Comparison of three 3D scanning techniques for paintings, as applied to Vermeer’s ‘Girl with a Pearl Earring’

Heritage Science

Table 4 Comparison of reference target measurements, sample no. 513E by Rubert & Co [41], as depicted in Fig. 6

Groove	Exp. depth	NPS				MS-OCT				Std-Res 3D scan
Groove	\(\Delta\) (\(\upmu \hbox {m}\))	N	\(\sigma\) (\(\upmu \hbox {m}\))	\(\Delta\) (\(\upmu \hbox {m}\))	Err. (\(\upmu \hbox {m}\))	N	\(\sigma\) (\(\upmu \hbox {m}\))	\(\Delta\) (\(\upmu \hbox {m}\))	Err. (\(\upmu \hbox {m}\))	N	\(\sigma\) (\(\upmu \hbox {m}\))
1 (t)	1000	1220	0.22	984	N/A	250	7.4	982	\(-\)2	22.5k	15.0
1 (b)	1000	20	0.05	984	N/A	250	6.2	982	\(-\)2	150	9.2
2 (t)	500	1050	0.42	496	N/A	400	5.8	490	\(-\)6	10.5k	10.2
2 (b)	500	10	0.12	496	N/A	300	1.6	490	\(-\)6	2400	17.7
3 (t)	200	910	0.21	195	N/A	990	4.5	194	\(-\)1	12k	10.3
3 (b)	200	200	0.08	195	N/A	550	1.4	194	\(-\)1	7500	9.3
4 (t)	30	1100	0.21	29	N/A	600	3.0	29	0	4500	10.8
4 (b)	30	10	0.05	29	N/A	400	4.1	29	0	750	10.4

Groove	Exp. depth	Std-Res 3D scan		High-Res 3D scan				3D digital microscopy
Groove	\(\Delta\) (\(\upmu \hbox {m}\))	\(\Delta\) (\(\upmu \hbox {m}\))	Err. (\(\upmu \hbox {m}\))	N	\(\sigma\) (\(\upmu \hbox {m}\))	\(\Delta\) (\(\upmu \hbox {m}\))	Err. (\(\upmu \hbox {m}\))	N	\(\sigma\) (\(\upmu \hbox {m}\))	\(\Delta\) (\(\upmu \hbox {m}\))	Err. (\(\upmu \hbox {m}\))
1 (t)	1000	972	− 12	7000	12.9	987	3	340k	3.5	987	3
1 (b)	1000	972	− 12	2250	8.6	987	3	240k	3.1	987	3
2 (t)	500	520	24	7750	12.2	496	0	348k	2.5	496	0
2 (b)	500	520	24	1000	7.2	496	0	228k	3.8	496	0
3 (t)	200	206	11	2250	8.6	206	11	560k	3.2	194	− 1
3 (b)	200	206	11	7000	8.3	206	11	456k	3.4	194	− 1
4 (t)	30	37	8	6250	10.1	35	6	125k	6.3	31	2
4 (b)	30	37	8	1050	10.3	35	6	155k	5.2	31	2

The Nano Point Scanner (NPS) measurements are taken as the gold standard. The grooves are labeled from the deepest (1) to most shallow (4) groove, where (t) denotes the measurement at the sample’s top surface and (b) the measurement at bottom of the groove. For every measurement region, N denotes the number of measurements, \(\sigma\) the standard deviation of those measurements, \(\Delta\) the height difference between the top and bottom (mean difference), and Err. the error with respect to the NPS measurement. Except N all the results are specified in \(\upmu \hbox {m}\). The errors (relative to the NPS measurements) are plotted is Fig. 7