Mechanical and Thermal Measurements by Images and Waves

The fundamentals of analogic image formation through optical components such as lenses, objectives, mirrors, and prisms are presented. Using the principles of geometric optics and ray tracing, classical mathematical models are derived to describe the typical transformation of coordinates from a three-dimensional real object space to its two-dimensional image on the camera's image plane. The main concepts and techniques employed in analog image processing systems are discussed, with a focus on their role in measurement applications. Essential criteria for selecting camera objectives and ensuring proper analog image generation useful for measurement purposes are also outlined.

Analog images represent the intensity distribution of electromagnetic waves within the visible spectrum, specifically wavelengths ranging from 0.4 to 0.7 μm, commonly referred to as light. These waves can also be interpreted as a flux of energy packets named photons. In the previous chapter, we explored how to select appropriate optical components to accurately project analog images onto a plane, for measurements purposes. To convert the incoming photon flux at this plane into electrical signals, and subsequently into a two-dimensional digital output (a numerical matrix), the most commonly used devices are photodiodes. These are typically arranged in arrays, such as Charge-Coupled Devices (CCD) or Complementary Metal–Oxide–Semiconductor (CMOS) sensors array. This chapter focuses on the processes of image sampling and quantization as performed by these sensor arrays. Furthermore, spatial Fourier transform and convolution operations applied to two-dimensional signals (i.e., the image matrices) are discussed. These mathematical tools are essential for determining the optimal sensor array parameters needed to achieve high-quality digitization of analog images for measurement purposes.

From high-quality analogue images that are properly digitized, many dimensional and shape-related measurements can be extracted using image processing techniques. These measurements play a crucial role across various domains, including the verification of dimensional tolerances in mechanical components, quality control in industrial manufacturing, support for civil engineering applications, and processes such as product design and reverse engineering. Additional applications extend to medical diagnostics, physical and materials analysis, precision agriculture, the development of digital twins, and the documentation and study of artworks. This chapter presents the foundational principles of performing 2D measurements through image-based methods. It addresses critical elements such as appropriate lighting strategies, core image processing algorithms for edge detection, and procedures for computing distances between points along edges to determine object dimensions. Furthermore, it explores techniques for detecting and analyzing key points, often referred to as blobs, examining their features, characteristic “signatures,” shapes, and classical geometric descriptors.

In this chapter, we present the fundamental principles behind the most used classical and modern techniques for measuring the 3D shape of objects or surrounding scenes using 2D image processing and structured light. These principles form the basis of what are widely known as optical “scanners”. Over the past few decades, these systems have significantly advanced in terms of measurement range (from small to very large objects), resolution, and measurement uncertainty. As a result, they have enabled a wide array of applications across various sectors. These include industrial use cases such as reverse engineering, quality assurance, and tolerance control of products and mechanical components. They are also applied to large-scale measurements, such as capturing the geometry of entire cars, ships, aircraft, and their parts; mapping buildings, bridges, and natural landscapes; and documenting cultural heritage through the 3D digitization of artworks, statues, monuments, and historical sites, for purposes of visualization, conservation, and restoration. The chapter discusses both active techniques (which use structured light) and passive techniques (which rely on natural illumination), alongside key image processing methods. These techniques enable the extraction of (x, y, z) coordinates for millions of surface points, collectively referred to as a point cloud. This point cloud forms the foundation for creating mathematical surface models and geometric primitives, measuring dimensional properties, comparing against CAD models, developing new models, or replicating objects through 3D printing, including scaled versions.

In this chapter, the principles of 3D shape measurement are presented, focusing on techniques that utilize various types of wave-based scanning. These methods operate by analyzing how waves, such as electromagnetic, ultrasonic, light or X-rays, are reflected or transmitted through objects. Today, such techniques are widely employed to reconstruct the three-dimensional geometry of objects and environments. Additionally, tomographic imaging using mainly but not only X-rays enables the non-contact acquisition of 3D volumetric data from within an object. All of these methods rely on the fundamental physical interactions between waves and matter, as introduced in Chap. 1. This chapter provides a deeper description of the key components involved in measurement systems and the data processing algorithms used. The aim is to enhance the reader’s understanding of the core principles, capabilities, and limitations of these 3D scanning techniques.

The fundamentals and applications of image generation and processing to measure displacement, velocity and deformation field on the surfaces of rigid and elastic solid bodies are here described. Those measurement techniques are widely applied in fields such as experimental mechanics, robotics, structural components optimization, qualification and analysis, as well as in material and component testing. Many of these techniques are based on bidimensional image cross-correlation and feature traking, known as Digital Image Correlation (DIC), are based on optical flow analysis, or on the use of fiducial markers placed on the object's surface where displacement and velocity can be measured. Many of these techniques, such as Digital Image Correlation (DIC), are based on bidimensional image cross-correlation and feature tracking, on optical flow analysis, or on the use of fiducial markers placed on the object's surface, where displacement and velocity can be measured. Illumination with polarized light of birefringent materials, such as mechanical components, specimens, or coating layers subjected to stress and deformation, can also be used to measure stress and strain fields through image analysis of polarized light. This technique is known as Photoelasticity. Interference patterns generated by laser illumination of a surface and its reflection combined with a reference light beam form the basis of highly sensitive surface deformation measurement techniques, such as Electronic Speckle Pattern Interferometry (ESPI), Shearography, and Speckle Interferometry.

This chapter presents the fundamental concepts, devices and techniques underlying the measurement of temperature fields through infrared radiation detection. It introduces the primary physical principles governing infrared emission, including Planck’s and Stefan–Boltzmann’s laws, and discusses the role of emissivity and infrared optics, along with the key components of a thermal camera. The performance characteristics of thermographic systems are described, with guidance on selecting and using them appropriately for surface temperature distribution measurements. Dynamic thermography enables the detection not only of steady-state temperature fields but also of temporal fluctuations, capturing a “temperature video” that can reveal subsurface defects and surface stress fields. The chapter illustrates the main techniques for stress field measurement using dynamic and differential thermography and highlights a range of applications in experimental mechanics, structural component qualification, model validation, and beyond.

In this chapter, we describe an interferometric measurement technique based on the use of laser beams and the Doppler effect, along with its two primary applications for measuring velocity in fluids and on solid surfaces. These two techniques are known as Laser Doppler Anemometry (LDA) and Laser Doppler Vibrometry (LDV). Complementary to LDA, the technique used to measure fluid velocity fields based on image analysis is called Particle Image Velocimetry (PIV). Its measurement principle is similar to that of Digital Image Correlation (DIC), as introduced in Chapter 7. However, PIV employs an optical and experimental setup specifically tailored for fluid flow applications, using tracer particles, light sheet lighting and high-speed imaging to capture and analyze the motion of fluids.

This chapter presents the most widely used techniques for measuring pressure fields through image and wave-based processing methods, highlighting how they contribute to the evaluation and enhancement of performance in dynamic fluid environments. The first category focuses on acoustic pressure field measurements, which utilize single microphones, microphone pairs, or microphone arrays. These systems capture the fluctuating pressure generated in the air by propagating sound waves. Such techniques are extensively employed in the analysis of noise fields, sound intensity, and sound power. They are essential tools in the study, control, and mitigation of noise in various conditions, including built environments, industrial products, and vehicles. Practical applications of these techniques, based on the author’s hands-on experience, are described here and in the previous chapter, particularly in the context of solving industrial acoustic problems. Another important application of pressure field measurement involves the interface between solid bodies, such as the contact point between a tire and the road, a foot and the ground, or a finger and an object held by a human or a robotic system. This section illustrates the main techniques used to measure such contact pressures, with a focus on methods involving visible and infrared image acquisition and analysis. Finally, pressure and shear stress measurements are critical for studying fluid–solid interactions, such as those encountered in optimizing the aerodynamic performance of vehicles (e.g., cars, aircraft, racing machines, and ships). The chapter describes the principal image-based measurement techniques used in this domain.