# Long-Distance Measurements Using a Chromatic Confocal Sensor
## 7 Conclusions  
In conclusion, our study demonstrates the practicality and effectiveness of integrating a chromatic confocal sensor into a fixed optical setup, emphasizing the optimization of both the illumination and the sensing components. By carefully selecting and calibrating the chromatic lenses, we achieved a 20-micrometer resolution over a significant distance of 620 mm, highlighting the system's adaptability for various applications. The development of a custom Python module further streamlined the sensor design process, eliminating the need for expensive commercial software. However, our experiments revealed an error margin of approximately 5% compared to the real data, underlining the importance of validating simulation results with empirical testing. Figure 14: Distance measured vs. distance displaced with 1000 interpolated points between real spectrum values. Error bars show three standard deviations. Figure 13: Distance measured vs. distance displaced with 10 interpolated points between real spectrum values. Error bars show three standard deviations. Our findings also show that oversampling effectively enhances the axial resolution without the need for high-resolution spectrometers, and low-pass filtering outperforms Gaus sian fitting in peak detection. Looking ahead, we aim to optimize the extension of the light source fiber optic output to minimize the spot size and further improve the axial resolution. Additionally, we will explore the use of positive and negative lenses to address the challenges associated with the wide measurement range of the primary chromatic lens. Furthermore, in long-distance measurements, environmental factors are crucial for obtaining reliable and accurate data. In the present work, these factors were not studied since the experiment was carried out in a temperature-controlled environment (less than 0.5 \({}^{\circ}\)C temperature variation). The current device has demonstrated its capability to measure the thickness of reflective samples, such as silicon wafers, and to track relative displacements. With proper calibration and the use of calibration curves, absolute distance measurements can also be achieved. By extending the working distance of chromatic confocal sensors from the typical range of hundreds of micrometers to tens of millimeters, as described by [PERSON] et al. [1], to around 600 nm, our method broadens the scope of applications for these sensors. Typically, confocal sensing offers the advantage of a wavelength versus distance response that is independent of the object's properties, whether reflective, diffuse, light, or dark. However, in our current work, the long working distance introduces challenges, such as a reduced sensitivity to low-reflectivity or diffuse surfaces. Although low reflectivity can be compensated by increasing exposure times, diffuse surfaces remain difficult to measure and would be an interesting subject for future characterization. The resolution is primarily influenced by three factors: noise in the light spectrum, meaning that a flat spectrum would ideally be preferable; spectrometer readout noise, which can be minimized by increasing the exposure times, an approach we attempted; and, most critically, the dispersion range of the main lens. These factors collectively impact the precision of the measurements. As discussed earlier, increasing the number of interpolation points between the real data reduces the positional uncertainty, as shown by the error bars in Figures 13 and 14, representing the standard deviation at each sample position. Thus, increasing the interpolation points infinitely will not increase the sensor's resolution further. These are physical limitations. Another limitation is the system's small tip/tilt tolerance of 0.38\({}^{\circ}\), which could easily be addressed by incorporating a tip/tilt stage to correct the sample orientation. This was not a primary focus of our study, as we concentrated on highly reflective and flat surfaces, such as silicon wafers and mirrors.