Measure for measure

Rudolf Hopfner explains how the vast majority of measurements for The Strad ’s latest poster were taken from micro-CT scans of the ‘Baron Knoop’ Bergonzi

One of the main strengths of micro-CT scans is the ability to take precise measurements at any given point. This is particularly important when dealing with the bodies or heads of stringed instruments. On a violin body, the longest straight lines do not exceed 30mm. They lie on the ribs perpendicular to the plates, and even in this case the word ‘straight’ has to be taken with a pinch of salt. The taking of measurements of the arching with analogous means is especially tricky and can lead to divergent results. The use of CT scans offers solutions to at least some of these problems. Nearly all the measurements for The Strad ’s poster of the Carlo Bergonzi ‘Baron Knoop’ violin have been taken digitally. Only the total length and the neck length were measured with traditional tools because the body and head had to be scanned separately.

The data of CT scans is saved in the form of voxels, the 3D equivalent of pixels in the 2D domain. The size of a voxel corresponds to the resolution of the scan. In case of the head of the Carlo Bergonzi violin this is 0.10674mm. The voxels are saved in slices oriented in the three main sectional planes (XY, XZ, YZ).

These planes roughly correspond with the axes of the instrument.

Usually the XY plane coincides with the edges of the belly and back. These slices already offer the first and most basic opportunity to take measurements. By counting the number of slices lying between points A and B we can calculate the distance. Figure 1 shows the rear view of the Bergonzi pegbox. The surface view is cut by six slices, positioned at the maxima of the volute, the pegbox and the apex of the scroll. The distance between the furthest points of the ears amounts to 365 slices. The multiplication with the voxel size gives a width of 39mm. The same procedure was followed for the width of the pegbox and the top of the volute. This brings us to the next problem: the edges of the volutes are chamfered and slightly rounded and it is not possible to define an ‘end point’.

But this problem also occurs if you use callipers.

Unfortunately the majority of measuring points doesn’t lie on one of these main sectional planes. It is possible to create oblique planes in any direction but this procedure is too time-consuming for taking dozens of measurements. Instead, it is much more convenient to work in the 3D domain with volumes or surfaces. One can imagine a surface as a very thin skin lying over the body of the instrument. These surfaces are the basis for different measuring procedures, for mappings and for mathematical calculations. It is possible to measure distances between two points anywhere on the surface. Figure 2 is a screenshot demonstrating how the width of the lower wing of the f-hole can be measured. Most of the measurements of the f-holes on the poster were measured in a similar way.

FIGURE 1 With six slices in lateral direction, the maxima of the volute, the pegbox and the apex of the scroll can be measured

IMAGES UNIVERSITY OF APPLIED SCIENCES UPPER AUSTRIA, RESEARCH GROUP COMPUTED TOMOGRAPHY

IT IS POSSIBLE TO MEASURE DISTA NCES BETWEEN TWO POINTS ANYWHERE ON THE SURFACE

FIGURE 2 The width of the wing can be measured using a surface reconstruction of the belly

FIGURE 3 Surface reconstructions allow the calculation of thickness maps as well as manual measurements

FIGURE 4A slice of the back of the ‘Baron Knoop’ Bergonzi is superimposed on tracings of a 1738 ‘del Gesù’ (green) and a Stradivari from 1728 (blue)

The basis for Figure 3 is also a surface reconstruction, though used in combination with a mapping algorithm. The surfaces consist of tiny triangles, almost 15 million of them in the case of the Bergonzi back. A special feature of our software allows us to calculate the distances of opposing triangles. The upper surface in figure 3 represents the arching of the back. As reference (or zero-level) an auxiliary plane, following the glue joint between the ribs and the back plate has been inserted. This is not in fact a plane from a geometrical point of view because it strictly follows the glue joint of the plate, which can sometimes be slightly warped. The numerical value of the calculation is assigned to a false colour on a colour map. The image shows the very regularly shaped channel of the back in deep blue, while the maxima are red. The red lines running around the edges are the result of measuring between the opposing triangles on the edges. Strictly speaking, the creation of maps is different from measuring because the output is not numerical. However, the combination of maps and numerical values as can be found on the poster images offers the maximum information.

Figure 4 is also the result of a visual comparison rather than a measurement. In an ongoing study of the shape of the arching of Bergonzi’s violins, we collected data from scans of his instruments to compare with those of Stradivari and Guarneri ‘del Gesù’. On figure 4a slice from the narrowest point of the back of the ‘Baron Knoop’ (orange), is accompanied by two curves, representing the arching of a 1738 ‘del Gesù’ (green) and a 1728 Stradivari (blue). These curves also come from slice images and had to undergo image processing. Paramount for visual comparison is the precise scaling of all images. The image shows that the backs of the Stradivari and the Guarneri are slightly wider than the Bergonzi. As a next step, the outlines of the two slices were established (using the ‘Find Edges’ function of our ImageJ software). In the final stage, the two layers received an overlay with blue and green respectively.

The juxtaposition distinctly shows that the height and shape of the arching in the middle bout of the Bergonzi and the Guarneri violins are very similar. The arching of the Bergonzi is slightly more pointed. In contrast to this, the channelling of the Stradivari is narrower and the arching much fuller. Generating these images may be time-consuming but they can give an immediate impression of details that are hard to detect in Excel spreadsheets or other lists with numerical values only.

Micro-CT scans: University of Applied Sciences Upper Austria, Research Group Computed Tomography.

CT image processing: Johanna Herr, BSc

Subscribers to The Strad receive a free poster of the ‘Baron Knoop’ Bergonzi with this issue. To obtain a rolled copy of the poster, please visit www.thestradshop.com