As light interacts with an object, several phenom- ena can be observed. Incident light can be reflected, absorbed, scattered (or backscattered), or transmit- ted. These parameters can all be calculated to more objectively characterize the optical properties of the material (Fig. 4.34). Esthetic dental materials such as ceramics, resin composites, and tooth structure Transmitted light
Reflected light
FIG. 4.33 Demonstration of opalescence in a ceramic restoration. The tooth appears brown under transmitted light and blue under reflected light.
TABLE 4.8 index of Refraction (n) of Various Materials
Material Index of Refraction
Feldspathic porcelain 1.504
Quartz 1.544
Synthetic hydroxyapatite 1.649 Tooth structure, enamel 1.655
Water 1.333
are turbid, or intensely light-scattering, materials.
In a turbid material the intensity of incident light is diminished considerably when light passes through the specimen. These considerations are important not only for shade matching but also in situations where the restorative material is used to conceal imperfections in the tooth being restored, such as stains or other flaws. The optical properties of restor- ative materials are described by the Kubelka-Munk equations, which develop relations for monochro- matic light between the reflection of an infinitely thick layer of a material and its absorption and scat- tering coefficients. These equations can be solved algebraically by hyperbolic functions derived by Kubelka.
Secondary optical constants (a and b) can be cal- culated as follows:
a=[R(B)−R(W)−RB+RW−R(B)R(W)RB
+R(B)R(W)RW+R(B)RBRW−R(W)RBRW
−R(W)RBRW/{2[R(B)RW−R(W)RB]} and
b=(a2−1)½
where RB is the reflectance of a dark backing (the black standard), RW is reflectance of a light backing (the white standard), R(B) is the light reflectance of a specimen with the dark backing, and R(W) is the light reflectance of the specimen with the light backing.
These equations are used under the assump- tions that (1) the material is turbid, dull, and of constant finite thickness; (2) edges are neglected;
(3) optical inhomogeneities are much smaller than the thickness of the specimen and are distributed uniformly; and (4) illumination is homogeneous and diffused.
Scattering Coefficient
The scattering coefficient is the fraction of inci- dent light flux lost by reversal of direction in an
elementary layer. The scattering coefficient, S, for a unit thickness of a material is defined as follows:
S= 1/bX Arctgh 1−a R+Rg +RRg/b R−Rg mm−1
where X is the actual thickness of the specimen, Ar ctgh is an inverse hyperbolic cotangent, and R is the light reflectance of the specimen with the backing of reflectance, Rg.
The scattering coefficient varies with the wave- length of the incident light and the nature of the colorant layer, as shown in Fig. 4.35 for several shades of a resin composite. Composites with larger values of the scattering coefficient are more opaque.
Absorption Coefficient
The absorption coefficient is the fraction of incident light flux lost by absorption in an elementary layer.
The absorption coefficient, K, for a unit thickness of a material is defined as follows:
K=S(a−1) mm−1
The absorption coefficient also varies with the wavelength of the incident light and the nature of the colorant layer, as shown in Fig. 4.36 for several shades of a resin composite. Composites with larger values of the absorption coefficient are more opaque and more intensely colored.
Incident light (Io)
Superficial reflection
Back scattering
Transmission Scattering
(S)
Thickness
Absorption (K)
FIG. 4.34 Schematic of the possible interactions of light with a solid.
CO
0400 0.8 1.0 1.4 1.8
Scattering coefficient (mm1) 2.2 2.6
500 600
Wavelength (nm)
700 CL
CU CY CDY CT CG
FIG. 4.35 Scattering coefficient versus wavelength for shades of a composite, C. Shades are O, opaque; L, light; U, uni- versal; Y, yellow; DY, dark yellow; T, translucent; and G, gray.
(From Yeh CL, Miyagawa Y, Powers JM. Optical properties of compos- ites of selected shades. J Dent Res. 1982;61(6):797–801.)
Light Reflectivity
The light reflectivity, RI, is the light reflectance of a material of infinite thickness, and is defined as follows:
RI=a−b
This property also varies with the wavelength of the incident light and the nature of the colorant layer.
The light reflectivity can be used to calculate a thickness, XI, at which the reflectance of a mate- rial with an ideal black background would attain 99.9% of its light reflectivity. The infinite optical thickness, XI, is defined for monochromatic light as follows:
XI=(1/bS)Arctgh[(1−0.999aRI)/0.999bRI] mm The variation of XI with wavelength is shown in Fig. 4.37 for a resin composite. It is interesting that composites are more opaque to blue than to red light, yet blue light is used to cure light-activated composites.
Contrast Ratio
Once a, b, and S are obtained, the light reflectance (R) for a specimen of any thickness (X) in contact with a backing of any reflectance (Rg) can be calculated using the following formula:
R=[1−Rg(a−bctghbSX)]/(a+bctghbSX−Rg) An estimate of the opacity of a 1-mm-thick speci- men can then be calculated from the contrast ratio (C) as follows:
C=RO/R
where R0 is the computed light reflectance of the specimen with a black backing.
CU CT CL CG CY CO CDY
400 Absorption coefficient (mm1)
500
Wavelength (nm)
600 700
0.0 0.5 1.0 1.5 2.0
FIG. 4.36 Absorption coefficient versus wavelength for shades of a composite, C. Shades are DY, dark yellow; O, opaque;
Y, yellow; G, gray; L, light; T, translucent; and U, universal.
(From Yeh CL, Miyagawa Y, Powers JM. Optical properties of com- posites of selected shades. J Dent Res. 1982;61(6):797–801.)
400
Infinite optical thickness (mm)
500
Wavelength (nm)
600 700
0.0 2.5 5.0 7.5 10.0
CO CDY CG CY CL CT CU
FIG. 4.37 Infinite optical thickness versus wavelength for shades of a composite, C. Shades are U, universal; T, translucent; L, light; Y, yellow; G, gray; DY, dark yellow; and O, opaque.
(From Yeh CL, Miyagawa Y, Powers JM. Optical properties of composites of selected shades. J Dent Res.
1982;61(6):797–801.)
Masking Ability
Dental restorations are often used to resolve esthetic problems, even when carious lesions are not pres- ent. This is the case in patients presenting staining due to intrinsic or extrinsic factors (examples of which are staining by antibiotics and smoking hab- its, respectively) or in restorations where an opaque reinforcing structure is required, as in the case of metallic or highly crystalline ceramic posts. The masking ability of restorative materials depends on their optical constants, as previously described, and on their thickness. In Fig. 4.34 examples of materials with the same thickness but different optical prop- erties are shown against a black and white back- ground to demonstrate variations in the masking ability.