A three-dimensional object printer comprising:

• a multi-nozzle extruder including a plurality of nozzles;
• a first actuator configured to move the multi-nozzle extruder in a first process direction and a second process direction within a print zone of the three-dimensional object printer, the second process direction being different than the first process direction;
• an optical sensor;
• and
• a controller operatively connected to the multi-nozzle extruder, the first actuator, and the optical sensor, the controller being configured to:
• move the multi-nozzle extruder in the first process direction using the first actuator;
• operate at least a first nozzle and a second nozzle in the plurality of nozzles in the multi-nozzle extruder to emit a first swath and a second swath, respectively, of an extrusion material onto a surface of a receiving member in the print zone during the moving of the multi-nozzle extruder in the first process direction;
• move the multi-nozzle extruder in the second process direction using the first actuator;
• operate at least the first nozzle and the second nozzle in the plurality of nozzles in the multi-nozzle extruder to emit a third swath and a fourth swath, respectively, of the extrusion material onto the surface of the receiving member in the print zone during the moving of the multi-nozzle extruder in the second process direction;
• generate scanned image data of the first swath, the second swath, the third swath, and the fourth swath using the optical sensor;
• identify a measured two-dimensional location of the second nozzle relative to the first nozzle with reference to a first location of the second nozzle in a first cross-process direction corresponding to a location of the second swath relative to the first swath in the scanned image data, the first cross-process direction being perpendicular to the first process direction, and a second location of the second nozzle in a second cross-process direction corresponding to a location of the fourth swath relative to the third swath in the scanned image data, the second cross-process direction being perpendicular to the second process direction;
• and
• identify an angle of roll for the multi-nozzle extruder with reference to the measured two-dimensional location of the second nozzle relative to the first nozzle and a predetermined geometric arrangement of the first nozzle and the second nozzle in the multi-nozzle extruder.