# Long-Distance Measurements Using a Chromatic Confocal Sensor
## 1 Introduction  
Accurate distance measurement is paramount in industrial settings, serving diverse applications such as manufacturing, optical metrology, robotics, and quality control. Various methods are available to measure distance and displacement, surface profiles, and vibrations [1]. The widely used methods for distance measurement include intensity-based sensors [2], triangulation sensors [3], time-of-flight sensors [4], confocal sensors [5; 6; 7; 8; 9; 10; 11], and interferometric sensors [12; 13; 14]. These techniques offer high precision, rapid response times, and non-contact measurement, enabling efficient and precise operations without direct interaction with the target. Among the methods mentioned above, only interferometry and chromatic confocal sensors can achieve a precision finer than one micrometer, providing extremely high resolution measurements [1; 6; 12]. The main disadvantage of interferometric sensors is that they are susceptible to slight motion and vibration [15]. Chromatic confocal sensors can be divided into two types: monochromatic confocal sensors [16; 17] and polychromatic confocal sensors [5; 6; 7; 8; 9; 11]. Their functionality is based on the well-known confocal microscopy, in which the narrow light from an aperture is focused on the sample and the scattered or reflected light after passing a pinhole is detected by a sensor. By applying an aperture, the out-of-focus light is rejected and the maximum intensity is obtained from the image plane [18]. Monochromatic sensors use a single wavelength, primarily a laser, illuminating the target with a small spot, and the reflected beam is gathered through a pinhole. The object's surface profile is constructed by scanning the entire sample surface and obtaining the intensity of the spots. In contrast, the polychromatic sensor uses a broadband light source. The light is focused on the sample using a chromatic lens. The sensor collects the spectrum of the light reflected by the sample; provided that the spectrum profile changes accordingly to the distance to the sample, the change in distance from the sensor to the sample canbe related to changes in the spectrum's peak. Polychromatic sensors are devices for the accurate measurement of the depth and topography of an object, even when the object contains various materials and colors. [PERSON] et al. [19] have developed a fast chromatic confocal sensor that is capable of working on different reflective surfaces. A similar work was done by [PERSON] et al. [20], in which they managed to measure the surface of non-specular reflective surfaces with an axial resolution of about 130 \(\upmu\)m.  
A key comparison in high-precision optical measurement lies between laser interferometry and confocal sensing, as both methods offer excellent resolution and working distance ratios, typically in the micrometer range [1]. Although laser interferometry can achieve a sub-nanometric resolution and accommodate larger working distances, confocal sensors present several advantages. Confocal sensing is more robust against vibrations, requires simpler calibration, and involves a less complex setup. Moreover, while this work primarily focuses on relative measurements, confocal sensors have the potential to provide absolute distance measurements by linking focus distances for different wavelengths with a calibration curve. In contrast, laser interferometry is generally more suited for displacement monitoring, rather than absolute distance measurement, making confocal sensing a versatile alternative in applications requiring precise distance tracking, such as industrial manufacturing [21]. Most works on confocal sensors in the recent literature have focused on working distances below 50 mm [22; 23]. In this study, we present the development of a polychromatic confocal sensor that employs a robust algorithm to measure the relative displacement of the sample.