2.1.

Dental Materials and Preparation Technique

Three different composite materials manufactured by Dentsply DeTrey (Konstanz, Germany) were investigated, each in the commonly available VITA shades shown in Table 1 . The VITA classification system has letters A to D to classify the groups of color appearance (e.g., yellowish). Within each group, numbers indicate decreasing brightness. The two hybrid composites, TPH Spectrum and Esthet-X, differ in composition with regard to their filler particles, and the ormocer Definite also has a different matrix material. For sample preparation, special preparation tools and a technique using ultrasound were developed to produce homogenous samples of adequate sample thickness and size, without air bubbles and with specular surfaces. For the spectrometric measurements, it was necessary to produce circular specimen disks each with a diameter of $22\mathrm{mm}$ for different sample thicknesses below $500\mu \mathrm{m}$ . To optimize the measurability of transmission and reflectance spectra TPH Spectrum samples were prepared with a sample thickness of 400 and $250\mu \mathrm{m}$ for Esthet-X samples and $200\mu \mathrm{m}$ for Definite samples. Three samples were prepared for each shade making a total of 75 samples. For direct reflectance measurements $R_{d,\mathrm{meas}}$ TPH Spectrum, Esthet-X, and Definite samples of color shade B2 with a thickness of $1000\mu \mathrm{m}$ were prepared. Samples were cured for $60\mathrm{s}$ in a laboratory VLC polymerization unit (Liculite, Dentsply DeTrey, Konstanz, Germany; VLC, visible light curing). The samples were stored in the dark and at room temperature for $24\mathrm{h}$ to enable them to be completely cured. Samples that showed inhomogeneities or air bubbles or had surface scratches were discarded.

Table 1

Investigated composite resins and color shades.

2.2.

Spectrometer Measurements

To determine the optical parameters, the diffuse reflectance $R_d$ , the total transmission $T_t$ , and the diffuse transmission $T_d$ (excluding the collimated transmission and the diffuse transmission within an aperture of $5.3\mathrm{deg}$ ) of the prepared material samples Spectrum, Esthet-X, and Definite were measured in the wavelength range from $400\text{to}700\mathrm{nm}$ in $5\text{-}\mathrm{nm}$ steps by the integrating sphere technique using an UV/VIS/NIR spectrometer (Lambda 900, Perkin-Elmer Corporation, Norwalk, Connecticut USA). The measurement of $T_d$ instead of the usually used collimated transmission allows measurement with only one integrating sphere. The experimental setup, described elsewhere,^{11, 12} enabled measurement of light transmission and reflectance with an error of less than 0.1%. To prove the validity of the simulated optical parameters and to compare the resulting color perception ( $R_{d,\mathrm{sim}}$ ; $L^{*}$ , $a^{*}$ , $b^{*}$ ), the diffuse reflectance $R_d\left(\lambda \right)$ of the samples Spectrum, Esthet-X, and Definite in the color shade B2 were also measured $\left(R_{d,\mathrm{meas}}\right)$ for the sample thickness $1000\mu \mathrm{m}$ .

2.3.

Monte Carlo Simulation

A specially developed iMCS simulation program was used that also takes into account the geometry of the optical setup and all radiation losses. Simulations with more than ${10}^6$ photon trajectories for each wavelength were calculated leading to statistical errors of less than 0.15%. Typical standard deviations of three determinations of ${\mu }_a$ , ${\mu }_s$ , and $1\text{-}g$ were in the range 3 to 5%. The iMCS used an estimated set of start parameters ${\mu }_a$ , ${\mu }_s$ , and $g$ from the Kubelka-Munk theory to calculate the resulting values $R_d$ , $T_t$ , and $T_d$ for each wavelength. These were then compared with the experimentally measured $R_d$ , $T_t$ , and $T_d$ values at the same wavelength. By systematic variation of ${\mu }_a$ , ${\mu }_s$ , and $g$ , deviation of the simulated $R_d$ , $T_t$ , and $T_d$ values from the measured ones was minimized until a set of optical parameters were found where the deviations were within the error threshold. Repeating this procedure wavelength by wavelength at $5\text{-}\mathrm{nm}$ increments, each within the spectral range of interest leads to a spectrum of ${\mu }_a\left(\lambda \right)$ , ${\mu }_s\left(\lambda \right)$ , and $g\left(\lambda \right)$ . Due to the high sensitivity of the simulation, it was possible to fit an adaptable phase function.^{8, 13} Scattering phase functions that do not describe realistic scattering processes do not enable successful simulations within the error tolerances. The type and parameters of the phase function can be determined by minimizing the error tolerances. These presimulations showed that the Henyey-Greenstein phase function⁴ was best suited for iMCS of the two hybrid composites, whereas the Reynolds-McCormick phase function⁷ (with an $\alpha$ factor of 1.5) was best suited for the ormocer. To increase the precision of the simulation, the absorption coefficients ${\mu }_a\left(\lambda \right)$ , determined on samples with a thickness of between 200 and $400\mu \mathrm{m}$ (material dependent, see Sec. 2.1), were corrected with measurements of composite samples with $5\text{-}\mathrm{mm}$ thickness and a modified iMCS determination of ${\mu }_a\left(\lambda \right)$ , keeping ${\mu }_s\left(\lambda \right)$ and $g\left(\lambda \right)$ at predetermined values for the thin samples.

The wavelength-dependent refractive index of the material is an important input parameter for the simulation as it primarily influences the reflection at interfaces^{5, 14} and therefore the precision of the simulation. As there is very little information available about the refractive index of dental composites, refractive indices of each composite were determined from $400\text{to}700\mathrm{nm}$ using an Abbe refractometer. The samples were molded on an optical glass surface to minimize errors due to surface roughness.

2.4.

Determination of the Color Perception Following the CIELAB System

Based on the determined ${\mu }_a$ , ${\mu }_s$ , and $g$ values, the diffuse reflectance values $R_d$ for a sample of Esthet-X, Spectrum, and Definite with an arbitrary color shade and thickness (in this case B2 and $1\mathrm{mm}$ ) were calculated using a forward Monte Carlo simulation program. Based on the material-dependent simulated reflectance spectra $R_{d,\mathrm{sim}}$ , the $X$ , $Y$ , and $Z$ standard color values were calculated according to DIN standard 5033 (Ref. 15) in $10\text{-}\mathrm{nm}$ steps in the range $400\text{to}700\mathrm{nm}$ , with respect to the standard light source D65 and the $2\text{-}\mathrm{deg}$ standard observer, and transformed to the $L^{*}$ , $a^{*}$ , $b^{*}$ values according the CIELAB system. Figure 1 shows the principle of the procedure used.

Fig. 1

Scheme of the determination of the color perception based on the optical parameters.

The determination of the $L^{*}$ , $a^{*}$ , $b^{*}$ values was repeated for samples with a thickness of $1\mathrm{mm}$ and color shade B2 based on measured reflectance spectra. All measured and calculated CIELAB values assume a black background. To compare the CIELAB values of the simulated reflectance spectra with those of the measured ones, color differences $\Delta E_{ab}^{*}$ were determined between measured and predicted values in accordance with Eq. 1 (DIN standard 6174)¹⁶:

3.1.

Determination of the Optical Parameters

Applying the iMCS, in contrast to the Kubelka-Munk method, enables a separation of optical properties into the optical parameters absorption and scattering coefficient with high precision.⁴ Figure 2 shows the results of the iMCS, i.e., the optical parameters ${\mu }_a\left(\lambda \right)$ , ${\mu }_s\left(\lambda \right)$ , $g\left(\lambda \right)$ , and ${\mu }_s^{\prime }\left(\lambda \right)$ $[={\mu }_s(1-g)]$ dependent on the wavelength, as for example, for the color shade B2 for all three composite resins.

Fig. 2

Wavelength-dependent comparison of optical parameters of the three composite resins for shade B2.

The maximum absorption at $400\mathrm{nm}$ is $0.38{\mathrm{mm}}^{-1}$ for Esthet-X, $0.32{\mathrm{mm}}^{-1}$ for Spectrum, and $0.17{\mathrm{mm}}^{-1}$ for Definite. All absorption values decrease below $0.03{\mathrm{mm}}^{-1}$ at $700\mathrm{nm}$ , leading to the perception of a yellowish color. The ormocer Definite shows the highest ${\mu }_s\left(\lambda \right)$ of $26{\mathrm{mm}}^{-1}$ at $400\mathrm{nm}$ and decreases continuously to values about $14{\mathrm{mm}}^{-1}$ at $700\mathrm{nm}$ . The scattering coefficient of Spectrum decreases from $8\text{to}5{\mathrm{mm}}^{-1}$ within the observed wavelength range. Esthet-X shows ${\mu }_s\left(\lambda \right)$ of $19{\mathrm{mm}}^{-1}$ at $400\mathrm{nm}$ decreasing more distinctly than Spectrum to $4{\mathrm{mm}}^{-1}$ at $700\mathrm{nm}$ . The anisotropy factor $g\left(\lambda \right)$ shows a strong forward scattering of Esthet-X and Definite with values of about 0.8 over the whole spectral range. Definite exhibits extreme forward scattering with values above 0.95 leading to the lowest effective scattering coefficient ${\mu }_s^{\prime }\left(\lambda \right)$ with values between 1.0 and $0.7{\mathrm{mm}}^{-1}$ . Esthet-X shows the highest effective scattering with values above $3{\mathrm{mm}}^{-1}$ at $400\mathrm{nm}$ , whereas Spectrum and Definite are lower, with values of 1.8 and $1.0{\mathrm{mm}}^{-1}$ at $400\mathrm{nm}$ . The effective scattering of all three resins decreases with wavelength converging to values in the range 0.6 to 0.8 at $700\mathrm{nm}$ .

Figure 3 shows the absorption coefficient depending on wavelength for Esthet-X in 10 different shades according to the VITAPAN classical^® system. At $400\mathrm{nm}$ , ${\mu }_a\left(\lambda \right)$ shows values in the range $0.4\text{to}0.6{\mathrm{mm}}^{-1}$ depending on the shades A1 to C3, whereas at $700\mathrm{nm}$ , the range decreases to values below $0.05{\mathrm{mm}}^{-1}$ . Scattering coefficient ${\mu }_s\left(\lambda \right)$ , anisotropy factor $g\left(\lambda \right)$ , and effective scattering cofficient ${\mu }_s^{\prime }\left(\lambda \right)$ show no significant dependency on the color shades (not shown).

Fig. 3

Absorption coefficient ${\mu }_a$ of Esthet-X for different shades dependent on the wavelength.

The decrease of absorption $\left[{\mu }_a\left(\lambda \right)\right]$ and effective scattering $\left[{\mu }_s^{\prime }\left(\lambda \right)\right]$ of all three composite resins with increasing wavelengths is in agreement with the results of other studies which use the Kubelka-Munk method.^{14, 17} Furthermore, the results support statements made by other authors that absorption takes place in the color pigments or matrix¹⁴ and scattering is mainly due to the filler particles.¹⁷ There are more differences in ${\mu }_a\left(\lambda \right)$ of the hybrid composites Spectrum and Esthet-X compared to the ormocer Definite than between Spectrum and Esthet-X which have the same matrix (Fig. 2). Scattering coefficient ${\mu }_s^{\prime }\left(\lambda \right)$ , anisotropy factor $g\left(\lambda \right)$ , and reduced scattering coefficient ${\mu }_s^{\prime }\left(\lambda \right)$ are less dependent on shades (data not shown), but differ greatly between the three materials, each containing different filler particles (Fig. 2).

Scattering is more influenced by different sizes and the kinds of filler particles than by the color pigments, the opposite being true for absorption. At short wavelengths from $400\text{to}500\mathrm{nm}$ , i.e., the blue part of visible light, Esthet-X shows a steeper curve for the scattering cofficient ${\mu }_s\left(\lambda \right)$ . From this it can be deduced that for the filler particle size distribution of the materials, Esthet-X contains a larger portion of small filler particles with dimensions relating to the blue wavelength range than the other two composites Spectrum and Definite. The shades of the composite materials were adjusted by the addition of color pigments, e.g., metal oxides. Within the investigated VITA color shades A to C, the degree of brightness is given by the shade numerals 1 to 3 (3.5), guided mainly by the concentration of color pigments. Shades A4, B4, and C4 as well as the range D2 to D4 were not investigated. In support of this, a strong correlation was found at $450\mathrm{nm}$ for the shade numerals and the absorption cofficient ${\mu }_a\left(\lambda \right)$ after running rank correlation according to Spearman.

The maximum lightness for shade numeral 1 (i.e., A1, B1 and C1) shows the lowest values for the absorption cofficient ${\mu }_a\left(\lambda \right)$ , focusing on the area of short wavelengths (Fig. 3). The situation changes for longer wavelengths. There was only a low correlation for shade numerals at $660\mathrm{nm}$ and a high correlation for shade letters (color groups). Statistical analysis using the H-test, according to Kruskal und Wallis, showed that significant differentiation of shades with $p<0.05$ is possible at 450 and $660\mathrm{nm}$ for all optical parameters, except for ${\mu }_s\left(\lambda \right)$ of Definite at $450\mathrm{nm}$ . Shade numerals within one shade letter could be significantly differentiated for the absorption coefficient ${\mu }_a\left(\lambda \right)$ at $450\mathrm{nm}$ for all materials, with the exception of C1 to C3 of Esthet-X. There was no significant differentiation at $450\mathrm{nm}$ for the shade letters.

3.2.

Comparison of the Reflectance Spectra

Figure 4 shows a comparison of the simulated and measured wavelength dependent diffuse reflectance $R_d\left(\lambda \right)$ for one sample with a thickness of approx. $1\mathrm{mm}$ and color B2 for each of Esthet-X $(d=1092\mu \mathrm{m})$ , Spectrum $(d=1099\mu \mathrm{m})$ , and Definite $(d=1032\mu \mathrm{m})$ . The $R_d\left(\lambda \right)$ value was directly measured as well as determined by simulation using the forward MCS on the basis of the optical parameters ${\mu }_a\left(\lambda \right)$ , ${\mu }_s\left(\lambda \right)$ , and $g\left(\lambda \right)$ using the iMCS and the thickness of the directly measured samples. The comparison shows very good agreement between calculated and measured diffuse reflectance data $R_d\left(\lambda \right)$ . This is also valid for Definite, which shows minimal deviations only at short wavelengths. This result indicates the validity of the determined material dependent optical parameters ${\mu }_a\left(\lambda \right)$ , ${\mu }_s\left(\lambda \right)$ , and $g\left(\lambda \right)$ , enabling a valid prediction of the reflectance spectra of a sample of arbitrary thickness and geometry.

Fig. 4

Comparison of the measured and simulated $R_d$ values of the different composites for shade B2 and a sample thickness of approx. $1\mathrm{mm}$ ; Table: Calculated color difference $\Delta E_{ab}^{*}$ between simulation and measurement. (Color online only.)

3.3.

Determination of the Color Perception Following the CIELAB System

According to Sec. 2.4, the CIELAB values $\Delta L^{*}$ , $\Delta a^{*}$ , and $\Delta b^{*}$ can be calculated from simulated or measured $R_d$ values to compare different materials or shades. As an example, Fig. 5 shows the comparison of the calculated CIELAB values for the composite materials Esthet-X, Spectrum and Definite for shade B2 with a $1\text{-}\mathrm{mm}$ sample thickness based on the simulated $R_d$ spectra. Perceptible color differences were found between the investigated composites, which were especially large between Esthet-X and Spectrum, as well as between Definite and Esthet-X. Only Spectrum and Definite exhibited values with $\Delta E_{ab}^{*}<2$ , which is defined as clinically undistinguishable.¹⁸ In general, Esthet-X had a more bluish hue. The exact values for the differences of CIELAB values $\Delta L^{*}$ , $\Delta a^{*}$ , and $\Delta b^{*}$ , the resulting color perception and the calculated color differences $\Delta E_{ab}^{*}$ are given in Table 2 .

Fig. 5

CIELAB values of the coordinates $L^{*}$ , $a^{*}$ , and $b^{*}$ for three different composite materials.

Table 2

The ΔL* , Δa* , and Δb* color perception and color differences ΔEab* of shade B2 using a 1-mm sample thickness for standard light D65 and a 2-deg standard observer.

Furthermore, the CIELAB values can be used to compare the perceptible color difference between simulated and measured reflectance spectra. This has been done for the simulated and directly measured $R_d$ spectra shown in Fig. 4. The table in Fig. 4 shows the respective $L^{*}$ , $a^{*}$ , and $b^{*}$ differences. The calculated color differences show values of $\Delta E_{ab}^{*}<0.5$ for the hybrid resin composites, which is defined as not visible for 50% of observers.¹⁸ Definite exhibits an $\Delta E_{ab}^{*}$ value of 1.71, which is within the clinically acceptable range of $\Delta E_{ab}^{*}<2$ . Grajower ¹⁷ used the Kubelka-Munk method to achieve a lower simulation precision with higher $\Delta E_{ab}^{*}$ deviations in the range of moderate perceptibility ( $\Delta E_{ab}^{*}=1.72$ to 4.58). Ikeda ¹⁹ also found perceptible color differences with $\Delta E_{ab}^{*}$ values from 1.7 to 7.4.