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Laser-based active thermography is a contactless non-destructive testing method to detect material defects by heating the object and measuring its temperature increase with an infrared camera. Systematic deviations from predicted behavior provide insight into the inner structure of the object. However, its resolution in resolving internal structures is limited due to the diffusive nature of heat diffusion. Thermographic super resolution (SR) methods aim to overcome this limitation by combining multiple thermographic measurements and mathematical optimization algorithms to improve the defect reconstruction.
Thermographic SR reconstruction methods involve measuring the temperature change in an object under test (OuT) heated with multiple different spatially structured illuminations. Subsequently, these measurements are inputted into a severely ill-posed and heavily regularized inverse problem, producing a sparse map of the OuT’s internal defect structure. Solving this inverse problem relies on limited priors, such as defect-sparsity, and iterative numerical minimization techniques. Previously mostly experimentally limited to one-dimensional regions of interest (ROIs), this thesis aims to extend the method to the reconstruction of two-dimensionalROIs with arbitrary defect distributions while maintaining reasonable experimental complexity. Ultimately, the goal of this thesis is to make the method suitable for a technology transfer to industrial applications by advancing its technology readiness level (TRL).
In order to achieve the aforementioned goal, this thesis discusses the numerical expansion of a thermographic SR reconstruction method and introduces two novel algorithms to invert the underlying inverse problem. Furthermore, a forward solution to the inverse problem in terms of the applied SR reconstruction model is set up. In conjunction with an additionally proposed algorithm for the automated determination of a set of (optimal) regularization parameters, both create the possibility to conduct analytical simulations to characterize the influence of the experimental parameters on the achievable reconstruction quality. On the experimental side, the method is upgraded to deal with two-dimensional ROIs, and multiple measurement campaigns are performed to validate the proposed inversion algorithms, forward solution and two exemplary analytical studies. For the experimental implementation of the method, the use of a laser-coupled DLP-projector is introduced, which allows projecting binary pixel
patterns that cover the whole ROI, reducing the number of necessary measurements per ROI significantly (up to 20x).
Finally, the achieved reconstruction of the internal defect structure of a purpose-made OuT is qualitatively and qualitatively benchmarked against well-established thermographic testing methods based on homogeneous illumination of the ROI. Here, the background-noise-free two-dimensional photothermal SR reconstruction results show to outclass all defect reconstructions by the considered reference methods.
Validation of artificial defects for Non-destructive testing measurements on a reference structure
(2018)
Non-destructive testing was established over the last decades as an important tool for assessing damages, material characterization and quality assurance in civil engineering. For example, Ground Penetrating Radar (GPR) can be used to scan large areas of concrete structures to determine the spatial position of the reinforcement. With the ultrasonic echo method, the thickness of concrete structures can be easily determined even if a high density of reinforcement is given. Various methods and processes have been developed for the validation of NDT procedures aiming at ensuring the quality of measurements in practical use. The Probability of Detection (POD) for example, is an available method to compare different technical devices with each other quantitatively regarding their performance. With this method, the best suited testing device for a specific inspection task under defined boundary conditions can be selected. By using the Guide to the Expression of Uncertainty in Measurement (GUM), it is possible to quantify the measurement uncertainty of an inspection procedure for a specific task. Another important aspect to improve the acceptance of non-destructive testing methods is the development of reference specimens.
Reference specimens serve for the calibration and further development of NDT methods under realistic conditions in different laboratories under the same conditions. This is an essential prerequisite for round robin tests. A particular challenge here is the most realistic representation of a damage that can occur at building sites. Possible damages include for example horizontal and vertical cracks or honeycombs in concrete. Such a reference structure was built for the development of a new design of power plant constructions. Comparative studies on the manufacturing of realistic honeycombs and delaminations were carried out in advance on a test specimen. The results of this study are presented here.
The aim of this presentation is to highlight how psychology can be used to prevent human error. It starts with examples of accidents, incidents and events that have happened due to too little attention being dedicated to human factors. It continues arguing that human factors are one of the main factors influencing the reliability of non-destructive testing and gives definitions of the main terms. Furthermore, it presents a method used to identify risks in mechanized NDT to be used for the purposes of the final disposal of spent nuclear fuel and presents a study, in which human-centred design and eye tracking have been used to optimism the inspection procedure. The conclusion is that human factors methods can be used to identify problems during the inspection process and generate mitigation strategies that can be used to decrease human error and enhance safety.
Validation of artificial defects for non-destructive testing measurements on a reference structure
(2018)
Non-destructive testing was established over the last decades as an important tool for assessing damages, material characterization and quality assurance in civil engineering. For example, Ground Penetrating Radar (GPR) can be used to scan large areas of concrete structures to determine the spatial position of the reinforcement. With the ultrasonic echo method, the thickness of concrete structures can be easily determined even if a high density of reinforcement is given. Various methods and processes have been developed for the validation of NDT procedures aiming at ensuring the quality of measurements in practical use. The Probability of Detection (POD) for example, is an available method to compare different technical devices with each other quantitatively regarding their performance. With this method, the best suited testing device for a specific inspection task under defined boundary conditions can be selected. By using the Guide to the Expression of Uncertainty in Measurement (GUM), it is possible to quantify the measurement uncertainty of an inspection procedure for a specific task. Another important aspect to improve the acceptance of Non-destructive testing methods is the development of reference specimens.
Reference specimens serve for the calibration and further development of NDT methods under realistic conditions in different laboratories under the same conditions. A particular challenge here is the most realistic representation of a damage that can occur at building sites. Possible damages include for example horizontal and vertical cracks or honeycombs in concrete. Such a reference structure was built for the development of a new design of power plant constructions. Comparative studies on the manufacturing of realistic honeycombs and delaminations were carried out in advance on a test specimen. The results of this study are presented here.
Influence of the real energy input on the sensitivity of thermographic testing in case of GFRP
(2018)
Thermographic testing (TT) is an upcoming nondestructive method, which requires no contact at all to the specimen and can be applied on larger areas simultaneously. The measurement concept is based on the production of a thermal imbalance at the surface of the object under test. When the surface of this object is heated by an external source for a certain time, the surface temperature drops subsequently, influenced by inner defects of the sample. This leads to thermal contrasts at the surface. It is crucial that those contrasts are large enough to be detectable above the noise level. In a first approximation, the observed temperature contrast at a defect is proportional to the energy which was really introduced into the specimen during the heating period. However, the real energy input in a TT experiment is almost always unknown due to distinct parameters of the experimental setup or the material investigated. Typically, only the power consumption of the heating sources is reported, sometimes combined with the distance to the specimen surface.
This contribution describes the thermographic inspection of a rear side thickness variation from 1 to 2 cm at GFRP. This could represent a rear side adhesive bond i.e. in a wind turbine rotor blade. The front side heating was realized by usual halogen lamps with variable radiation power. The detected temperature contrast at the front side will be related to the different energy inputs determined by means of a simple analytical model applied to the experimental data. Additionally, the experimental data are compared with results of FEM simulations performed by COMSOL Multiphysics.
The results clearly demonstrate the key role of the real energy input in a real TT setup, if detection limits have to be evaluated.
Post-tensioning systems provide safe and efficient construction solutions for long span bridges. Despite the improved grouting practices over the past decade, existing post-tensioning systems may have significant amount of grout defects, which could lead to corrosion of the strands. Condition assessment of post-tensioning systems is necessary to allow bridge owners to take timely, proactive actions to mitigate or prevent further Deterioration and unanticipated tendon failures. A detailed experimental study conducted to assess the performance of nondestructive evaluation techniques in detecting grout defects within internal tendons is presented herein.
Nondestructive evaluation techniques that include Ground Penetrating Radar, Impact Echo, Ultrasonic Tomography, and Ultrasonic Echo are evaluated in terms of detecting the location and severity of fabricated grout defects in a full-scale post-tensioned U-girder mock-up specimen. While Ground Penetrating Radar can identify the location and profile of the internal tendons, particularly metal ducts due to strong reflections, this method did not provide any information about the defect conditions within the tendon. Both Impact Echo and Ultrasonic Echo techniques are effective in identifying the Location of grout defects, but could not differentiate between water, void, or compromised grout conditions. The study clearly demonstrates the need for NDE techniques that are applicable to anchorage regions, and that are capable of estimating the severity and nature of grout defects in internal tendons.
Laser thermography has its roots in the late-1960s when Kubiak first used a focused light source to raster-scan a specimen containing surface breaking cracks and employed an infrared detector to monitor the blocking effect of the cracks on the heat flow. Nowadays, this technique has evolved into the flying-spot laser thermography. In the mid-1970s, when Rosencwaig and Gersho worked out the theory for the photoacoustic effect, they laid the foundation for the development of the photothermal testing methodology. The decisive difference to the flying-spot technique is that in the photothermal methodology, a high-frequency modulated laser beam is used, which explicitly uses the concept of the thermal wave.
Starting in the 1980s, infrared cameras came into play and enabled full-field thermal imaging, but this time, slow thermal light sources were used. Today, flash lamps (pulsed planar heating) and halogen lamps (modulated planar heating) have been established as the standard light sources for the specific regimes of pulsed and lock-in thermography.
Only recently, the availability of novel technologies – fast and high-resolution infrared cameras, innovative brilliant laser sources and high-performance data acquisition and processing technology – has enabled a paradigm shift from the separated photothermal and thermographic methodologies to a versatile tool for NDE that combines both approaches. In addition, the heating can also be spatially structured using laser arrays. This new degree of freedom allows the development of completely new thermography NDE methods.
In the talk, we present current activities with kilowatt-class high-power laser sources for advanced flying-spot, pulsed, lock-in and laser-projected thermography.
Vortrag über die Aktivitäten des Fachbereichs 8.2 in der zerstörungsfreien Prüfung im Bauwesen.
Among the photothermal methods, full-field thermal imaging is used to characterize materials, to determine thicknesses of layers, or to find inhomogeneities such as voids or cracks. The use of classical light sources such as flash lamps (impulse heating) or halogen lamps (modulated heating) led to a variety of nondestructive testing methods, in particular lock-in and flash-thermography.
In vertical cavity surface emitting lasers (VCSELs), laser light is emitted perpendicular to the surface with a symmetrical beam profile. Due to the vertical structure, they can be arranged in large arrays of many thousands of individual lasers, which allows power scaling into the kilowatt range. Recently, a high-power yet very compact version of such a VCSEL-array became available that offers both the fast timing behavior of a laser as well as the large illumination area of a lamp.
Moreover, it allows a spatial and temporal control of the heating because individual parts of the array can be controlled arbitrarily in frequency, amplitude, and phase. In conjunction with a fast infrared camera, such structured heating opens up a field of novel thermal imaging and testing methods. As a first demonstration of this ansatz, we chose a testing problem very challenging to conventional thermal infrared testing: The detection of very thin subsurface defects perpendicularly oriented to the surface of metallic samples. First, we generate destructively interfering thermal wave fields which are then affected by the presence of defects within their reach. It turned out that this technique allows highly sensitive detection of subsurface defects down to depths in excess of the usual thermographic rule of thumb, with no need for a reference or surface preparation.
With the mandatory introduction of the May 2011 directive for reassessment of bridges in Germany, the administrations of the federal and state governments have the duty to prove the stability of their bridge stock. Verification of bridge stability will be realized with consideration of the newly increased traffic loads. Particularly in older bridges, the verification can only be achieved if calculative surplus load capacity of the original structural design is taken into account in the recalculation. One option for considering these reserves is the exact determination of the dead weight of the bridge. Within this case study, it will be demonstrated how the problem can be practically solved.
In order to determine the dead weight of a concrete bridge, its volume has to be calculated. as a first step, a 3D laser scanner is used to record the internal geometry of a hollow box bridge girder. For the determination of the thickness of the concrete member, the non-destructive technique ultrasonic echo is applied. The construction must be segmented in approximately equidistant parts in order to be able to carry out an economic and efficient investigation. The description of the segmentation of the point cloud, carried out in a 2D model, was presented in the first part of the publication. The subject of this presentation is the merging of 2D cross sections into a 3D model, from which the weight of the bridge can be calculated.
Flash thermography is a fast and reliable non-destructive testing method for the investigation of defects in carbon fiber reinforced polymer (CFRP) materials. In this paper numerical simulations of transient thermography data are presented, calculated for a quasi-isotropic flat bottom hole sample. They are compared to experimental data. These simulations are one important step towards the quantitative reconstruction of a flaw by assessing thermographic data. The applied numerical model is based on the finite-element method, extended by a semi-analytical treatment of the boundary of the sample, which is heated by the flash light. A crucial part for a reliable numerical model is the prior determination of the material parameters of the specimen as well as of the experimental parameters of the set-up. The material parameters in plane and in depth diffusivity are measured using laser line excitation. In addition, the absorption and heat transfer process of the first layers is investigated using an IR microscopic lens. The performance of the two distinct components of CFRP during heating – epoxy resin and carbon fibers – is examined. Finally, the material parameters are optimized by variation and comparison of the simulation results to the experimental data. The optimized parameters are compared to the measured ones and further methods to ensure precise material parameter measurements are discussed.
The combination of tomographic, microstructural data with other experimental techniques and with modeling is paramount, if we want to extract the maximum amount of information on material and component properties. In particular, quantitative image analysis, statistical approaches, direct discretization of tomographic reconstructions represent concrete possibilities to extend the power of the tomographic 3D representation to insights into the material and component performance. This logic thread holds equally for industrial and academic research, and valorizes expensive experiments such as those carried out at synchrotron sources, which cannot be daily repeated.
I will show a few examples of possible use of X-ray tomographic data for quantitative assessment of damage evolution and microstructural properties, as well as for non-destructive testing. Examples of micro-structured inhomogeneous materials will be given, such as Composites, Ceramics, Concrete, and Additively manufactured parts. I will also show how X-ray refraction computed tomography (CT) can be highly complementary to classic absorption CT, being sensitive to internal interfaces.
The combination of tomographic, microstructural data with other experimental techniques and with modeling is paramount, if we want to extract the maximum amount of information on material and component properties. In particular, quantitative image analysis, statistical approaches, direct discretization of tomographic reconstructions represent concrete possibilities to extend the power of the tomographic 3D representation to insights into the material and component performance. This logic thread equally holds for industrial and academic research, and valorizes expensive experiments such as those carried out at synchrotron sources, which cannot be daily repeated.
I will show a few examples of possible use of X-ray tomographic data for quantitative assessment of damage evolution and microstructural properties, as well as for non-destructive testing. Examples of micro-structured inhomogeneous materials will be given, such as Composites, Ceramics, Concrete, and Additively manufactured parts. I will also show how X-ray refraction computed tomography (CT) can be highly complementary to classic absorption CT, being sensitive to internal interfaces.
Additionally, I will present a new technique in our portfolio, Neutron Diffraction, which is extremely well suited to the study of internal stresses, both residual and under external load.
Non-destructive testing (NDT) is regarded as one of the key elements in ensuring quality of engineering systems and their safe use. A failure of NDT to detect critical defects in safetyrelevant components, such as those in the nuclear industry, may lead to catastrophic consequences for the environment and the people. Therefore, ensuring that NDT methods are capable of detecting all critical defects, i.e. that they are reliable, is of utmost importance. Reliability of NDT is affected by human factors, which have thus far received the least amount of attention in the reliability assessments. With increased use of automation, in terms of mechanised testing (automation-assisted inspection and the corresponding evaluation of data), higher reliability standards are believed to have been achieved. However, human inspectors, and thus human factors, still play an important role throughout this process, and the risks involved in this application are unknown. The overall aim of the work presented in this dissertation was to explore for the first time the risks associated with mechanised NDT and find ways of mitigating their effects on the inspection performance. Hence, the objectives were to (1) identify and analyse potential risks in mechanised NDT, (2) devise measures against them, (3) critically address the preventive measures with respect to new potential risks, and (4) suggest ways for the implementation of the preventive measures. To address the first two objectives a risk assessment in form of a Failure Modes and Effects Analysis (FMEA) was conducted (Study 1). This analysis revealed potential for failure during both the acquisition and evaluation of NDT data that could be assigned to human, technology, and organisation. Since the existing preventive measures are insufficient to defend the system from identified failures, new preventive measures were suggested. The conclusion of the study was that those preventive measures need to be carefully considered with respect to new potential risks, before they can be implemented, thus serving as a starting point for further empirical studies. To address the final two objectives, two preventive measures, i.e. human redundancy and the use of automated aids in the evaluation of NDT data, were critically assessed with regard to potential downfalls arising from the social interaction between redundant individuals and the belief in the high reliability of automated aids. The second study was concerned with the potential withdrawal of effort in sequential redundant teams when working collectively as opposed to working alone, when independence between the two redundant individuals is not present. The results revealed that the first redundant inspector, led to believe someone else will conduct the same task afterwards, invested the same amount of effort as when working alone. The redundant checker was not affected by the information about the superior experience of his predecessor and—instead of expected withdrawal of effort—exhibited better performance in the task. Both results were in contradiction to the hypotheses, the explanations for which can be found in the social loafing and social compensation effects and in the methodological limitations. The third study examined inappropriate use of the aid measured in terms of (a) agreement with the errors of the aid in connection to the frequency of verifying its results and in terms of (b) the overall performance in the task. The results showed that the information about the high reliability of the aid did not affect the perception of that aid’s performance and, hence, no differences in the actual use of the aid were to be expected. However, the participants did not use the aid appropriately: They misused it, i.e. agreed with the errors committed by the aid and disused it, i.e. disagreed with the correct information provided by the aid, thereby reducing the overall reliability of the aid in terms of sizing ability. Whereas aid’s misuse could be assigned to low propensity to take risks and reduced verification behaviour because of a bias towards automation, the disuse was assigned to the possible misunderstanding of the task. The results of these studies raised the awareness that methods used to increase reliability and safety, such as automation and human redundancy, can backfire if their implementation is not carefully considered with respect to new potential risks arising from the interaction between individuals and complex systems. In an attempt to minimise this risk, suggestions for their implementation in the NDT practice were provided.
The combination of tomographic, microstructural data with other experimental techniques and with modeling is paramount, if we want to extract the maximum amount of information on material and component properties. In particular, quantitative image analysis, statistical approaches, direct discretization of tomographic reconstructions represent concrete possibilities to extend the power of the tomographic 3D representation to insights into the material and component performance. This logic thread holds equally for industrial and academic research, and valorizes expensive experiments such as those carried out at synchrotron sources, which cannot be daily repeated.
Air voids in concrete like honeycombs are one of the major concerns regarding quality assurance for the construction of infrastructure buildings like bridges or tunnels. This paper shows that voids in reinforced concrete walls or slabs can be detected by two standard ground coupled GPR antennas in transmission mode using a two-side zero-offset profiling configuration like in borehole radar applications. For the detection of voids only the amplitudes of the direct wave in transmission mode are evaluated. Even when the depth of the void can not be detected in this configuration, the major advantage of the zero-offset profiling in transmission mode is a lower interference with the surrounding reinforcement compared to a regular one-side reflection profiling. The capability of the two-side zero-offset profiling is demonstrated on a test specimen with a set of polystyrene balls of two different sizes representing voids like honeycombs in concrete. GPR measurements are realized by an automated scanning system in order to allow for a synchronous movement of the antennas. In transmission mode voids can be detected at greater depths compared to reflection mode, since the travel path of the direct wave is half as long. Another characteristic of the transmission mode is that the direct wave through the air voids is faster and arrives earlier than the direct wave in the surrounding concrete. Hence it can be separated from the strong reflection of the reinforcement. Finally the measurements in transmission mode are less sensitive to the antenna frequency and polarization than in reflection mode.
Non-Destructive Evaluation (NDE) of structures is complex due to the uniqueness of almost all structures and their sizes. A single NDT method typically is not sufficient to meet the testing requirements, which cover different areas, such as material and structural properties. Measuring geometrical properties require other test methods than e.g. the detection of corrosion. Automation has proven to be necessary for aquiring large amounts a of high quality data in a short time. Examples of succesful method combinations from different areas of non-destructive testing in civil engineering are briefly described and their application is shown. Some of the examples also include automated inspection.
A discussion is provided on the relation between non-destructive testing (NDT) and fracture mechanics. The basic tasks behind this are to guarantee the safety of a component at a potential hazard loading event, to specify inspection intervals or, alternatively, of demands on NDT for a fixed inspection regime, to plan accompanying measures for cases of temporary continued operation of structures in which cracks have been detected, and, finally, fatigue strength considerations which take into account initial defects.
The aim of this work is to evaluate the feasibility of the direct radiography on weld
inspection in oil pipelines and gas pipeline during the manufacturing process. To that, 6 specimens
with 6 different thickness and varied height of reinforced weld with 5 different kinds of defects
were made. All samples were radiographied using Class I films and flat panel. For all specimens the
inspection length was 8''. Thus, with the flat panel the detector-to-object distance varied so that it
may adequate to several diameters of the tubes.
The detector-to-object distance was calculated based on the physical size of the detector
taking into consideration a safe distance between the tube curvature and the flat panel extremities,
keeping the lowest possible magnification factor so that it could be obtained the length of the
inspection. Images with 6 integration time for each experimental arrangement were obtained.
The images obtained with the Flat Panel/YXLON system were analyzed according to their
quality by using the Contrast parameters (essential wire) (DNV 2007/ IS0 12096 with
reinforcement and ISO 10893-7 basis material), Basic Spatial Resolution BSR (ISO 10893-7)
and normalized signal-to-noise ratio - SNRN (ISO 10893-7) and by detectability using as reference
the conventional radiography.
The results showed that for all thickness, the exposure time used to meet the image quality
requirements were below with direct radiography. However the BSR were not reached for thickness
of 4.85, 6.40 and 9.67 mm, therefore the compensation principle established by ISO 10893-7 was
considered, that is, one more contrast wire for a less wire pair.
The digital technique proved to be more sensitive to real defects found on welds than the
conventional technique. Then it can be conclude that the digital radiography utilizing the flat panel
can be applicable to the oil and gas segment with advantages over conventional technique as to
quality aspects, productivity, environment, safety and health.
Inspection of steel bridges
(2007)
Development of reference materials for surface technology in the micrometer and nanometer range
(2004)
Non Destructive Testing of Concrete Railway Tracks by Impulse Response and Impact Echo Techniques
(2003)
Nondestructive testing (NDT) methods are applicable in many ways for defect detection as well as optimization of packaging production processes. The visual inspection method is the technique which is mostly used, although neither the customer nor a skilled inspector may be aware of this.
Techniques like ultrasound for wall thickness measurement, the application of x-ray techniques or the use of dye penetrant techniques for crack detection are rather well known to the NDT family. However, acoustic emission techniques can also be helpful for the characterization of packaging materials. In this paper the employment of x-ray computer tomography (CT) for measurement of wall thickness in plastic jerrycans, especially on the edges, and its possible optimization of production processes will be discussed.
A comparison of the CT and ultrasonic examinations of wall thickness and the reliability of this measured data are also important points for the discussion, especially if some safety factors can be derived from the results.
The leakage test is also good for jerrycans, IBCs or other kinds of drums for the transportation and storage of dangerous goods. The disadvantage of this kind of test is that a lack of quality, e.g. wall thickness deterioration, cannot be detected if the wall thickness withstands the internal pressure. Therefore, especially for Quality assurance, the other, previously mentioned techniques are better for a statistical assessment of a batch. This paper is focused on the comparison of different NDT results with special emphasis on the large range of material mechanical properties.
Austenitic welds and dissimilar welds are extensively used in primary circuit pipes and pressure vessels in nuclear power plants, chemical industries and fossil fuelled power plants because of their high fracture toughness, resistance to corrosion and creep at elevated temperatures. However, cracks may initiate in these weld materials during fabrication process or stress operations in service. Thus, it is very important to evaluate the structural integrity of these materials using highly reliable non- destructive testing (NDT) methods. Ultrasonic non-destructive inspection of austenitic welds and dissimilar weld components is complicated because of anisotropic columnar grain structure leading to beam splitting and beam deflection. Simulation tools play an important role in developing advanced reliable ultrasonic testing (UT) techniques and optimizing experimental parameters for inspection of austenitic welds and dissimilar weld components. The main aim of the thesis is to develop a 3D ray tracing model for quantitative evaluation of ultrasonic wave propagation in an inhomogeneous anisotropic austeniticweld material. Inhomogenity in the anisotropic weld material is represented by discretizing into several homogeneous layers. According to ray tracing model, ultrasonic ray paths are traced during its energy propagation through various discretized layers of the material and at each interface the problem of reflection and transmission is solved. The influence of anisotropy on ultrasonic reflection and transmission behaviour in an anisotropic austenitic weld material are quantitatively analyzed in three dimensions. Theultrasonic beam directivity in columnar grained austenitic steel material is determined three dimensionally using Lamb’s reciprocity theorem. The developed ray tracing model evaluates the transducer excited ultrasonic fields accurately by taking into account the directivity of the transducer, divergence of the ray bundle, density of rays and phase relations as well as transmission coefficients. The ray tracing model is able to determine the ultrasonic wave fields generated by a point source as well as finite dimension array transducers.