The aim of the study reported here is the development of a new method which allows rapid and accurate in-vitro measurements of three-dimensional (3D) shape of laser ablated craters in hard dental tissues and the determination of crater volume, ablation rate and speed. The method is based on the optical triangulation principle. A laser sheet projector illuminates the surface of a tooth, mounted on a linear translation stage. As the tooth is moved by the translation stage a fast digital video camera captures series of images of the illuminated surface. The images are analyzed to determine a 3D model of the surface. Custom software is employed to analyze the 3D model and to determine the volume of the ablated craters. Key characteristics of the method are discussed as well as some practical aspects pertinent to its use. The method has been employed in an in-vitro study to examine the ablation rates and speeds of the two main laser types currently employed in dentistry, Er:YAG and Er,Cr:YSGG. Ten samples of extracted human molar teeth were irradiated with laser pulse energies from 80 mJ to the maximum available energy (970mJ with the Er:YAG, and 260mJ with the Er,Cr:YSGG). About 2000 images of each ablated tooth surface have been acquired along a translation range of 10mm, taking about 10s and providing close to 1 million surface measurement points. Volumes of 170 ablated craters (half of them in dentine and the other half in enamel) were determined from this data and used to examine the ablated volume per pulse energy and ablation speed. The results show that, under the same conditions, the ablated volume per pulse energy achieved by the Er:YAG laser exceeds that of the Er,Cr:YSGG laser in almost all regimes for dentine and enamel. The maximum Er:YAG laser ablation speeds (1.2mm 3 /s in dentine and 0.7mm 3 /s in enamel) exceed those obtained by the Er,Cr:YSGG laser (0.39 mm 3 /s in dentine and 0.12mm 3 /s in enamel). Since the presented method proves to be easy to use and allows quite rapid measurements it may become a valuable tool to study the influence of various laser parameters on the outcome of laser ablation of dental tissues.
1. Introduction Erbium-doped solid-state laser systems have become an established tool for effective, precise and minimally invasive preparation of hard dental tissues, such as enamel and dentine  . Hydroxyapatite and water, major constituents of these tissues, exhibit very high optical absorptivity at the wavelengths of Er lasers  . Short pulses of Er laser light with high peak power are employed to overheat the tissue locally to such a high degree that it is explosively removed (ablated) from the surface [2–4] . Much of current research and development work in this area is directed into process optimization through adapting the laser parameters to account for the differences in physical properties of the treated tissues [5–8] . A key issue in this kind of experimental work is the instrumentation and method employed to character- ize the outcome of the ablation process. The parameters widely used for this purpose are the linear and volume ablation rate defined as crater depth and volume per laser pulse, respectively. The procedure to measure the ablation rate usually involves irradiation of a tooth with a number of consecutive laser pulses to produce a measurable crater and measurement of the crater depth or volume. In early experiments the linear ablation rate was used as the key parameter to characterize the process. Li et al.  for example examined the laser ablated craters under an optical microscope and determined the crater depth by means of an ocular micrometer. Majaron et al.  used optical stereo-microscopy to determine the crater depths achieving the longitudinal resolution of 20 m m. These two methods are rather subjective and thus less appropriate for the application in ablation optimization research. Sarafetinides et al.  sectioned the teeth into slices of equal thickness and measured the time needed to perforate a slice at a constant pulse repetition frequency (PRF) to determine the linear ablation rate. This method suffers from a fundamental drawback that the thermal response of a slice differs from the one of an unsliced tooth. To achieve a good precision the ablated depth per laser pulse should be short in respect to slice thickness. Recent reports have established the volume ablation rate as the key parameter. Forrester et al.  have used scanning electron microscopy (SEM) to determine the volume of laser ablated craters. The scanning process is rather slow and it would take hours to measure large number of craters required in the ablation optimization research. Rode et al.  used the extended depth of field digital imaging to construct a three-dimensional (3D) model of a laser ablated crater. The key issue with this method is to establish good lighting conditions and acquire good contrast images. Due to the irregular crater shape it may be necessary to repeat measurements several times before an acceptable result is obtained. This seriously restricts measurement speed that can be achieved in practice. Ohmi et al.  have demonstrated the possibility of in situ monitoring of laser ablation of hard tooth tissue using an optical coherence tomography (OCT) set-up. This method requires a rather complex set-up which may require special skills to adjust and align. Mercer et al.  have employed X-ray microtomography (XMT) to determine 3D models of laser ablated craters at micrometer resolution. The technique allows acquisition of complex 3D crater surfaces with high precision and virtually no limitations with respect to its depth. But the process is quite time consuming: it takes few hours to acquire and evaluate a 3D model of a single ablated crater.
Mehl et al.  have employed a 3D laser scanner to determine the volume ablation rate. Impressions of teeth were taken before and after the laser ablation and measured by a triangulation laser scanner. This article presents a method which employs the same basic principle but allows the measurement of crater volume directly on teeth in-vitro without the need to make impressions. The article presents the key characteristics of the method, the set- up and some practical aspects pertinent to its use. An experiment is also described where the method is employed to study the process of laser ablation of hard tooth tissues by two main laser types currently employed in dentistry, Er:YAG and Er,Cr:YSGG.dental laser tips
2. The method
The method is based on the optical triangulation principle  ( Fig. 1 ). The tooth surface is illuminated by a laser beam, formed into a light plane. A bright laser line is visible on the illuminated tooth surface. A camera, oriented at a specific (triangulation) angle with respect to the laser beam axis, is used to acquire an image of the irradiated surface. The image is transferred to a personal computer (PC) where it is analysed to determine a surface profile. In order to measure the complete tooth surface, the tooth is translated in a direction perpendicular to the laser line using a precision translation stage driven by a stepping motor. A sequence of surface profiles is acquired along the way and transformed into a 3D surface model. The triangulation angle employed in this set-up is 15 1 and has been determined by preliminary tests as a suitable compromise trading off lower height resolution for higher probability of unobstructed view of the laser line in the crater. To practically realise such a small triangulation angle a small mirror is used to redirect the laser beam by 90 1 towards the tooth surface. The diode laser projector (Stocker Yale Lasiris SNF-501L-660T-10-10) is thus positioned parallel to the tooth translation axis. The width of the laser line as specified by the producer is 40 m m at the particular projection distance of 10cm.
There are several problems that limit the applicability of this set-up for measurements on unmodified tooth surfaces. The red light of the laser projector partially penetrates into the tooth body and that influences adversely the accuracy of profile measure- ment. Another problem is that more light is diffusely reflected form a crater than from the unablated parts of a tooth surface because the ablated craters exhibit higher surface roughness. This causes an increase of the difference between the maximum and minimum measured light intensities. This dynamic range increase readily exceeds the capabilities of the imaging sensor and thus corrupts the accuracy of profile measurement. In order to overcome these problems a thin layer of the white powder is sprayed on the examined tooth surface. The powder is used in non-destructive testing for the detection of surface cracks. If applied to a dry surface the powder dries in about 5s. The powder layer is few micrometers thick. In this way rather uniform and enhanced diffuse optical reflectivity is achieved over the whole sprayed tooth surface and prevents light penetration. The visibility of the craters is greatly enhanced while their morpho- logical dental laser tips
characteristics are not deteriorated excessively. Inspection of a powder sprayed surface under a microscope shows grainy surface appearance with particle size of about 10 m m which is comparable to the resolution of the triangulation system. This procedure of surface modification works well for ‘‘normal’’ craters with depth to diameter ratio less than one which is common in the dentistry practice. It might not work well for deeper and narrower craters which are rare in practice. It should be difficult to deposit the powder at the bottom of such a crater as uniform as on the surface outside the crater, so the optical reflectivity of the modified surface might not be as uniform as in the case of the ‘‘normal’’ craters.
3. The validation experiment
In order to examine accuracy and repeatability of the set-up, a CNC precision milled aluminium alloy block was manufactured. Nine holes were drilled into the block, with different shapes and sizes covering approximately the range of the expected crater sizes (volumes). Three kinds of repeatability tests were performed with the block: repetitive volume, depth and diameter measure- ments (a) without sample repositioning, (b) with sample repositioning and (c) by renewing the powder layer between the successive measurements. Sample repositioning means that the block was taken off the translation stage after every measurement and then positioned back onto the translation stage at different coordinates and tilt angles. Renewing the powder layer means that the block was taken off the translation stage, cleaned with water and then dried, sprayed with the white powder again and positioned back onto the translation stage. Each kind of repeatability test was performed five times on each hole. Percent deviation (standard deviation divided by mean value) was used a repeatability measure. The worst result was obtained in the volume measurements of a conical borehole (2.60mm surface diameter, 60 1 aperture angle, and 1.50mm depth). The deviation results were as follows: 0.8% without sample repositioning, 1.5% with sample repositioning and 1.8% with renewing surface modification. The reference hole diameters were determined using optical microscope with accuracy 7 0.01mm and depths were deter- mined using a mechanical stylus with accuracy 7 0.001mm. Volumes were calculated on the basis of diameter and depth measurements taking into account the shapes of the holes. The results were compared with the results obtained by the triangulation set-up. Good agreement was found — the average disagreement was o 5%.
A new method was developed to measure volume rate of ablation of hard dental tissues by the Er lasers. The method is based on a laser triangulation set-up with a measurement range of 20 10 5mm 3 and a resolution of 156nm 20 m m 5 m m along the three respective axes. dental laser tips
In order to obtain reliable volume measurements using this set-up modification of a tooth surface by a white powder spray was found to be necessary. Repeatability of volume measurement was found to be better than 1.8% in the worst case when the samples were cleaned, re-sprayed and repositioned between consecutive measurements. Accuracy of volume measurement was checked by comparison with the results obtained by optical microscopy and mechanical stylus measurement and found to be better than 5%. The method was employed in an in-vitro study to examine the volume ablation rates and speeds attainable by two main laser types currently employed in dentistry, Er:YAG and Er,Cr:YSGG. The maximum Er:YAG ablation speeds measured on extracted human molar teeth were 1.2mm 3 /s in dentine, and 0.7mm 3 /s in enamel, compared to measured maximum ablation speeds of Er,Cr:YSGG of 0.39mm 3 /s in dentine and 0.12mm 3 /s in enamel. The obtained ablation slope efficiency was highest with the Er:YAG laser, with approximately 0.075mm 3 /J in dentine, and 0.035mm 3 /J in enamel. The method proved to be easy to use and allows much faster determination of crater volume, ablation rate and speed than most of the alternative measurement methods. It may become a valuable tool to study the influence of various laser parameters on the outcome of laser ablation of dental tissues.