rus
Issue #1/2020
V. L. Minaev, G. N. Vishnyakov, A. D. Ivanov, G. G. Levin
Methods for Controlling Geometric Parameters and Internal Stresses of Additive Technology Products
Methods for Controlling Geometric Parameters and Internal Stresses of Additive Technology Products
DOI: 10.22184/1993-7296.FRos.2020.14.1.42.54
The creation of measuring systems for additive processes is hindered by the lack of diagnostic
and control systems for manufactured products. The quality of the parts obtained by the methods of additive technologies varies greatly due to inadequate dimensional tolerances, surface roughness, as well as defects and the presence of fields of mechanical stresses. This leads to the fact that the slightest deviation of external conditions arising in the manufacturing process, can cause a mismatch of the final product in shape or properties. The measuring system should have the potential to be integrated into a single production complex. This is due to the fact that the result of measuring the geometric parameters of specific products must be compared with the mathematical model developed in the CAD system, and measurements of defects, latent stresses, product structures must be transferred to the CAE system to decide on the suitability of the product or to develop an algorithm and technologies for its further
processing. To control the parameters of products of additive technologies, a system based on the methods of structured light and shearography is proposed.
The creation of measuring systems for additive processes is hindered by the lack of diagnostic
and control systems for manufactured products. The quality of the parts obtained by the methods of additive technologies varies greatly due to inadequate dimensional tolerances, surface roughness, as well as defects and the presence of fields of mechanical stresses. This leads to the fact that the slightest deviation of external conditions arising in the manufacturing process, can cause a mismatch of the final product in shape or properties. The measuring system should have the potential to be integrated into a single production complex. This is due to the fact that the result of measuring the geometric parameters of specific products must be compared with the mathematical model developed in the CAD system, and measurements of defects, latent stresses, product structures must be transferred to the CAE system to decide on the suitability of the product or to develop an algorithm and technologies for its further
processing. To control the parameters of products of additive technologies, a system based on the methods of structured light and shearography is proposed.
Теги: additive technologies parameters control shearography аддитивные технологии контроль параметров шерография
Methods for Controlling
Geometric Parameters
and Internal Stresses of Additive Technology Products
V. L. Minaev, G. N. Vishnyakov, A. D. Ivanov, G. G. Levin
FSUE “All-Russian Research Institute of Optical Physics
Measurements”, Moscow, Russia
The creation of measuring systems for additive processes is hindered by the lack of diagnostic and control systems for manufactured products. The quality of the parts obtained by the methods of additive technologies varies greatly due to inadequate dimensional tolerances, surface roughness, as well as defects and the presence of fields of mechanical stresses. This leads to the fact that the slightest deviation of external conditions arising in the manufacturing process, can cause a mismatch of the final product in shape or properties. The measuring system should have the potential to be integrated into a single production complex. This is due to the fact that the result of measuring the geometric parameters of specific products must be compared with the mathematical model developed in the CAD system, and measurements of defects, latent stresses, product structures must be transferred to the CAE system to decide on the suitability of the product or to develop an algorithm and technologies for its further processing. To control the parameters of products of additive technologies, a system based on the methods of structured light and shearography is proposed.
Keywords: additive technologies, parameters control, shearography
Received: 20.12.2019
Accepted: 14.01.2020
INTRODUCTION
Digital technologies, the development of which determines the current state of the country, includes, as one of the main links, additive technologies that ensure the development of new generation industrial production and the modernization of traditional industries. The technology of “three-dimensional printing” (3D) began to develop in the late 80s of the last century. The pioneer in this area is 3D Systems, which developed the first device, the Stereolithography Apparatus, in 1986. The first laser machines – stereolithographic (SLA) and then powder (SLS) machines – were very expensive, the choice of materials was quite narrow, until the mid‑90s they were mainly used in research and development activities related to defense industry. In the future, after the widespread dissemination of digital technologies in the field of design, modeling and machining, 3D technologies began to develop rapidly.
For 3D‑technologies, two main terms with the word “additive” are currently recommended – Additive Fabrication (AF) and Additive Manufacturing (AM), while most tend to the latter. From 2010 to 2015, the global market for additive technologies grew by an average of 27% per year and reached a volume of $5.1 billion, of which approximately 40% are equipment and materials, and 60% are engineering services (development of mathematical models, technology and synthesis of parts).
In developing the technology of layer-by-layer synthesis, computer technologies are used for modeling and manufacturing products – CAD (Computer-Aided Design), CAM (Computer-Aided Manufacturing) systems. In recent years, computer-aided engineering (CAE) systems have also been included in automated systems – systems designed to assess the behavior of a real product under operating conditions using mathematical modeling methods using calculation methods (finite element method, finite difference method, finite volume method) in order to evaluate how the computer model of the product will behave under real operating conditions.
CAD / CAM / CAE technologies have the broadest and most significant impact on accelerating innovation, reducing and lowering the cost of developing new products, and, as a result, increasing competitiveness.
All products created using additive technologies must use CAD / CAM / CAE systems. They include the synthesis of parts of complex technical systems, including the development of 3D models, construction of supports, synthesis technologies (radiation power, scanning strategy, scanning speed and step, etc.). At the same time, the process of formation of the structural-phase state of new-generation metal, ceramic and polymer materials in the process of additive technologies with the subsequent thermal and barothermic processing of critical parts is taken into account.
The main problem that prevents the widespread adoption of additive technologies is the lack of diagnostic systems and control of manufactured products. The quality of parts obtained by additive technology varies greatly due to inadequate dimensional tolerances, surface roughness, as well as defects, thereby limiting their widespread use. This variability can be minimized by process control, but there are no adequate measurement processes available today. This leads to the fact that the slightest deviations of external conditions arising during the manufacturing process, cause the discrepancy of the final product in shape or properties.
It is also extremely important to monitor parts formed using additive technologies for defects. Due to the peculiarities of the physical processes occurring during the formation of such products, not only defects, usually characteristic of the materials used, but also fields of mechanical stresses can arise in them. Given that the use of additive technologies is most appropriate in the manufacture of expensive products of complex shape and with desired properties, control of technological processes and diagnostics of final products is one of the key links in the wide distribution of these technologies.
It should be noted that the result of measuring the geometric parameters of specific products must be compared with the mathematical model developed in the CAD system, and measurements of defects, latent stresses, product structures must be transferred to the CAE system to decide on the suitability of the product or to develop an algorithm and technologies for its further processing. Thus, the measuring system should have the potential to be integrated with a single production complex.
When creating measuring systems for additive technologies, a combination of various methods of reliable non-destructive testing can be used, which in the general case requires solving the following problems. First, in each case, it is necessary to determine a list of characteristics of products of additive production that need measurements. Secondly, determine the most appropriate measurement methods that allow you to create a system for assessing the quality of products of additive production. Analysis of modern industrial technologies allows us to formulate the basic requirements for measuring and diagnostic equipment that are used in their implementation. These include: non-contact measurements, high performance, on-site measurements, high detectability of defects, measurement of characteristics that form impacts on the material in real time. Thirdly, to develop methods and equipment for non-destructive testing of products obtained using additive technologies with the necessary level of reliability. Create appropriate measuring instruments and develop a system of their metrological support.
To develop methods of metrological control and testing of products made by layered synthesis. Finally, what may be most important, integrate the created measuring systems into a comprehensive digital production system as much as possible. This requires the creation of specialized software interfaced with modern CAD / CAM / CAE systems.
Currently, FSUE “All-Russian Research Institute of Optical Physics Measurements” is working on the creation of methods and means for measuring the parameters of additive manufacturing products, namely:
The physical world around us is three-dimensional (3D); however, conventional cameras can only receive two-dimensional (2D) images that do not have depth information. This fundamental limitation significantly narrows the ability to perceive and understand the complexity of real-world objects. The past few decades have been marked by tremendous progress in the research, development and commercialization of imaging technologies, which has been stimulated by the needs of applications in various market segments, progress in the development of sensors for electronic processing of images with high resolution and high speed, as well as increasing computing power.
The task of obtaining three-dimensional images relates to those methods that allow you to capture genuine 3D data, i. e. the values of some parameters of a three-dimensional object, such as a density distribution, depending on three-dimensional coordinates (x, y, z). Examples of obtaining images from the field of medicine are computed tomography (CT), NMR imaging, during which volume pixels (or voxels) of the measured object are obtained, including its internal structure.
In contrast, when acquiring an image, surfaces deal with measuring the coordinates (x, y, z) of a point on an object. Since in the general case the surface is not flat, it is described in three-dimensional space, and therefore the measurement result can be considered as a map of depth z depending on the position (x, y) in the Cartesian coordinate system, and represent it in the form of a matrix {zij = (xi, yj), i = 1, 2, ... , L, j = 1, 2, ... , M}. This process also has many other names: 3D surface measurement, distance determination, distance measurement, depth mapping, surface scanning, etc. These terms are used in various fields of application and usually refer to different methods of obtaining data that differ only in the details of the system design, implementation and / or data formats.
More general systems for obtaining three-dimensional surface images are able to register a scalar value, such as the reflection coefficient associated with each point on a non-planar surface. The result is a point cloud {Pi = (xi, yi, zi, fi), i = 1, 2, ... , N}, where fi is the reflection coefficient at each i-th point of the surface in the data array. Similarly, a color image of the surface is represented using {Pi = (xi, yi, zi, ri, gi, bi), i = 1, 2, ... , N}, where vector (ri, gi, bi) represents the red, green and blue components associated with the i-th point. surface. The spectral properties of a surface can also be described using larger vectors.
One of the main methods for obtaining three-dimensional surface images is based on the use of “structured light”, i. e. illumination of an object using specially designed two-dimensional templates (banners) with intensity varying in space and subsequent registration, and analysis of the images obtained. As shown in Figure 1, a spatially changing two-dimensional structured illumination is generated using a special projector or a light source modulated with a spatial light modulator. The intensity of each pixel in the structured light pattern is represented by a digital signal {Iij = (i, j), i = 1, 2, ... , I, j = 1, 2, ... , J}, where (i, j) are the coordinates (x, y) of the projected template. Typically projected structured light patterns are two-dimensional patterns.
To obtain a two-dimensional image of a scene illuminated by structured light, a camera is used.
The optical axis of the projector and camera should form a certain angle. If the scene is a flat surface without any spatial variations of the surface, then the pattern displayed on the image is similar to the projected pattern of structured light. However, if the surface of the scene is non-planar, then its irregularities distort the projected pattern of structured light. The principle of the method of obtaining a three-dimensional surface image using structured light is to identify the three-dimensional surface shape based on the distortion of the projected structured light pattern. The accurate profiles of three-dimensional surfaces of objects in a scene can be calculated using various principles and algorithms of structured light.
As shown in Fig. 1, the geometric relationship between the camera, the structured light projector and the point P on the surface of the object can be expressed using the principle of triangulation, according to the formula:
. (1)
The key to obtaining a three-dimensional image based on triangulation is a method for identifying a single element of a projected template in the resulting image.
In a more general sense, structured light patterns can create spatial variations in all directions (x, y, z), thus becoming genuine 3D structured light projection systems. For example, the intensity of the projected light may vary along the optical path due to interference of coherent light. However, most systems for obtaining three-dimensional surface images using structured light use two-dimensional patterns.
Fig. 2 presents a system for obtaining three-dimensional images when illuminated with structured light, demonstrating the principle of its operation. An arbitrary three-dimensional surface of an object is illuminated using a projected pattern of structured light. In this particular case, the structured light pattern is a color picture spatially repeated over many periods that resembles the radiation spectrum of the visible optical range. The camera captures an image of the three-dimensional surface of an object when illuminated by structured light. Based on the distortion of the structured light pattern visible in the image, compared with the undistorted projected pattern, the three-dimensional geometric surface of the object can be accurately calculated.
In the reviews [1, 2] and the monograph [3], various strip projection methods are considered, and the review [2] focuses only on single-frame methods that can be used to study dynamic objects.
The team of scientists of FSUE “All-Russian Research Institute of Optical Physics Measurements” developed a scanner-profilometer to measure the surface shape for dentistry. In dental CAD / CAM systems, digital 3D images of teeth are used for the automated production of dental restorations (crowns, prostheses, etc.). The appearance of the scanner-profilometer is shown in Fig. 3.
This device implements a triangulation measurement scheme. The results of the scanner showed sufficient accuracy for its use in the field of dentistry, which amounted to 45.5 microns. A set of special measures was developed to determine the metrological characteristics of the scanner. In addition, experimental studies were conducted to measure the surface shape of various objects. For example, in the experiment to determine the shape, a test object in the form of a truncated cone was used. The dimensions of the test object: the base is 10 × 10 mm, the height of the truncated cone is 6 mm, the angle between the generatrix surface of the cone and its height is 10˚. In fig. Figure 4 shows the images obtained using the profilometer.
The surface shape obtained during the measurement was compared with the original CAD model. The standard deviation of the measured surface of the test object from the base in the areas of the respective planes is 45.5 μm, the maximum deviation is 74.5 μm.
Electronic speckle interferometry (Elecrtonic Speckle Pattern Interferometry ESPI) is a method similar to holographic interferometry, it is designed to measure changes in the optical path caused by deformation of opaque bodies or a change in the refractive index inside transparent media [4]. The ESPI method uses electronic devices, such as CCD cameras, to record optical information. The speckle pattern, which is recorded using the ESPI system, can be considered as a hologram of a focused image of a diffusely reflecting object (Fig. 5). Thanks to digital recording and processing, the ESPI method is also called Digital Speckle Pattern Interferometry DSPI. Another name is TV holography. However, instead of reconstructing the image from the hologram, the ESPI method uses speckle pattern correlation.
The schematic diagram of ESPI is shown in Fig. 5. The image of the object on the CCD matrix is constructed by a lens system. Due to the coherence of the illuminating radiation, the image of the object will be a speckle picture.
The size of an individual speckle is dSp = λb / a, where λ is the radiation wavelength, a is the lens aperture diameter, and b is the distance from the lens to the image plane (Fig. 5). The speckle size should be consistent with the resolution (pixel size) of the matrix receiver. This can be achieved by reducing the aperture of the imaging system.
The speckle pattern of the surface of the object on the matrix receiver is combined with a spherical reference wave. The point source of this reference wave should be located in the center of the imaging lens. Thanks to this axial (in-line) scheme, the spatial period of the interference fringes will be larger than the pixel size of the CCD matrix. In practice, the system for forming the reference beam is connected to a beam splitting cube or is mounted directly into the aperture of the imaging lens through an optical fiber.
The light intensity at the matrix receiver is equal to:
(2)
where is the complex amplitude of the reference wave, and is the complex amplitude of the object wave in the image plane. The expression (is the phase difference between the reference and object waves, which randomly varies from point to point. This hologram of a focused image of a diffusely reflecting object is recorded by a matrix receiver and recorded in a computer memory.
Thus, expression (2) describes a low-frequency hologram of a focused image of an object, which is a speckle modulated by interference fringes. Such a low-frequency hologram can also be called a speckle interferogram.
The device shown in fig. 3, sensitive to normal movements, in a direction perpendicular to the plane of the object (out-of-plane). A shift by dz leads to a phase shift:
. (3)
After the deformation of the object, the second holographic speckle pattern is recorded:
(4)
Further, these two holographic speckle patterns are subtracted by the formula:
(5)
It should be emphasized that it is not the wave fields that are subtracted, but the intensities of the two speckle patterns (holograms). It can be seen from expression (5) that the intensity of the difference speckle pattern will be minimal at those points where ∆ϕ = 0, 2π, ... The intensity of the difference pattern reaches its maximum for those parts of the surface of the object for which deformation (displacement) leads to a phase shift ∆ϕ = π, 3π, ... The resulting picture of the subtraction looks like a system of dark and light bands, very similar to a holographic interferogram. However, there is a significant difference from holographic interferometry, which consists in the appearance of speckles in the bands and the loss of 3D information in such a correlation process.
As indicated above, the circuit in Fig. 5 is only sensitive to normal movements. Tangential displacements (in-plane) can be measured using the circuit shown in Fig. 6. Two plane waves illuminate the object symmetrically at angles ±θ to the z axis. The image of the object is built by a TV camera. As before, the speckle size should be consistent with the pixel size, for example, by changing the diameter of the lens aperture. The phase change caused by tangential displacements can be inferred from simple geometric relationships similar to calculations of displacements in holographic interferometry. The phase change of the upper beam in Fig. 6 is equal to:
, (6)
where is the displacement vector. The unit vectors , , are defined in Fig. 3. The corresponding phase shift for the lower beam is:
. (7)
Then the total phase shift will be equal to:
. (8)
The vector is parallel to the x axis and its length is 2 sin θ. Therefore, the total phase shift, measured in such a scheme, will be equal to:
.
Just like in holographic interferometry, the phase cannot be determined from a single speckle pattern. The phase from the speckle interferogram can be reconstructed by the method of phase steps. In this phase step method for ESPI, it is necessary to register at least 3 speckle interferograms with mutual phase shift in each state (before and after the load). Any of the known phase-step algorithms can be used.
In the initial state, the phase difference between the reference and object beams . is calculated by the method of phase steps. After deformation of the object, again, by the method of phase steps, another phase difference is calculated. The desired phase shift caused by the deformation of the object is obtained by subtracting these two phase shifts.
It follows that in modern ESPI methods, the sought phase shift ∆ϕ is not restored from formula (5), i. e. not from the difference of two speckle interferograms, but from the speckle interferograms themselves by the phase-step method. Therefore, the difference between the methods of digital holographic interferometry and electron speckle interferometry is blurred.
For the experiment to determine the deformation, we used a schearograph shown in Figure 7 (a) and a flat plate 55 × 45 mm in size, on one side of which there was a cellular structure made by the additive technology method. In the cellular structure, when printing, a section of cell links with dimensions of 7 × 7 mm was specially omitted. This section imitated a defect of delamination of the surface from the cellular substrate. To obtain a deformed state, plate heating with hot air was used. Qualitative detection of this defect on the flat side of the plate is shown in Fig. 7.
Thus, the presented methods of structured light and schearography satisfy the requirements of non-invasiveness and high accuracy and can be used to control the parameters of products of additive technologies.
This work was financially supported by the Ministry of Education and Science of the Russian Federation as part of the implementation of agreement No. 14.625.21.0041 dated 26.09.2017 (unique identifier for applied research RFMEFI62517X0041).
References
Jason Geng. Structured-light 3D surface imaging: a tutorial. Advances in Optics and Photonics. 2011; 3(2): 128–160.
Zhang Z. H. Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques. Optics and Lasers in Engineering. 2012; 50:1097–1106.
Song Zhang. High-Speed 3D Imaging with Digital Fringe Projection Techniques (Optical Sciences and Applications of Light). – CRC Press; 1 edition (March 1, 2016).
Schars U., Jueptner W. Digital Holography. Digital hologram recording, numerical reconstruction, and related techniques. – Springer-Verlag Berlin Heidelberg. 2005.
About authors
Minaev Vladimir Leonidovich, Doctor of Engineering, minaev@vniiofi.ru, FSUE “All-Russian Research Institute of Optical Physics Measurements”,
https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0002-4356-301X
Vishnyakov Gennady Nikolaevich, Doctor of Engineering, FSUE “All-Russian Research Institute of Optical Physics Measurements”,
https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0003-0237-4738
Ivanov Alexey Dmitrievich, Cand. of Engineering, FSUE “All-Russian Research Institute of Optical Physics Measurements”, https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0002-0609-6600
Levin Gennady Genrikhovich, Doctor of Engineering, FSUE “All-Russian Research Institute of Optical Physics Measurements”,
https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0002-4158-5143
Geometric Parameters
and Internal Stresses of Additive Technology Products
V. L. Minaev, G. N. Vishnyakov, A. D. Ivanov, G. G. Levin
FSUE “All-Russian Research Institute of Optical Physics
Measurements”, Moscow, Russia
The creation of measuring systems for additive processes is hindered by the lack of diagnostic and control systems for manufactured products. The quality of the parts obtained by the methods of additive technologies varies greatly due to inadequate dimensional tolerances, surface roughness, as well as defects and the presence of fields of mechanical stresses. This leads to the fact that the slightest deviation of external conditions arising in the manufacturing process, can cause a mismatch of the final product in shape or properties. The measuring system should have the potential to be integrated into a single production complex. This is due to the fact that the result of measuring the geometric parameters of specific products must be compared with the mathematical model developed in the CAD system, and measurements of defects, latent stresses, product structures must be transferred to the CAE system to decide on the suitability of the product or to develop an algorithm and technologies for its further processing. To control the parameters of products of additive technologies, a system based on the methods of structured light and shearography is proposed.
Keywords: additive technologies, parameters control, shearography
Received: 20.12.2019
Accepted: 14.01.2020
INTRODUCTION
Digital technologies, the development of which determines the current state of the country, includes, as one of the main links, additive technologies that ensure the development of new generation industrial production and the modernization of traditional industries. The technology of “three-dimensional printing” (3D) began to develop in the late 80s of the last century. The pioneer in this area is 3D Systems, which developed the first device, the Stereolithography Apparatus, in 1986. The first laser machines – stereolithographic (SLA) and then powder (SLS) machines – were very expensive, the choice of materials was quite narrow, until the mid‑90s they were mainly used in research and development activities related to defense industry. In the future, after the widespread dissemination of digital technologies in the field of design, modeling and machining, 3D technologies began to develop rapidly.
For 3D‑technologies, two main terms with the word “additive” are currently recommended – Additive Fabrication (AF) and Additive Manufacturing (AM), while most tend to the latter. From 2010 to 2015, the global market for additive technologies grew by an average of 27% per year and reached a volume of $5.1 billion, of which approximately 40% are equipment and materials, and 60% are engineering services (development of mathematical models, technology and synthesis of parts).
In developing the technology of layer-by-layer synthesis, computer technologies are used for modeling and manufacturing products – CAD (Computer-Aided Design), CAM (Computer-Aided Manufacturing) systems. In recent years, computer-aided engineering (CAE) systems have also been included in automated systems – systems designed to assess the behavior of a real product under operating conditions using mathematical modeling methods using calculation methods (finite element method, finite difference method, finite volume method) in order to evaluate how the computer model of the product will behave under real operating conditions.
CAD / CAM / CAE technologies have the broadest and most significant impact on accelerating innovation, reducing and lowering the cost of developing new products, and, as a result, increasing competitiveness.
All products created using additive technologies must use CAD / CAM / CAE systems. They include the synthesis of parts of complex technical systems, including the development of 3D models, construction of supports, synthesis technologies (radiation power, scanning strategy, scanning speed and step, etc.). At the same time, the process of formation of the structural-phase state of new-generation metal, ceramic and polymer materials in the process of additive technologies with the subsequent thermal and barothermic processing of critical parts is taken into account.
The main problem that prevents the widespread adoption of additive technologies is the lack of diagnostic systems and control of manufactured products. The quality of parts obtained by additive technology varies greatly due to inadequate dimensional tolerances, surface roughness, as well as defects, thereby limiting their widespread use. This variability can be minimized by process control, but there are no adequate measurement processes available today. This leads to the fact that the slightest deviations of external conditions arising during the manufacturing process, cause the discrepancy of the final product in shape or properties.
It is also extremely important to monitor parts formed using additive technologies for defects. Due to the peculiarities of the physical processes occurring during the formation of such products, not only defects, usually characteristic of the materials used, but also fields of mechanical stresses can arise in them. Given that the use of additive technologies is most appropriate in the manufacture of expensive products of complex shape and with desired properties, control of technological processes and diagnostics of final products is one of the key links in the wide distribution of these technologies.
It should be noted that the result of measuring the geometric parameters of specific products must be compared with the mathematical model developed in the CAD system, and measurements of defects, latent stresses, product structures must be transferred to the CAE system to decide on the suitability of the product or to develop an algorithm and technologies for its further processing. Thus, the measuring system should have the potential to be integrated with a single production complex.
When creating measuring systems for additive technologies, a combination of various methods of reliable non-destructive testing can be used, which in the general case requires solving the following problems. First, in each case, it is necessary to determine a list of characteristics of products of additive production that need measurements. Secondly, determine the most appropriate measurement methods that allow you to create a system for assessing the quality of products of additive production. Analysis of modern industrial technologies allows us to formulate the basic requirements for measuring and diagnostic equipment that are used in their implementation. These include: non-contact measurements, high performance, on-site measurements, high detectability of defects, measurement of characteristics that form impacts on the material in real time. Thirdly, to develop methods and equipment for non-destructive testing of products obtained using additive technologies with the necessary level of reliability. Create appropriate measuring instruments and develop a system of their metrological support.
To develop methods of metrological control and testing of products made by layered synthesis. Finally, what may be most important, integrate the created measuring systems into a comprehensive digital production system as much as possible. This requires the creation of specialized software interfaced with modern CAD / CAM / CAE systems.
Currently, FSUE “All-Russian Research Institute of Optical Physics Measurements” is working on the creation of methods and means for measuring the parameters of additive manufacturing products, namely:
- measurement of geometric parameters in a wide range of product sizes using structured light methods;
- measurement of strains and stresses by speckle interferometry methods.
The physical world around us is three-dimensional (3D); however, conventional cameras can only receive two-dimensional (2D) images that do not have depth information. This fundamental limitation significantly narrows the ability to perceive and understand the complexity of real-world objects. The past few decades have been marked by tremendous progress in the research, development and commercialization of imaging technologies, which has been stimulated by the needs of applications in various market segments, progress in the development of sensors for electronic processing of images with high resolution and high speed, as well as increasing computing power.
The task of obtaining three-dimensional images relates to those methods that allow you to capture genuine 3D data, i. e. the values of some parameters of a three-dimensional object, such as a density distribution, depending on three-dimensional coordinates (x, y, z). Examples of obtaining images from the field of medicine are computed tomography (CT), NMR imaging, during which volume pixels (or voxels) of the measured object are obtained, including its internal structure.
In contrast, when acquiring an image, surfaces deal with measuring the coordinates (x, y, z) of a point on an object. Since in the general case the surface is not flat, it is described in three-dimensional space, and therefore the measurement result can be considered as a map of depth z depending on the position (x, y) in the Cartesian coordinate system, and represent it in the form of a matrix {zij = (xi, yj), i = 1, 2, ... , L, j = 1, 2, ... , M}. This process also has many other names: 3D surface measurement, distance determination, distance measurement, depth mapping, surface scanning, etc. These terms are used in various fields of application and usually refer to different methods of obtaining data that differ only in the details of the system design, implementation and / or data formats.
More general systems for obtaining three-dimensional surface images are able to register a scalar value, such as the reflection coefficient associated with each point on a non-planar surface. The result is a point cloud {Pi = (xi, yi, zi, fi), i = 1, 2, ... , N}, where fi is the reflection coefficient at each i-th point of the surface in the data array. Similarly, a color image of the surface is represented using {Pi = (xi, yi, zi, ri, gi, bi), i = 1, 2, ... , N}, where vector (ri, gi, bi) represents the red, green and blue components associated with the i-th point. surface. The spectral properties of a surface can also be described using larger vectors.
One of the main methods for obtaining three-dimensional surface images is based on the use of “structured light”, i. e. illumination of an object using specially designed two-dimensional templates (banners) with intensity varying in space and subsequent registration, and analysis of the images obtained. As shown in Figure 1, a spatially changing two-dimensional structured illumination is generated using a special projector or a light source modulated with a spatial light modulator. The intensity of each pixel in the structured light pattern is represented by a digital signal {Iij = (i, j), i = 1, 2, ... , I, j = 1, 2, ... , J}, where (i, j) are the coordinates (x, y) of the projected template. Typically projected structured light patterns are two-dimensional patterns.
To obtain a two-dimensional image of a scene illuminated by structured light, a camera is used.
The optical axis of the projector and camera should form a certain angle. If the scene is a flat surface without any spatial variations of the surface, then the pattern displayed on the image is similar to the projected pattern of structured light. However, if the surface of the scene is non-planar, then its irregularities distort the projected pattern of structured light. The principle of the method of obtaining a three-dimensional surface image using structured light is to identify the three-dimensional surface shape based on the distortion of the projected structured light pattern. The accurate profiles of three-dimensional surfaces of objects in a scene can be calculated using various principles and algorithms of structured light.
As shown in Fig. 1, the geometric relationship between the camera, the structured light projector and the point P on the surface of the object can be expressed using the principle of triangulation, according to the formula:
. (1)
The key to obtaining a three-dimensional image based on triangulation is a method for identifying a single element of a projected template in the resulting image.
In a more general sense, structured light patterns can create spatial variations in all directions (x, y, z), thus becoming genuine 3D structured light projection systems. For example, the intensity of the projected light may vary along the optical path due to interference of coherent light. However, most systems for obtaining three-dimensional surface images using structured light use two-dimensional patterns.
Fig. 2 presents a system for obtaining three-dimensional images when illuminated with structured light, demonstrating the principle of its operation. An arbitrary three-dimensional surface of an object is illuminated using a projected pattern of structured light. In this particular case, the structured light pattern is a color picture spatially repeated over many periods that resembles the radiation spectrum of the visible optical range. The camera captures an image of the three-dimensional surface of an object when illuminated by structured light. Based on the distortion of the structured light pattern visible in the image, compared with the undistorted projected pattern, the three-dimensional geometric surface of the object can be accurately calculated.
In the reviews [1, 2] and the monograph [3], various strip projection methods are considered, and the review [2] focuses only on single-frame methods that can be used to study dynamic objects.
The team of scientists of FSUE “All-Russian Research Institute of Optical Physics Measurements” developed a scanner-profilometer to measure the surface shape for dentistry. In dental CAD / CAM systems, digital 3D images of teeth are used for the automated production of dental restorations (crowns, prostheses, etc.). The appearance of the scanner-profilometer is shown in Fig. 3.
This device implements a triangulation measurement scheme. The results of the scanner showed sufficient accuracy for its use in the field of dentistry, which amounted to 45.5 microns. A set of special measures was developed to determine the metrological characteristics of the scanner. In addition, experimental studies were conducted to measure the surface shape of various objects. For example, in the experiment to determine the shape, a test object in the form of a truncated cone was used. The dimensions of the test object: the base is 10 × 10 mm, the height of the truncated cone is 6 mm, the angle between the generatrix surface of the cone and its height is 10˚. In fig. Figure 4 shows the images obtained using the profilometer.
The surface shape obtained during the measurement was compared with the original CAD model. The standard deviation of the measured surface of the test object from the base in the areas of the respective planes is 45.5 μm, the maximum deviation is 74.5 μm.
Electronic speckle interferometry (Elecrtonic Speckle Pattern Interferometry ESPI) is a method similar to holographic interferometry, it is designed to measure changes in the optical path caused by deformation of opaque bodies or a change in the refractive index inside transparent media [4]. The ESPI method uses electronic devices, such as CCD cameras, to record optical information. The speckle pattern, which is recorded using the ESPI system, can be considered as a hologram of a focused image of a diffusely reflecting object (Fig. 5). Thanks to digital recording and processing, the ESPI method is also called Digital Speckle Pattern Interferometry DSPI. Another name is TV holography. However, instead of reconstructing the image from the hologram, the ESPI method uses speckle pattern correlation.
The schematic diagram of ESPI is shown in Fig. 5. The image of the object on the CCD matrix is constructed by a lens system. Due to the coherence of the illuminating radiation, the image of the object will be a speckle picture.
The size of an individual speckle is dSp = λb / a, where λ is the radiation wavelength, a is the lens aperture diameter, and b is the distance from the lens to the image plane (Fig. 5). The speckle size should be consistent with the resolution (pixel size) of the matrix receiver. This can be achieved by reducing the aperture of the imaging system.
The speckle pattern of the surface of the object on the matrix receiver is combined with a spherical reference wave. The point source of this reference wave should be located in the center of the imaging lens. Thanks to this axial (in-line) scheme, the spatial period of the interference fringes will be larger than the pixel size of the CCD matrix. In practice, the system for forming the reference beam is connected to a beam splitting cube or is mounted directly into the aperture of the imaging lens through an optical fiber.
The light intensity at the matrix receiver is equal to:
(2)
where is the complex amplitude of the reference wave, and is the complex amplitude of the object wave in the image plane. The expression (is the phase difference between the reference and object waves, which randomly varies from point to point. This hologram of a focused image of a diffusely reflecting object is recorded by a matrix receiver and recorded in a computer memory.
Thus, expression (2) describes a low-frequency hologram of a focused image of an object, which is a speckle modulated by interference fringes. Such a low-frequency hologram can also be called a speckle interferogram.
The device shown in fig. 3, sensitive to normal movements, in a direction perpendicular to the plane of the object (out-of-plane). A shift by dz leads to a phase shift:
. (3)
After the deformation of the object, the second holographic speckle pattern is recorded:
(4)
Further, these two holographic speckle patterns are subtracted by the formula:
(5)
It should be emphasized that it is not the wave fields that are subtracted, but the intensities of the two speckle patterns (holograms). It can be seen from expression (5) that the intensity of the difference speckle pattern will be minimal at those points where ∆ϕ = 0, 2π, ... The intensity of the difference pattern reaches its maximum for those parts of the surface of the object for which deformation (displacement) leads to a phase shift ∆ϕ = π, 3π, ... The resulting picture of the subtraction looks like a system of dark and light bands, very similar to a holographic interferogram. However, there is a significant difference from holographic interferometry, which consists in the appearance of speckles in the bands and the loss of 3D information in such a correlation process.
As indicated above, the circuit in Fig. 5 is only sensitive to normal movements. Tangential displacements (in-plane) can be measured using the circuit shown in Fig. 6. Two plane waves illuminate the object symmetrically at angles ±θ to the z axis. The image of the object is built by a TV camera. As before, the speckle size should be consistent with the pixel size, for example, by changing the diameter of the lens aperture. The phase change caused by tangential displacements can be inferred from simple geometric relationships similar to calculations of displacements in holographic interferometry. The phase change of the upper beam in Fig. 6 is equal to:
, (6)
where is the displacement vector. The unit vectors , , are defined in Fig. 3. The corresponding phase shift for the lower beam is:
. (7)
Then the total phase shift will be equal to:
. (8)
The vector is parallel to the x axis and its length is 2 sin θ. Therefore, the total phase shift, measured in such a scheme, will be equal to:
.
Just like in holographic interferometry, the phase cannot be determined from a single speckle pattern. The phase from the speckle interferogram can be reconstructed by the method of phase steps. In this phase step method for ESPI, it is necessary to register at least 3 speckle interferograms with mutual phase shift in each state (before and after the load). Any of the known phase-step algorithms can be used.
In the initial state, the phase difference between the reference and object beams . is calculated by the method of phase steps. After deformation of the object, again, by the method of phase steps, another phase difference is calculated. The desired phase shift caused by the deformation of the object is obtained by subtracting these two phase shifts.
It follows that in modern ESPI methods, the sought phase shift ∆ϕ is not restored from formula (5), i. e. not from the difference of two speckle interferograms, but from the speckle interferograms themselves by the phase-step method. Therefore, the difference between the methods of digital holographic interferometry and electron speckle interferometry is blurred.
For the experiment to determine the deformation, we used a schearograph shown in Figure 7 (a) and a flat plate 55 × 45 mm in size, on one side of which there was a cellular structure made by the additive technology method. In the cellular structure, when printing, a section of cell links with dimensions of 7 × 7 mm was specially omitted. This section imitated a defect of delamination of the surface from the cellular substrate. To obtain a deformed state, plate heating with hot air was used. Qualitative detection of this defect on the flat side of the plate is shown in Fig. 7.
Thus, the presented methods of structured light and schearography satisfy the requirements of non-invasiveness and high accuracy and can be used to control the parameters of products of additive technologies.
This work was financially supported by the Ministry of Education and Science of the Russian Federation as part of the implementation of agreement No. 14.625.21.0041 dated 26.09.2017 (unique identifier for applied research RFMEFI62517X0041).
References
Jason Geng. Structured-light 3D surface imaging: a tutorial. Advances in Optics and Photonics. 2011; 3(2): 128–160.
Zhang Z. H. Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques. Optics and Lasers in Engineering. 2012; 50:1097–1106.
Song Zhang. High-Speed 3D Imaging with Digital Fringe Projection Techniques (Optical Sciences and Applications of Light). – CRC Press; 1 edition (March 1, 2016).
Schars U., Jueptner W. Digital Holography. Digital hologram recording, numerical reconstruction, and related techniques. – Springer-Verlag Berlin Heidelberg. 2005.
About authors
Minaev Vladimir Leonidovich, Doctor of Engineering, minaev@vniiofi.ru, FSUE “All-Russian Research Institute of Optical Physics Measurements”,
https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0002-4356-301X
Vishnyakov Gennady Nikolaevich, Doctor of Engineering, FSUE “All-Russian Research Institute of Optical Physics Measurements”,
https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0003-0237-4738
Ivanov Alexey Dmitrievich, Cand. of Engineering, FSUE “All-Russian Research Institute of Optical Physics Measurements”, https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0002-0609-6600
Levin Gennady Genrikhovich, Doctor of Engineering, FSUE “All-Russian Research Institute of Optical Physics Measurements”,
https://www.vniiofi.ru, Moscow, Russia.
ORCID: 0000-0002-4158-5143
Readers feedback
