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Production sequence of Si-spheres and interferometrical determination of the sphere volume

Calibration of size and form of microspheres by stitching AFM images using ICP point-to-plane algorithm


The sphere is a fundamental geometric object in dimensional metrology. It is the most used form of probing elements in tactile measurement tools, such as coordinate measuring machines (CMM) and stylus profilometers. For bigger spheres, techniques for size and form metrology have been well developed and low measurement uncertainty has been achieved. As an example, the measurement of highly enriched 28Si Avogadro spheres with a diameter d of approximately 93 mm can be achieved with a measurement uncertainty down to 0.9 nm using a special Fizeau interferometer at PTB. However, the metrology of size and form error of small size spheres, particularly microspheres, remains as a challenge.

The PTB has recently developed a new method for accurate measurements of size and form of microspheres by acquiring a set of seven AFM images at different orientations of the sphere under test. The AFM images are finely aligned with each other using the Iterative Closest Point (ICP) point-to-plane algorithm. They are then fused to one data set, from which the size and form can be evaluated.

Using this method, the AFM tip geometry is an important influencing factor as the measured AFM image is the dilated result of the measured structure by its tip geometry. To realise traceable calibration of the microsphere, the AFM tip geometry needs to be traceably calibrated, too. To solve this problem, the AFM tip geometry was traceably calibrated to a line width standard type IVPS100-PTB, whose feature geometry was calibrated with a traceable route to the lattice constant of crystal silicon.

Measurement setup, scan strategy, and data evaluation processes have been developed. To illustrate the measurement stability of the developed method, four sets of repeated measurements were performed on a microsphere with a nominal radius of 200 µm. The finally evaluated form errors of four measurements are depicted in figure 1a to 1d, respectively. It can be clearly seen that the results agree well with each other, indicating the stability and robustness of the developed method. Some slight discrepancies are visible, e.g. at the marked position “A” and “B” which are attributed to the profile “jump” effects in AFM measurements. They can be further eliminated by marking them as outliers and thus being removed from data sets. The standard deviation of the evaluated radius values of four repeated measurements reaches 5 nm, indicating promising performance.

Fig.1: Measured form errors of a microsphere with a nominal radius of 200 µm based on four repeated measurements shown as (a), (b), (c) and (d).


1) Gaoliang Dai, Johannes Degenhardt, Xiukun Hu, Helmut Wolff, Rainer Tutsch, Eberhard Manske, 2022 Traceable calibration of size and form of microspheres by stitching AFM images using ICP point-to-plane algorithm, submitted to the journal “Measurement Science and Technology”



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