In high precision manufacturing, such as semiconductor fabrication, we clearly would like to achieve nanometer-level precision in multi-axis stage positioning, over a span of several hundred millimeters of motion. Achieving high precision in machines requires, first of all, being able to measure motion with high precision. The main measurement errors are caused by measurement error of metrology and stage error motion. When the stage error motion is highly repeatable, it can be calibrated and compensated by software. That is an economical way to improve the accuracy of multi-axis precision machine.; This dissertation will develop a measurement model of multi-axis precision machine using multi X-Y encoders based on rigid body kinematics. Stage design configurations are optimized to minimize measurement error caused by stage error motion.; In the presented real-time self-calibration algorithm, the error of X-Y grating is modeled as 2-D periodic band-limited signal, which is further decomposed into superposition of 1-D signals. This avoids calibration uncertainty blowing up due to the curse of dimensionality. The difference between outputs of dual XY grating-based metrology is employed to produce measurement equations, which will counteract measurement error coming from the same quasi-static error sources, such as thermal induced error and stage error motion. This algorithm is based on the translation property of the DFT. In our approaches, perfect translation is implemented by translating the sensor head. The error propagation property of separating systematic error of metrology in spatial frequency domain is investigated, and it is proved that a DFT based calibration algorithm is insensitive to measurement noise during calibration. The main calibration uncertainty caused by non-periodic errors are minimized by virtual closure, square reversal and orthogonal decomposition.; The scales are fabricated by interferometric lithography, where a laser source is split and recombined to form regular fringes. To obtain a two-dimensional scale, a second exposure must be performed with the scale rotated at 90 degrees to the original exposure. The scale error is a smooth function due to the deviation of the spherical wave exposure from the ideal case of plane wave interference. This results in an error function with low spatial frequency content; this makes not only software error compensation easier to implement, but a faster self-calibration process.; Both numerical simulations and experimental results are presented. With the experiments, it is shown that a X-Y grating with an error function reaching 1000nm in magnitude can be reduced, with self-calibration, to measurement-noise limited error (in our case, 10 nm). With the calibrated X-Y grating arrays, all six geometry errors of a stage in each axis of motion can be measured accurately, simultaneously and more efficiently in just two setups.
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