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The calibration of the angle encoder is necessary to improve the accuracy of angle measurement in precision rotating devices. Due to the characteristics of in situ calibration of encoders, self-calibration methods depending on special arrangements of multiple scanning heads have been widely used. Conventional works usually arrange the scanning heads in a regularly distributed way, generally involving too many scanning heads, especially when more high order Fourier components of the encoder error are calibrated. This paper presents an optimization-based arrangement method for self-calibration of angle encoders. Fourier approaches are used to determine the error of encoder from the angle differences measured between scanning heads. The relations between detectable Fourier components of the error and angular intervals of the heads are obtained from the properties of transfer functions. The optimal arrangements for two and three scanning heads, including the adjustment tolerances of the heads with the range of tested Fourier orders, are presented. The results of simulations and experiments demonstrate that the proposed optimal schemes can realize the same performance of calibration but with fewer scanning heads, compared to the conventional methods.

Conventional methods for the calibration of angle encoders typically only consider the graduation error of the encoder's circular scale. However, the radial motion of the circular scale during its rotation, due to its eccentricity and the axis of rotation radial error motion, can also introduce noticeable errors to the angle measurement in most practical applications. Based on the analysis of the influence of radial motion, an optimal-arrangement-based fourscanning-heads error separation technique for in situ self-calibration of angle encoders is presented. This Fourier-based technique uses the basic self-calibration model to measure the first-order Fourier component of the encoder error which includes the contribution of eccentricity. Meanwhile, the separation technique is utilized to separate the residual Fourier components of the graduation error from the measurement deviation due to radial error motion. The effect of the scanning heads' angular position errors on the calibration results is discussed. Optimal arrangements of the four heads are achieved to avoid the suppression of the Fourier components, and reduce the propagation of errors. Numerical results and experimental comparisons demonstrate the effectiveness of the proposed method. Moreover, this technique can also be used for measuring the spindle radial error motion for some users.

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The fine alignment between a template with nano patterns and a wafer substrate, especially the parallelism between the two surfaces, is critical to Nano Imprint Lithography. A fine alignment system featuring active orientation adjustment which is composed of an imprint unit and a 6-DOF micromanipulator is proposed in this work. Deformations of a compact flexure layer caused by imprint loads are measured by four identical force sensors embedded in the imprint unit. The tilt of the flexure layer can thus be eliminated by adjusting the orientation of the 6-DOF micromanipulator. Kinematics and stiffness analysis are then developed, followed by dynamic performance evaluations. Based on the proposed system, an imprint tool is further developed and corresponding experiments are conducted. A saw shape grating pattern with 1.6 μm linewidth and a lattice pattern with 0.9 μm period are both imprinted with a minimum feature of 30 nm well reserved on the substrate. A maximum parallelism error of 14 nm across the template surface is also demonstrated by further section analyses on the imprinted patterns, hence the feasibility and superiority of the proposed method is verified.