Abstract
Form errors of a planar scale grating, such as pitch deviations and out-of-flatness, are major contributors to the final measurement uncertainty of an interferential scanning-type planar encoder. Following the previous work, in which a method has been proposed to evaluate both the out-of-flatness and the pitch deviations of a planar scale grating by a Fizeau interferometer in Littrow configuration, uncertainty analysis on this method is performed in this paper. Theoretical equations are derived to make quantitative uncertainty analysis while taking possible error factors into account. To overcome the drawbacks of a traditional uncertainty matrix approach, a new procedure is proposed to evaluate the uncertainty in the PV (peak-to-valley) deviation of a surface form, so as to assure the quality of measurement. Experiments are finally conducted to demonstrate the feasibility of proposed uncertainty evaluation method.
Highlights
An optical encoder, which is mainly composed of an optical sensor head and a scale grating, is one of the most commonly used sensors for precision positioning in production engineering [1], due to the advantages of non-contact measurement, a high resolution, and a wide bandwidth [2]
A reflective-type planar scale grating in a size of 35 mm × 30 mm that was fabricated by interference lithography was tested
The experiment has beams that were obtained by a Fizeau interferometer in the Littrow configuration
Summary
An optical encoder, which is mainly composed of an optical sensor head and a scale grating, is one of the most commonly used sensors for precision positioning in production engineering [1], due to the advantages of non-contact measurement, a high resolution, and a wide bandwidth [2]. In the case of incremental type one-axis encoders, a diffraction grating having periodic line pattern structures is employed as a scale for measurement of relative translational displacement between the scale grating and an optical sensor head [3]. Among the components in a multi-axis planar encoder system [5], a planar scale grating having periodical structures along the X- and Y-directions is one of the key components that influence the accuracy of measurement, since the period of interference signal in the optical head, which will be interpolated and used to calculate the displacement, is directly influenced by the pitch of the scale grating, in principle [4]. The X- and Y-directional pitch deviations, as well as the out-of-flatness of the scale grating, are required to be evaluated and calibrated over the entire surface of a scale grating for high precision measurement applications [7]
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