# Optical Coherence Tomography Investigations and Modeling of the Sintering of Ceramic Crowns

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Samples Preparation

**Group L**: with samples represented by crowns pressed at 840 °C, that is, 50 °C below the normal temperature of 890 °C prescribed by the manufacturer for these ceramics.

**Group N**: with samples represented by crowns pressed at the normal temperature of 890 °C.

**Group H**: with samples represented by crowns pressed at 940 °C, that is, 50 °C above the normal temperature. The choice of these temperature limits is based on our experience regarding the possible extreme variations of the sintering temperature inside the dental oven.

#### 2.2. In-House Developed MS/SS-OCT System

_{1}and DC

_{2}. DC

_{1}has a splitting ratio of 20/80, while DC

_{2}is a 50/50 balanced splitter that feeds a balance detection receiver balanced photo-detector (BPD) (Thorlabs, Newton, NJ, USA, model PDB460C). In the sample arm of the interferometer, the beam was collimated by the achromatic lens L

_{1}(focal length 15 mm), and conveyed towards a scanner head GXY made of two orthogonal galvanometer scanners (Cambridge Technology, Bedford, MA, USA, model 6115) and focused on the sample by the scanning lens, L

_{2}, (25 mm focal length). The optical power onto the sample was 2.2 mW, while the optical components in the sample arm determined a lateral resolution of 10 µm. The reference arm consisted of two collimating lenses, L

_{3}and L

_{4}, both similar to L

_{1}, as well as two flat mirrors (M

_{1}and M

_{2}) placed on a translation stage (TS). By adjusting the position of the TS, the optical path difference (OPD) in the interferometer can be adjusted.

#### 2.3. Image Processing

_{surface}), measured from the plane corresponding to OPD = 0 (Figure 3). All of the en-face images were acquired from a similar depth position, chosen at approximately z

_{en-face}= 0.375 mm (distance measured in air) from the top of the vestibular surface of each sample in the B-scan image (Figure 3).

_{en-face}= 0.375 mm is capable of providing a good reflectivity signal in order to characterize the granulation in the en-face OCT image acquired from inside the material. The larger the depth, the less the signal backscattered due to the absorption and scattering in the sample. The depth of z

_{en-face}= 0.375 mm was selected as a compromise between the loss of signal and the granulation dependence on the curvature of the top surface. We thus ensured, as the optical power on the sample was kept constant, that any change in the image brightness of the sample was only due to the changes in its optical properties, and not to the differences due to the different investigation depths inside the samples or to the shape of the teeth prostheses if the investigations were made at their (uneven) surface.

## 3. Results

#### 3.1. OCT Imaging

**Group L**: samples sintered at 840 °C (i.e., 50 °C below the normal temperature prescribed by the manufacturer). In the en-face OCT image in Figure 4(a1), a decrease in reflectivity can be seen with regard to the Group N in Figure 4(b1); also, band-like shapes with alternations between more and less reflective areas can be noticed, even if the non-reflective area is wider spread. These findings can be easily processed on the images processed using MATLAB (Figure 4(b2)).

**Group N**: with samples sintered at the normal temperature prescribed by the manufacturer, (i.e., 890 °C). From the en-face OCT image in Figure 4(b1), the reflectivity has a much more normal distribution than for the other two groups (Figure 4(a1,c1)); however, a slight alternation of more reflective with not-so reflective areas can be spotted on all of the similar samples. This can also be seen in the MATLAB processed image shown in Figure 4(b2), obtained from averaging the reflectivity values along the y-axis for each x position (as explained in Section 2.3).

**Group H**: with samples sintered at 940 °C (i.e., 50 °C above the normal temperature). An even stronger alternation between the reflective and non-reflective areas, with a decreasing trend in width can be noticed in both the en-face OCT image (Figure 4(c1)), and in the profile obtained using MATLAB (Figure 4(c2)); also, particularly bright spots with regard to Group N are seen. Temperature affects sintering as a result of the temperature-dependence of the viscosity of silicates [35,36,37,38,39]. Thus, increasing the sintering temperature for dental porcelain leads to several consequences, namely: a decreased apparent specific density of the fired porcelain because of an increased volume; an increased total porosity; an increase of the average size of the pore; fewer but larger, and also more spherical pores, under the influence of surface tension; an increased liquid content, as bubbles in the compact expand when the viscosity decreases to a certain level by increasing the temperature; and losses of the surface detail, as there is a marked increase in the pyroplastic flow of the porcelain (thus the material may appear glassy and often takes on the greenish tinge of natural glass).

#### 3.2. Modeling of the OCT Reflectivity Curves—For Dental Pressed Ceramics

^{2}ρ/dx

^{2}. The gradients are also shown in Figure 6(a3,b3,c3), for the considered parabolic functions.

#### 3.3. Modeling of the OCT Reflectivity Curves—For Metal Ceramic Prostheses

^{2}ρ/dx

^{2}were obtained in Table 4 and Table 5, and the gradients also in Figure 6(a3,b3).

^{2}ρ/dx

^{2}are obtained in Table 6, with the gradient also being shown in Figure 8(b3).

^{2}ρ/dx

^{2}= 0.

## 4. Discussion

- Referring to the OCT investigations:

- The reflectivity profiles in Figure 4(a2,b2,c2) are used to complete this assessment. Based on these profiles, several remarks can be made, as follows:

_{surface}plane (Figure 3), and thus to the plane of the en-face OCT image).

_{min}, and as the extreme one (ρ

_{min})

_{peak}, clearly indicates a lower-than-normal oven temperature (Group L, Figure 6(a1,a2)). However, this indicator is not sufficient to draw a correct decision in terms of the temperature. It has to be correlated with other aspects, as for Group H, both values, ρ

_{min}and (ρ

_{min})

_{peak}are close to those for Group N (Figure 6(b1,b2)).

_{max}and (ρ

_{max})

_{peak}, have little relevance to distinguish between Group N and the other groups, as can be seen from their fluctuations in both Table 7 and Table 8 (i.e., for both materials).

_{peak}also grow—see Table 7 and Table 8 (however, with a slight decrease for Group H50 in Table 8). In Equations (2) and (3), (ρ

_{min})

_{peak}and (ρ

_{max})

_{peak}were obtained by (also) considering the small, high spatial frequency variations of the reflectivity ρ, (i.e., the envelopes of reflectivity profiles, in Figure 6, Figure 7 and Figure 8). They can be therefore influenced by issues such as the noise or different attenuations produced by different layers of materials on top of the considered en-face image. In contrast, ρ

_{min}and ρ

_{max}are obtained by considering the minimum and the maximum values of the averaged graphs of ρ(x).

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Dental Pressed Ceramics: Modeling of the Reflection Curves

#### Appendix A.1.1. Group L: Dental Pressed Ceramics

^{−2}; b = −33.33 mm

^{−1}; c = 60.

^{−2}; b = −16.33 mm

^{−1}; c = 69.53.

#### Appendix A.1.2. Group N: Dental Pressed Ceramics

^{2}; b = 24 mm; c = 60. The value of the function in x

_{i}is also obtained, as follows:

_{i}≈ 70.

^{−2}; b = −41.6 mm

^{−1}; c = 127.6.

#### Appendix A.1.3. Group H: Dental Pressed Ceramics

^{−2}; b = 42.85 mm

^{−1}; c = 60. Also, from Figure 6(c2), f(0) = ρ

_{0}= f(x

_{i}) and f′(0) = −f′(x

_{i}) = 42.85 mm

^{−1}.

_{m}, which is done from the supplemental condition, as follows:

_{m}= 2.33 mm. Using this value, the parameters in Figure 6(b3), and Equation (A13), one has the following: a = 23.12 mm

^{−2}; b = −107.76 mm

^{−1}; c = 170.5. The exact value of g(x

_{max}) is also obtained, that is, 64.57.

## Appendix B

#### Appendix B.1. Metal Ceramic Prostheses: Modeling of the Reflection Curves

#### Appendix B.1.1. Group L100: Metal Ceramic Prostheses

^{−2}, b = −10.07 mm

^{−1}, c = 27.7, while g(x

_{i}) = g(x

_{max}) = −0.59 mm

^{−1}.

#### Appendix B.1.2. Group L30: Metal Ceramic Prostheses

^{−2}; b = 10 mm

^{−1}; c = 25. Also using Figure 7(b2), one has the following: f(0) = ρ

_{0}and f′(0) = −f′(2x

_{M}) = 10 mm

^{−1}.

#### Appendix B.1.3. Group H30: Metal Ceramic Prostheses

^{−2}; b = −11.08; c = 31.

^{−2}, b = 10.22 mm

^{−1}, c = 61.

^{−2}, b = 55.38 mm

^{−1}, c = 55.3.

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**Figure 1.**Aspects from the samples preparation: (

**a**) making of the wax ups; (

**b**) pressed ingots used in the study; (

**c**) positioning of dental material in the oven in order to press the ceramic ingot; (

**d**) ceramic pressing procedure; (

**e**) example of a final dental ceramic crown.

**Figure 2.**In-house developed Master Slave (MS)/swept source (SS)-optical coherence tomography (OCT) system. Components: SS—swept source; DC

_{1,2}single mode directional couplers (20/80 and 50/50, respectively); GXY dual axis XY galvanometer scanner; L

_{1–4}, achromatic lenses; BPD—balanced photo-detector; TS—translation stage.

**Figure 3.**Example of an OCT B-scan/cross-section to show the method of selection of the depth from where the en-face images were selected. For all of the samples, their outer surface at z

_{surface}was adjusted with respect to OPD = 0, to produce all of the en-face OCT images (for all samples) from a similar depth (z

_{en-face}).

**Figure 4.**Examples of the OCT study of the samples pressed at different temperatures: (

**a1**–

**a3**), Group L: sample pressed at 840 °C (50 °C below the normal temperature). (

**b1**–

**b3**), Group N: sample pressed at the normal temperature of 890 °C, prescribed by the manufacturer. (

**c1**–

**c3**), Group H: sample pressed at 940 °C (50 °C above the normal temperature). Steps of the analysis: Row (

**1**), en face OCT image of the sample; Row (

**2**), MATLAB processing of the en face OCT image; Row (

**3**), B-scan (cross-section) OCT image—with the yellow line marking the sectioning plane used to obtain the en face OCT image (taken at a constant depth in the sample, considered from the zero OPD).

**Figure 5.**Examples of OCT B-scans/cross-sections of samples from the three groups considered in the study: (

**a**) Group L; (

**b**), Group N; (

**c**) Group H. Material defects and margins of the pressed ceramic core can be remarked.

**Figure 6.**(

**a1**–

**a3**), reflectivity profiles obtained using MATLAB from the en-face OCT images in Figure 4—for pressed ceramic. Row (

**2**): reflectivity graphs, obtained as averages of these reflectivity graphs. Row (

**3**): gradient of the reflectivity, obtained from Appendix A.1.1, Appendix A.1.2 and Appendix A.1.3, as well as shown in Table 1, Table 2 and Table 3, respectively. Column (

**a**), Group L: sample pressed at 840 °C (50 °C below the normal temperature). (

**b1**–

**b3**), Group N: sample pressed at the normal temperature of 890 °C, prescribed by the manufacturer. (

**c1**–

**c3**), Group H, sample pressed at 940 °C (50 °C above the normal temperature).

**Figure 7.**Row (

**1**): reflectivity profiles extracted from our previous work [11] (reproduced with permission from MDPI) from en-face OCT images for metal ceramic dental prostheses. Rows (

**2**) and (

**3**): reflectivity graphs (i.e., averages of the reflectivity profiles) and gradient of the reflectivity, respectively, obtained from Appendix B.1.1 and Appendix B.1.2, and shown in Table 4 and Table 5. (

**a1**–

**a3**), Group L100: for the sample pressed at 830 °C (100 °C below the normal temperature). (

**b1**–

**b3**), Group L30: for the sample pressed at 900 °C (30 °C below the normal temperature). (

**c1**–

**c3**), Group N: for the sample pressed at the normal temperature of 930 °C, prescribed by the manufacturer.

**Figure 8.**Row (

**1**): reflectivity profiles, extracted from our previous work [11] (reproduced with permission from MDPI) from en-face OCT images for metal ceramic dental prostheses. Rows (

**2**) and (

**3**): reflectivity graphs (i.e., averages of the reflectivity profiles) and gradient of the reflectivity, respectively, obtained from Appendix B.1.3 and in the text, as well as shown in Table 6, for Group H30. (

**a1**–

**a3**), Group N: for the sample pressed at the normal temperature of 930 °C, prescribed by the manufacturer. (

**b1**–

**b3**), Group H30: for the sample pressed at 960 °C (30 °C above the normal temperature). (

**c1**–

**c3**), Group H50: for the sample pressed at 980 °C (50 °C above the normal temperature).

x | $\left[0,{x}_{m}\right)=\left[0,1.5\right)$ | $\left[{x}_{m},{x}_{\mathrm{max}}\right)=\left[1.5,3.25\right)$ |

ρ(x) | $f(x)=\frac{\left({\rho}_{0}-{\rho}_{\mathrm{min}}\right)}{{x}_{m}}\left(\frac{{x}^{2}}{{x}_{m}}-2x\right)+{\rho}_{0}$ | $\begin{array}{l}g(x)=\frac{{\rho}_{\mathrm{max}}-{\rho}_{\mathrm{min}}}{{\left({x}_{\mathrm{max}}-{x}_{m}\right)}^{2}}x\left(x-2{x}_{m}\right)+\\ +\frac{{\rho}_{\mathrm{min}}\left({x}_{\mathrm{max}}-2{x}_{m}\right){x}_{\mathrm{max}}-{\rho}_{\mathrm{max}}{x}_{m}^{2}}{{\left({x}_{\mathrm{max}}-{x}_{m}\right)}^{2}}\end{array}$ |

$f(x)=11.11{x}^{2}-33.33x+60$ | $g(x)=15.35{x}^{2}-16.33x+69.53$ | |

dρ/dx | ${f}^{\prime}(x)=2\frac{\left({\rho}_{0}-{\rho}_{\mathrm{min}}\right)}{{x}_{m}}\left(\frac{x}{{x}_{m}}-1\right)$ | ${g}^{\prime}(x)=2\frac{{\rho}_{\mathrm{max}}-{\rho}_{\mathrm{min}}}{{\left({x}_{\mathrm{max}}-{x}_{m}\right)}^{2}}\left(x-{x}_{m}\right)$ |

${f}^{\prime}(x)=22.22\cdot x-33.33$ | ${g}^{\prime}(x)=30.7\cdot x-16.33$ | |

d^{2}ρ/dx^{2} | ${f}^{\u2033}(x)=2\frac{\left({\rho}_{0}-{\rho}_{\mathrm{min}}\right)}{{x}_{m}^{2}}=22.22\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${g}^{\u2033}(x)=2\frac{{\rho}_{\mathrm{max}}-{\rho}_{\mathrm{min}}}{{\left({x}_{\mathrm{max}}-{x}_{m}\right)}^{2}}=30.7\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ |

x | $\left[0,{x}_{i}\right)=\left[0,2\right)$ | $\left[{x}_{i},{x}_{\mathrm{max}}\right)=\left[2,3.25\right)$ |

ρ(x) | $f(x)=\frac{{\rho}_{\mathrm{max}}-{\rho}_{0}}{{x}_{M}}\left(-\frac{{x}^{2}}{{x}_{M}}+2x\right)+{\rho}_{0}$ | $\begin{array}{l}g(x)=\frac{{\rho}_{i}-{\rho}_{0}}{{\left({x}_{\mathrm{max}}-{x}_{i}\right)}^{2}}x\left(x-2{x}_{\mathrm{max}}\right)+\\ +\frac{{\rho}_{i}{x}_{\mathrm{max}}^{2}-{\rho}_{0}\left(2{x}_{\mathrm{max}}-{x}_{i}\right){x}_{i}}{{\left({x}_{\mathrm{max}}-{x}_{i}\right)}^{2}}\end{array}$ |

$f(x)=-9.6{x}^{2}+24x+60$ | $g(x)=6.4{x}^{2}-41.6x+127.6$ | |

dρ/dx | ${f}^{\prime}(x)=2\frac{{\rho}_{\mathrm{max}}-{\rho}_{0}}{{x}_{m}}\left(-\frac{x}{{x}_{M}}+1\right)$ | ${g}^{\prime}(x)=2\frac{{\rho}_{i}-{\rho}_{0}}{{\left({x}_{\mathrm{max}}-{x}_{i}\right)}^{2}}\left(x-{x}_{\mathrm{max}}\right)$ |

${f}^{\prime}(x)=-19.2\cdot x+24$ | ${g}^{\prime}(x)=12.8\cdot x-41.6$ | |

d^{2}ρ/dx^{2} | ${f}^{\u2033}(x)=-2\frac{\left({\rho}_{\mathrm{max}}-{\rho}_{0}\right)}{{x}_{m}^{2}}=-19.2\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${g}^{\u2033}(x)=2\frac{{\rho}_{i}-{\rho}_{0}}{{\left({x}_{\mathrm{max}}-{x}_{i}\right)}^{2}}=12.8\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ |

x | $\left[0,{x}_{i}=2{x}_{M}\right)=\left[0,1.4\right)$ | $\left[{x}_{i},{x}_{\mathrm{max}}\right)=\left[1.4,3.25\right)$ |

ρ(x) | $f(x)=\frac{{\rho}_{\mathrm{max}}-{\rho}_{0}}{{x}_{M}}\left(-\frac{{x}^{2}}{{x}_{M}}+2x\right)+{\rho}_{0}$ | $\begin{array}{l}g(x)=\frac{{\rho}_{0}-{\rho}_{\mathrm{min}}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}x\left(x-2{x}_{m}\right)+\\ +\frac{{\rho}_{0}{x}_{m}^{2}+4{\rho}_{\mathrm{min}}\left(2{x}_{m}-{x}_{M}\right){x}_{M}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}\end{array}$ |

$f(x)=30.61{x}^{2}-42.85x+60$ | $g(x)=23.12{x}^{2}-107.76x+170.5$ | |

dρ/dx | ${f}^{\prime}(x)=2\frac{{\rho}_{\mathrm{max}}-{\rho}_{0}}{{x}_{m}}\left(-\frac{x}{{x}_{M}}+1\right)$ | ${g}^{\prime}(x)=2\frac{{\rho}_{o}-{\rho}_{\mathrm{min}}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}\left(x-{x}_{m}\right)$ |

${f}^{\prime}(x)=61.22\cdot x-42.85$ | ${g}^{\prime}(x)=46.24\cdot x-107.76$ | |

d^{2}ρ/dx^{2} | ${f}^{\u2033}(x)=-2\frac{\left({\rho}_{\mathrm{max}}-{\rho}_{0}\right)}{{x}_{m}{x}_{M}}=30.61\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${g}^{\u2033}(x)=2\frac{{\rho}_{0}-{\rho}_{\mathrm{min}}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}=46.24\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ |

x | $\left[0,{x}_{i}\right)=\left[0,1\right)$ | $\left[{x}_{i},{x}_{\mathrm{max}}\right)=\left[1,3.25\right)$ |

ρ(x) | $f(x)=\frac{{\rho}_{i}-{\rho}_{0}}{{x}_{i}^{2}}{x}^{2}+{\rho}_{0}$ | $\begin{array}{l}g(x)=\frac{4({\rho}_{i}-{\rho}_{\mathrm{min}})x(x-{x}_{i}-{x}_{\mathrm{max}})}{{\left({x}_{\mathrm{max}}-{x}_{i}\right)}^{2}}+\\ +\frac{{\rho}_{i}{\left({x}_{i}+{x}_{\mathrm{max}}\right)}^{2}-4{\rho}_{\mathrm{min}}{x}_{i}{x}_{\mathrm{max}}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}\end{array}$ |

$f(x)=3{x}^{2}+27$ | $g(x)=2.37{x}^{2}-10.07x+361.25$ | |

dρ/dx | $f(x)=2\frac{{\rho}_{i}-{\rho}_{0}}{{x}_{i}^{2}}x$ | ${g}^{\prime}(x)=2\frac{{\rho}_{o}-{\rho}_{\mathrm{min}}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}\left(x-{x}_{m}\right)$ |

${f}^{\prime}(x)=6x$ | ${g}^{\prime}(x)=4.74\cdot x-10.07$ | |

d^{2}ρ/dx^{2} | ${f}^{\u2033}(x)=6\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${g}^{\u2033}(x)=2\frac{{\rho}_{0}-{\rho}_{\mathrm{min}}}{{\left(2{x}_{M}-{x}_{m}\right)}^{2}}=2.37\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ |

x | $\left[0,{x}_{i}\right)=\left[0,1\right)$ | $\left[{x}_{i},{x}_{\mathrm{max}}\right)=\left[1,3.25\right)$ |

ρ(x) | $f(x)=\frac{{\rho}_{i}-{\rho}_{0}}{{x}_{i}^{2}}{x}^{2}+{\rho}_{0}$ | $g(x)={\rho}_{0}$ |

$f(x)=3{x}^{2}+27$ | $g(x)=25$ | |

dρ/dx | ${f}^{\prime}(x)=2\frac{{\rho}_{i}-{\rho}_{0}}{{x}_{i}^{2}}x$ | ${g}^{\prime}(x)=0$ |

${f}^{\prime}(x)=6x$ | ||

d^{2}ρ/dx^{2} | ${f}^{\u2033}(x)=6\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${g}^{\u2033}(x)=0$ |

x | $\left[0,\frac{{x}_{\mathrm{max}}}{3}\right)=\left[0,1.08\right)$ | $\left[\frac{{x}_{\mathrm{max}}}{3},\frac{2{x}_{\mathrm{max}}}{3}\right)=\left[1.08,2.17\right)$ | $\left[\frac{2{x}_{\mathrm{max}}}{3},{x}_{\mathrm{max}}\right)=\left[2.17,3.25\right)$ |

ρ(x) | $f(x)=\frac{12A}{{x}_{\mathrm{max}}^{2}}x\left(3x-{x}_{\mathrm{max}}\right)+{\rho}_{0}$ | $g(x)=\frac{36A}{{x}_{\mathrm{max}}^{2}}x\left(x-{x}_{\mathrm{max}}\right)+{\rho}_{0}+10A$ | $h(x)=\frac{6A}{{x}_{\mathrm{max}}^{2}}x\left(3x-10{x}_{\mathrm{max}}\right)+{\rho}_{0}+24A$ |

$f(x)=10.22{x}^{2}-11.08x+31$ | $g(x)=-10.22{x}^{2}-10.22x+61$ | $h(x)=10.22{x}^{2}+55.38x+55.3$ | |

dρ/dx | ${f}^{\prime}(x)=20.44x-11.08$ | ${g}^{\prime}(x)=-20.44x-10.22$ | ${h}^{\prime}(x)=20.44x+55.38$ |

d^{2}ρ/dx^{2} | ${f}^{\u2033}(x)=20.44\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${g}^{\u2033}(x)=-20.44\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ | ${h}^{\u2033}(x)=20.44\phantom{\rule{4.pt}{0ex}}{\mathrm{mm}}^{-2}$ |

The notation ${\rho}_{0}-{\rho}_{\mathrm{min}}={\rho}_{\mathrm{max}}-{\rho}_{0}=A$ in Figure 8(b2) was used. |

**Table 7.**Parameters of the reflectivity profiles, graphs, and functions—for pressed ceramic dental prostheses.

Parameter (Figure 6) | Group L | Group N | Group H |
---|---|---|---|

(ρ_{min})_{peak} | 34 | 58 | 41 |

(ρ_{max})_{peak} | 84 | 91 | 89 |

Δρ_{peaks} = (ρ_{max})_{peak} − (ρ_{min})_{peak} | 50 | 33 | 48 |

k_{peaks} = (ρ_{max})_{peak}/(ρ_{min})_{peak} | 2.47 | 1.57 | 2.17 |

ρ_{min} | 35 | 60 | 41 |

ρ_{max} | 82 | 85 | 89 |

Δρ = ρ_{max} − ρ_{min} | 47 | 15 | 48 |

k = ρ_{max}/ρ_{min} | 2.34 | 1.42 | 2.17 |

(dρ/dx)_{max} = max{|f′(x)|, |g′(x)|} | 53.71 | 24 | 42.86 |

(d^{2}ρ/dx^{2})_{max} = max{|f″(x)|, |g″(x)|} | 30.69 | 19.2 | 61.22 |

**Table 8.**Parameters of the reflectivity profiles, graphs, and functions—for metal ceramic dental prostheses.

Parameter (Figure 7 and Figure 8) | Group L100 | Group L30 | Group N | Group H30 | Group H50 |
---|---|---|---|---|---|

(ρ_{min})_{peak} | 16 | 27 | 21 | 26 | 19 |

(ρ_{max})_{peak} | 28 | 34 | 32 | 38 | 34 |

Δρ_{peaks} = (ρ_{max})_{peak} − (ρ_{min})_{peak} | 12 | 7 | 11 | 12 | 15 |

k_{peaks} = (ρ_{max})_{peak}/(ρ_{min})_{peak} | 1.75 | 2 | 1.52 | 1.46 | 1.79 |

ρ_{min} | 17 | 25 | 25 | 26 | 19 |

ρ_{max} | 27 | 32 | 25 | 43 | 34 |

Δρ = ρ_{max} − ρ_{min} | 10 | 7 | 0 | 17 | 15 |

k = ρ_{max}/ρ_{min} | 1.59 | 1.28 | 1 | 1.65 | 1.79 |

(dρ/dx)_{max} = max{|f′(x)|, |g′(x)|} | 14.81 | 10 | 0 | 11.08 | 2.77 |

(d^{2}ρ/dx^{2})_{max} = max{|f″(x)|, |g″(x)|} | 14 | 10 | 0 | 20.44 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Duma, V.-F.; Sinescu, C.; Bradu, A.; Podoleanu, A.
Optical Coherence Tomography Investigations and Modeling of the Sintering of Ceramic Crowns. *Materials* **2019**, *12*, 947.
https://doi.org/10.3390/ma12060947

**AMA Style**

Duma V-F, Sinescu C, Bradu A, Podoleanu A.
Optical Coherence Tomography Investigations and Modeling of the Sintering of Ceramic Crowns. *Materials*. 2019; 12(6):947.
https://doi.org/10.3390/ma12060947

**Chicago/Turabian Style**

Duma, Virgil-Florin, Cosmin Sinescu, Adrian Bradu, and Adrian Podoleanu.
2019. "Optical Coherence Tomography Investigations and Modeling of the Sintering of Ceramic Crowns" *Materials* 12, no. 6: 947.
https://doi.org/10.3390/ma12060947