# Long-Distance Measurements Using a Chromatic Confocal Sensor
## 5 Calibration  
To enhance the quality of the measurements, the chromatic confocal sensor must be calibrated by establishing a calibration curve. This calibration curve serves as a reference standard, enabling the straightforward tracking of sample displacement by correlating spectral changes with known displacements.  
The calibration procedure consisted of mounting a 50 mm diameter flat mirror on a linear translation stage. The sample was positioned at 620 mm from the aspheric lens, and a total distance of 800 \(\upmu\)m was scanned with a step size of 20 \(\upmu\)m.  
The experiment was carried out in a dark room environment, and the exposure time was set to 200 ms to ensure the optimal conditions for measurement accuracy. To increase the repeatability of the measurement, 3000 spectra were acquired for each sample position. These displacements were carried out in the direction opposite to the lens, resulting in the anticipated movement of tracked peaks towards longer wavelengths.  
This calibration step also works as a validation of the provided simulator software; for this, we simulated the same setup used for calibration. The comparison of calibration curves, both experimental and simulated, reveals a similarity, as depicted in Figure 11, and Table 2 provides a comparison of the slopes of both curves, indicating an estimated difference of 5%. It is important to note that the simulated spectra exhibit an infinite signal-to-noise ratio (SNR), and the extent of the light source is negligible; the spectral resolution was down-sampled by a factor of five, and the number of rays used was 220,000, suggesting potential areas for simulation enhancement. However, these findings suggest that the module serves as a reliable initial step in the design of a chromatic confocal sensor.  
The discrepancy between the real and simulated data, apart from those mentioned above, is mainly due to the position of the sample inside the working range. As shown  
\begin{table}
\begin{tabular}{c c c} \hline  & **Slope** & **R-Squared** \\ \hline Simulated & 0.00129 & 0.994 \\ \hline Real & 0.00137 & 0.996 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of fitter lines over real and experimental data.  
Figure 11: Two calibration lines: simulated (blue) and experimental (orange).  
in Figure 5, we can clearly see that the spacing between the foci of shorter wavelengths is bigger than the spacing between the ones of higher wavelengths. Furthermore, it is worth noting that if we are in the range of higher wavelengths and if we go through a sufficiently small range, we can approximate the calibration curve to a straight line.  
Moreover, the wavelengths are normalized because the detected peak wavelength does not match the one in the real data, which is due to the coatings of the lenses, which will strongly affect the transmitted intensity of each wavelength and, therefore, the detected wavelength peak, and it is not considered in the simulation.  
Lastly, we only aimed at the region where the biggest sensitivity had been achieved experimentally. Furthermore, the motive of this work was to measure the thickness of a silicon wafer from a long distance. The thickness of a single wafer is around 775 \(\upmu\)m, which is the reason for the small range of 800 \(\upmu\)m being used inside the working range.