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Self-calibration of a Cross Grid Encoder The cross grid encoder is an optical device to measure the machine's 2D contouring error along an arbitrary path by using a grid plate with a two-coordinate phase grating on glass. The cross grid encoder can measure the two-dimensional contouring error for an arbitrary reference trajectory. It can be used to measure straightness errors, squareness errors, or contouring errors for circular paths, by the single setup.

Just as general linear encoders, the cross grid encoder may have non-negligible measurement error caused mostly by the misalignment of grids. In the case of a general linear encoder, such a measurement error can be calibrated and then compensated by comparing with the reference encoder. For the cross grid encoder, since there is no reference two-dimensional encoder available, such calibration and compensation are very difficult.     The objective of this research is to propose a self-calibration scheme of the cross grid encoder to calibrate its measurement accuracy over the entire region by only using the cross grid encoder itself and the machine to be measured, without using any reference.   >> Publications: JJ10, CJ31, CJ27         Figure 1: A cross grid encoder. KGM by Heidenhain was used in our experiments.       Figure 2: An example of measurement results (not related to the machine in Fig. 1). By using the cross grid encoder, straightness errors are measured. For different Y positions, the machine is moved toward the X direction by 140 mm, and the error in the direction normal to the feed direction is magnified and plotted. By using the cross grid encoder, such an error map can be obtained relatively easily. It should be, however, noted that the measurement result also contains the measurement error of the cross grid encoder. In this figure, the straightness error seems to vary significantly for different Y positions. Is this the machine's error? Or it is attributable to the measurement error?

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