# The Difficulty of Measuring the Roughness of Glossy Surfaces Using the Triangulation Principle
## 1 Introduction
Their wider practical use will undoubtedly be supported not only by increasing demands on the accuracy and quality of the existing production technologies but also by the development of new materials and technological methods, such as nanotechnology, etc. [18]. The use of spatial surface inspection offers a demonstrably significant improvement in the properties of functional surfaces, as well as progress in production processes, e.g., energy savings, etc. Therefore, it is in the interest of the technical development of production and inspection technologies to create all the prerequisites for the comprehensive use of spatial surface evaluation in regular production and metrological practice [19]. Experimental setups for optical topography methods have a similar basic structure, which consists of an optical source (for easier setup and calibration of the experimental setup, a light source is often used, that is, an optical source shining at a wavelength of 380-760 nm), an optical detector and a measured object. The optical source generates a light beam that is projected onto the surface of the measured object through the so-called optical probe, which can be point, linear, area, or intense, and subsequently reflects and refracts. An optical detector, which usually consists of a camera with a CCD or CMOS sensor, captures the reflected light beam and generates an image that is subsequently processed and analyzed. Different surface analysis methods vary in the type of optical probe used and how it interacts with the surface being measured [20]. In various laboratory or industrial measurement applications, measuring and assessing objects' spatial form by the contactless measurement of their height or thickness of a 3D profile is essential. Laser profilometry is designed to carry out these tasks quickly and efficiently [21]. Contact-free measurement methods replace contact measurements of surfaces sensitive to mechanical damage, such as soft materials, etc. Contact-free measurement avoids damaging the measured surface, and the inspected surface is monitored by a focused measuring head. The program-controlled adjustment of the measuring head is quick and easy [1]. 3D profilometry using a laser is one of the most recently developed approaches to measure surface roughness, while pulse thermography is used to combine the effect of surface roughness with thermal radiometry [22]. Laser profilometry uses a well-known triangulation principle (Figure 2). The principle consists of the projection of a linear laser beam onto the measured object and the detection of its deformed image on the measured surface by a camera on the computer. The light source, the measured object, and the camera form a triangle whose parameters (distance of the camera and light source from the reference plane, their angle to the reference plane) are known. In this way, each scanned image can be used to create a real 3D profile [23]. The sought topographical deviation \(\Delta\)r is the distance of each point of the measured surface whose coordinates correspond to the pixels of the camera chip matrix from the reference plane. This topographic distance is determined by the relation  
\[\Delta\mathrm{r}=\frac{\Delta\mathrm{u}}{\mathrm{b}+\mathrm{a}\Delta\mathrm{u }}, \tag{1}\]  
where:  
\(\Delta\)r-- sought topographic deviation,  
\(\Delta\)u--the number of pixels on the matrix of the camera chip by which the display of the point is shifted during projection onto the reference plane and the measured point,  
a, b--parameters of the mapping algorithm, which can be calculated from the known parameters of the experimental setup or obtained from the calibration of this setup. The possibilities of profilometry do not end with the basic laser line-camera configuration. For example, a substantial increase in accuracy can be achieved in certain cases by using a projection grid instead of a line [11]. Laser profilometry is a non-contact optical method of measuring the profile of a scanned object surface, which then allows the creation of a 3D model of the object.