Mathematical model for assessing true irradiance received by luting materials while curing through modern CAD/CAM resin composites


  • Transmitted irradiance is affected by surface reflection, attenuation and scattering.

  • A correction calculating true transmitted irradiance can be implemented.

  • The model can be applied for individual treatment conditions.

  • The control group (glass-ceramic) offers the lowest absorption coefficient.


Statement of problem

Measurement of irradiance passing through a dental restoration for properly curing a dual- or light-polymerized luting composite is imprecise due to surface reflection.


To provide a mathematical correction of measured transmitted irradiance for predicting true transmitted light intensity through CAD/CAM restorations.


A total of 432 specimens were fabricated. Seven modern CAD/CAM resin-based composites (RBCs) and one CAD/CAM glass-ceramic (control group) were sectioned and polished into specimens of 0.5–5 mm thickness (in 0.5 mm steps, n = 6). Irradiance of a violet-blue LED light curing unit (LCU) (power modes: Standard, High and Plasma) was measured after passing through each specimen with a spectrometer. Data was compared based on 95% confidence intervals and using univariate ANOVA followed by Tukey HSD ( α = 0.05).


The measured transmitted irradiance passing through the specimens decreased exponentially. Significantly highest values of transmitted irradiance were measured for 0.5 mm thick specimens for all materials ( p < 0.05). The decadic absorption coefficient for CAD/CAM-RBCs ranged from 0.292 mm −1 to 0.387 mm −1 while the control group (glass-ceramic) reached a significantly lower value of 0.283 mm −1 . The reflection ratio for all materials ranged from 12.6% to 18.5%.


A correction can be implemented to predict the true transmitted irradiance after passing through a dental restoration as function of initial irradiance, specimen thickness and material specific parameters. For a practitioner, this model may be applied depending on the specific treatment conditions, the individual LCU’s radiant emittance and restoration thickness for the tested materials.


The central idea of a dental restoration is the creation of an esthetic and functional artificial dentition that would not be distinguishable from natural teeth. Enamel and dentin feature inherent translucency, thus optical characteristics of a natural hard tooth tissue should be comprised when thinking of an esthetic reconstruction . The optical appearance determines the esthetical aspects, while the translucency effects the light curing of a luting agent. The composition of a resin-based composite (RBC) and the spectral distribution of the light curing unit (LCU) influence the transmittance of light , accordingly organic matrix composition, inorganic filler content, shape and size have impact on the optical behavior . In order to understand light transmission through RBCs, it is important to consider multiple optical phenomena that lead to attenuation of light: absorption, scattering and reflection . For filler particles that are smaller in size than the wavelength of light, Rayleigh scattering describes the scattering of light at the interface of spherical particles, while the Beer-Lambert Law merges true absorption and scattering into one exponential decrease .

The recent development of Computer-Aided Design and Computer Aided Manufacturing (CAD/CAM) RBCs leads to improved mechanical and optical characteristics, closing the gap between direct RBC filling and CAD/CAM-ceramic restoration. Generally spoken, benefits of monolithic CAD/CAM RBCs compared to CAD/CAM ceramics are seen in a comfortable fabrication of tooth colored dental restorations without needing a time consuming finishing, an additional sintering process or glaze firing as well as in a higher cost efficiency due to less abrasive wear concerning the milling process . Using high pressure and high temperature during polymerization, the industrial manufacturing of dental CAD/CAM RBCs enables an extended range of indication for these high-performance materials . Designed for indirect restorations, CAD/CAM RBCs feature a more homogeneous polymerization by using chemical instead of photo-initiators and a reduced amount of monomer release in contrast to direct RBCs . As bruxism can be seen as a limitation for using ceramic restorations, CAD/CAM RBCs offer an eligible alternative . The possibility of repairing CAD/CAM RBCs with direct RBC materials in the event of marginal crack or finite breakout offers a further advantage as no buffered hydrofluoric acid is needed for the repair compared to ceramic restorations .

When luting modern CAD/CAM RBC restorations, manufacturers recommend the use of a luting material based on a dual curing RBC. It has been shown that the additional occurrence of light when luting with dual curing RBCs results in significantly enhanced micro-tensile bond strength and degree of conversion of the luting composite . For limited wall thicknesses of up to 2–3 mm, a purely light initiated luting system is allowed for few materials (Voco Grandio Blocs and Ivoclar Vivadent Tetric CAD). The amount of light reaching the luting RBC has impact on the restoration’s longevity , accordingly detailed knowledge about irradiance that is available for the luting agent is advisable.

Truly transmitted irradiance cannot be measured precisely due to loss of light at optical interfaces. So far only few publications take account of reflection loss when analyzing the translucency of dental restorative materials . Therefore, the present study aims to predict the exact amount of transmitted irradiance by defining a calculation model based on the CAD/CAM material’s optical features, the absorption coefficient and reflection ratio.

Following null hypotheses are tested:

  • 1.

    At a given specimen thickness, transmitted irradiance is identical for all investigated CAD/CAM materials.

  • 2.

    Reflectance has no effect on the transmission of irradiance. Measured and true transmitted irradiance are equal, hence a correction model is not reasonable.

Materials and methods

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).

Table 1
Investigated CAD/CAM materials: one glass-ceramic (control group) and seven modern CAD/CAM composites.
Abbr. Manufacturer Trade name (size) Color LOT Filler (wt%)
IEC Ivoclar Vivadent, Schaan, Liechtenstein e.max CAD (C 14) A3 HT W86363
ITC Ivoclar Vivadent Tetric CAD (C 14) A3 HT W93631 71
GCS GC, Tokyo, Japan Cerasmart (12) A3 HT 1702011 71
SBH SHOFU, Kyoto, Japan Block HC A3 HT 071601 61
CBC Coltene, Altstatten, Switzerland Brilliant Crios (14) A3 HT I35186 71
3LU 3M, St Paul, MN, USA Lava Ultimate (14 L) A3 HT N933658 80
VGB Voco, Cuxhafen, Germany Grandio blocs (14 L) A3 HT 1709591 86
DLC DMG, Hamburg, Germany LuxaCam Composite (14 L) A3 769515 70

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).

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.

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 .

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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.

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<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='Truetransmittedirradiance,It,true=It+Ir,bottom’>Truetransmittedirradiance,??,????=??+??,??????Truetransmittedirradiance,It,true=It+Ir,bottom

Fig. 1
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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Aug 5, 2020 | Posted by in Dental Materials | Comments Off on Mathematical model for assessing true irradiance received by luting materials while curing through modern CAD/CAM resin composites
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