The use of multidimensional standards, such as spatial arrays of spheres on pins, is particularly efficient.  This  type of standard can be used to check many or even  all  of  the  lengths  required  to  test the  coordinate  measuring machine against the specification in one tomographic scan. When using sphere standards for checking the length measurement error, it is necessary to apply a correction to the results. This is because the determination of the deviation of the sphere centers can be done with much lower measurement errors than the measurement of gage block lengths.  The diameter deviation of the sphere does not affect the result, as the average of a relatively large amount of measurement points is used for each measured element. These effects are captured separately by the following methods and are considered in the overall result, For each  measured  length,  an  additional short  length  is  measured  bi-directionally and its measurement error is added to the sphere center distance error using the correct sign. This is done, for example, by measuring a short gage block or a two point diameter in the appropriate orientation on a sphere. The overall result thus corresponds to the measurement of a gage block. Alternatively, the length measurement error is derived as an approximation by adding the sphere center spacing error and the probing errors PS and PF (with consideration of the correct signs). This provides a coarse and generally overestimation of the length measurement error.

Seen in image above (opposite): Determining the length measurement error: a) Multisphere standard b) Measurement of a two point diameter c) Measurement of a sphere center distance d) Length measurement error as the sum of the diameter deviation and the deviation of  the sphere center distance e) Analysis for seven different orientations (simplified display without calibration uncertainty): the measurement errors are well within the limits indicated by the red lines.