2.1

Specimen preparation

Seven CAD/CAM-RBCs and one CAD/CAM glass-ceramic were investigated, as shown in Table 1 . The glass-ceramic (IEC) acted as a control group. The investigated materials were selected in a common color for dental restorations (A3, Vita shade guide). When low and high translucent versions were available for one brand, the high translucent one was chosen. This applies for all materials except for DLC. The CAD/CAM blocks were sectioned using a water-cooled low speed diamond saw (IsoMet, Buehler, Lake Bluff, IL, USA) matching the following thicknesses: 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 5 mm (each n = 6), resulting in a total of 432 specimens. The glass-ceramic was cut accounting for a crystallization shrinkage of 0.25% and was then sintered in accordance with the manufacturer’s instructions (820 °C for 10 min and 840 °C for 7 min). Subsequently, each specimen was sequentially polished plane-parallel on both sides using rotating silicon carbide paper (P320 up to P4000, LECO, St. Josef, MI, USA) providing constant water rinsing by using an automatic polishing machine (Exact Advanced Technologies, Norderstedt, Germany).

After manufacture, the specimens were cleaned with ethanol (80 v/v%) and a lint-free cotton cloth to remove remaining grease and wax that was needed for specimen fixation during the polishing procedure. The definitive thickness was measured with a precision digital caliper (Garant, Hoffmann Group, Munich, Germany).

2.2

Irradiance measurements

Using a violet-blue light-emitting diode (LED) LCU (VALO, Ultradent Products Inc., South Jordan, UT, USA), irradiance (390–480 nm) passing through each specimen was measured by a calibrated spectrometer sensible to an 360–540 nm wavelength interval, triggered at a minimum of 20 mW/cm ² (MARC Resin Calibrator, BlueLight Analytics Inc., Halifax, Canada). The LCU provides three curing modes (Standard, High and Plasma power mode), at which the exposure time was set to 10 s for Standard mode and, restricted by the LCU, to 3 s for High and Plasma power mode. With the aid of a mechanical fixation arm, the LCU was positioned centered and perpendicular to the specimen and the optical sensor of the spectrometer.

Irradiance and spectral distribution were measured for each of the three curing modes with increasing exposure distance (direct contact to sensor up to 10 mm in 1 mm steps) with no specimen in the optical pathway. Then, specimens were positioned centrally and in direct contact to the LCU and the sensor’s surface. Inferentially, irradiance passing through the given CAD/CAM materials was measured at the bottom of the specimens while being exposed to light at the specimen’s top surface.

2.3

Definition of terms and mathematical analysis

Reflection occurs on every interface of optical translucent media that differ in refractive index. Based on the Fresnel equations, reflected and transmitted irradiance can be quantified depending on initial irradiance and angle of incidence, as well as the perpendicular and parallel polarization to the plane of incidence. For light entering a specimen normal to its surface, the Fresnel equations can be reduced to the form presented in Eq. (1) , where the surface reflection ratio R is presented as a function of the reflection coefficient r (distinguished from parallelly and perpendicularly polarized fraction) and refractive index n of each involved optical media. Generalizing, the reflection ratio R can be described as the proportion of reflected to incident irradiance I .

In the present study, it can be assumed that the reflection ratio R is independent of polarization angle and identical for entering or leaving a medium with higher optical density, resulting in an identical surface reflection ratio R at the top and bottom of each specimen.

If the flat, planar surface of a restoration material is exposed to an incident irradiance I ₀ perpendicular to the surface and the reflected irradiance is I _{r , top} ( Fig. 1 ), the irradiance occurring directly subsurface ( I _{0, true} ) can be described as seen in Eq. (2) . After attenuation by absorption and scattering within a specimen with given thickness d , the irradiance at the specimen’s bottom surface is the true transmitted irradiance I _{t , true} (Eq. (3) ). After reflection at the bottom surface ( I _{r , bottom} ), the apparently transmitted irradiance I _t can be directly measured by the spectrophotometer. The parameters thickness d , incident irradiance I ₀ and apparent irradiance I _t were measured experimentally for each of the eight investigated CAD/CAM materials in each thickness for the three curing modes delivered by the LCU.

Schematic sketch of the optical pathway through a specimen (specimen thickness d , radiant emittance I ₀ , true initial irradiance I _{0, true} , reflected irradiances I _{r , top} and I _{r , bottom} , true transmitted irradiance I _{t , true} , measurable transmitted irradiance I _t ).

Absorption of light through a medium is best described by Beer-Lambert law, in the following expressed as absorbance on a decadic basis, with the decadic absorption coefficient a as specific parameter for each CAD/CAM material. This results in a linear plot, while the slope equals the absorption coefficient a as a function of the thickness d . It may be distinguished between true and apparent absorbance: for the true absorbance A (Eq. (4) ), this results in a linear equation through the origin, while the irradiances directly subsurface (reduced by the reflected fraction at top and bottom surface) are applied.

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