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In order to achieve nanometer accuracy, metrologists need to identify the sources of error and develop solutions to eradicate or minimize their effects. A stabilized low power dual-frequency laser heterodyne interferometer (ZMI-1000A) designed to measure linear and angular displacement with nominal measurement resolution 1.24 nm and 0.0025 arcsec, respectively, is used to achieve measurement of displacements over different travelling axes by comparison with the electronically reference measurements of the stage over wide range 500 mm. The repeatability and reversal error of linear stage over the working distance have agreed opto-electronically and the positioning uncertainty been reduced. A multivariable framework was implemented for the x -axis due to the cross coupling between the forward and backward course of the linear stage. Thermal error reduction is achieved using environmental temperature control (20 ± 0.2 °C) to help reduce thermal errors.

Nanometer positioning accuracy over a long term traveling stage based on heterodyne interferometry