International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003
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Acquisition and processing requirements for high quality 3D reconstructions from GPR investigationsMaurizio Lualdi, Luigi Zanzi, Luigia Binda
Politecnico di Milano, Italy
In the last few years, the GPR technology has been improved to meet the requirements needed for radar investigations on building elements. Many manufacturers have developed new high frequency shielded antennas to ensure very high resolution images. 3D GPR reconstructions are particularly useful for the diagnostic investigation of historic buildings. They can be applied to find details or inclusions inside a structural element (wall, pillar, roof or floor) when the complex geometry cannot be understood by standard 2D GPR investigations. The detection of voids, metal or timber elements, the location of timber beams and the detail of their connection to the bearing wall, are examples of problems that can find a reliable answer provided that the GPR technique is applied in 3D mode.
In order to carry out a successful 3D GPR survey it is necessary to acquire a dense grid of GPR traces. Accuracy in antenna position and orientation is very important for a successful application of a 3D migration software to produce images that can be directly interpreted by the end-users. An array of antennas helps to ensure a regular spacing in the cross-line direction of the survey but the array is heavy and large so that it might be inappropriate to investigate vertical elements like walls, pillars and columns and difficult to adapt to the shape of the surface decorations especially in historical buildings.
For these reasons, an important objective of the ONSITEFORMASONRY project (EESD project EVK4-2001-00091) is the development of a new positioning system for 3D GPR acquisitions executed with a small high frequency antenna. The requirements to reach the goal are discussed referring to examples that demonstrate the feasibility and cost-effectiveness of 3D experiments when a proper positioning system is available. Position accuracy and spatial sampling requirements are closely related and the acquisition time can be significantly reduced when the positioning system ensures a high level of accuracy (i.e., few mm). Accurate acquisitions are an essential pre-condition for a reliable application of a 3D data focusing program. A dedicated focusing program is discussed with special attention to some important aspects related with the antenna configuration and the near-field condition of the radar experiments on building elements.
The diffusion of 3D radar investigations is still limited by the slow development of dedicated equipment and acquisition tools. The technology available on the market is not advanced enough to make 3D experiments fast, accurate and cost effective.
The most serious problems concern the acquisition technique, specifically the system for monitoring the antenna position, and the processing software. Antenna positioning is a critical issue because a 3D effective reconstruction needs data collected with a position accuracy of about l/20, i.e., about half a centimeter when a 1GHz antenna is used. The solutions available on the market for monitoring the antenna position along a profile (1D positioning) are effective and easy-to-use. On the contrary, no effective solutions exist for monitoring the antenna position when a flat surface is surveyed (2D positioning). At present, the suppliers of high frequency antennas do only propose the use of thin plastic pads marked with the lines of the planned parallel profiles. Accuracy in preserving the correct position and orientation of the antenna strongly depends on the skill and care of the operator. As a result, the quality in positioning is not ensured and the acquisition time is normally inversely proportional to the spatial accuracy of the collected data. A correct antenna orientation is as much important as a correct antenna position since radar antennas are polarized and directive so that the energy reflected or diffracted by the targets depends on the respective antenna-target orientation. When the correct orientation is not ensured the data suffer from fluctuations of the signal intensity that might reduce the reliability of the final data interpretation (Reppert et al., 2002). A few examples of feasibility studies for the design of new positioning systems are documented in the scientific literature. One of the most advanced is discussed by Doerksen (2002) and consists of an optical mouse mounted on one side of the antenna. It is an interesting and applicable technique but it still suffers from the problem that it cannot ensure a regular spatial distribution of the collected data and it does not control the antenna orientation unless two mouse are used.
Another important issue is the 3D processing software; in fact the benefits of a good migration program and of a good 3D graphic software can be very much appreciated by the end users. Commercial software for radar processing is evolving but only in the last few years the suppliers have been distributing products for 3D processing and the quality of these products has not reached the required level yet. Specifically, some software products present good performances in terms of 3D graphics but they are not advanced enough concerning the migration operation. The migration is a specific processing operation aimed to represent the scattering targets honoring their position and geometry, within the resolution limits given by the signal frequency. It is a computationally expensive operation and in the same time it is a delicate task since the quality of the final result strongly depends on a balanced selection of some critical parameters. As a result, a good 3D software program must be computationally efficient but also flexible enough to offer the operator the necessary options for optimizing the most critical parameters.
Potential of 3D experiments
The 3D reconstructions of the investigated element are especially useful when the issue is a morphological problem such as the detection of targets that consist of a single or a number of scattering objects.
For instance, the existence of timber, metal or concrete beams or the existence of metal chains or tie rods, i.e., the existence of linear elements that are observed as diffraction hyperbolas in the plane of the radar profiles orthogonal to the direction of these elements, can be effectively documented by a 3D reconstruction from which the end-user can easily extract quantitative results such as position, depth and also dimensions provided that the wavelength is short enough compared to the target size.
All the above examples relate to images produced from radar data collected with high accuracy and processed with software programs specifically designed for 3D reconstructions. The quality of the reconstructions demonstrates the potential of this methodology. Nevertheless, the success of a method is not only associated with the quality of the results but also with the cost-benefit ratio compared to those offered by the most conventional methods. This is the motivation for technological improvements in the direction of facilitating the acquisition of accurate 3D data (problem of the positioning system) and in the direction of improving the quality of the 3D software programs.
Requirements for 3D acquisitions
The main requirement that must be fulfilled to collect a dataset that can be successfully transformed into a realistic 3D reconstruction is expressed by the Nyquist Theorem. According to Nyquist, the area must be surveyed with a density of the measuring points sufficient to prevent spatial aliasing problems. When this requirement is not satisfied we can expect a severe degradation of the migration results and a decrease of resolution. In principle, the Nyquist requirement is
where Dx is the maximum distance between two measuring points and l is the wavelength of the highest frequency in the antenna band.
As an example, equation (1) requires that the trace spacing for a medium with a velocity of 7.5 cm/ns surveyed with a frequency band extending from 500 MHz to 1500 MHz is lower than 1.25 cm. As a result, a good positioning system for a high frequency antenna should be able to ensure a trace spacing in the order of 1 cm and with a relative accuracy that must be a small fraction of this spacing. If we accept a relative accuracy of 1%, the absolute accuracy of the positioning system in a
To validate experimentally the spatial sampling requirement, we planned a 3D experiment with a 1GHz antenna over a reinforced concrete floor. The acquisition was performed manually being extremely careful in preserving the position accuracy and the correct antenna orientation. The data were collected with a very dense spatial sampling and then were progressively decimated to explore the spacing that should not be exceeded to preserve the quality of the final result.
In fig.6, a vertical section of the collected data volume after progressive decimation can be observed. The corresponding sections obtained after the application of the processing sequence, including migration, is shown in fig.7. The example shows that the spatial sampling can be drastically reduced without affecting the quality of the result. This is true up to a spacing of about 2.76 cm that is an interval much longer than the interval required by the Nyquist theorem as discussed above. Actually, this result is not in contradiction with the Nyquist theory since the requirement expressed by equation (1) is the most restrictive requirement corresponding to the most unfavourable situation that occurs when a very near-surface target is illuminated laterally with a surface wave. In such a case the diffraction curve that appears in the radar section, under the assumption of a constant velocity medium and a monostatic system, consists of two symmetric dip lines departing from the surface in the position of the target (fig.8). Instead, the diffraction curves for deeper targets are hyperbolas that asymptotically tend to the lines of the surface target. The Nyquist theory requires that the delay of the reflection time between two subsequent measuring points is lower than half a period of the wave. By applying this condition to a generic point belonging to a diffraction hyperbola we get the following equation (fig.8)
where f is the wave frequency. Of course, equation (2) degenerates into equation (1) when the target depth is zero. In real experiments the diffraction hyperbolas are observed with a limited aperture because of absorption and antenna directivity. Thus, we understand from fig.8 that when we observe buried targets, condition (1) can be relaxed into a less restrictive condition given by equation (2) to be applied where the diffraction dip is higher, i.e., at the limit of the diffraction aperture.
By applying equation (2) to the data of fig.6 we come to a maximum trace spacing of about 2.5cm that basically corresponds to the experimental conclusions documented by fig.7 where we start to observe some degradations only when we move from a spacing of 2.76 cm to a spacing of 3.68 cm. The degradation consists of a minor decrease of resolution although all the rebars are still clearly visible. To observe more severe degradations of the final image we have to increase the interval up to 5.52 cm. If we look at the subsampled raw data that produced these results (fig.6), it is amazing to see how the quality of the final image is stable in comparison with the apparent severe degradations observed on the raw data. This is a very interesting conclusion that comes from the discussed example: provided that the data are collected with a high position and orientation accuracy, there is no need to oversample the data, i.e., the spatial sampling in both X and Y directions can be set up according to the nominal values required by the Nyquist theorem. This means that a 3D 1GHz survey over a 1 square meter concrete slab can be successfully executed with only 40 parallel profiles (80 if both X and Y directions must be surveyed). Moreover, the test has demonstrated that 25 profiles for each direction, i.e., a spacing of 4 cm, although a little beyond the theoretical limit, are enough to preserve a quality and a resolution sufficient to solve most of the practical applications so that the acquisition time can be further reduced. This tolerance regarding the Nyquist limit is a consequence of the fact that the final image is often insensitive to the highest frequency components of the nominal antenna spectrum since these components are usually received with very low energy because of absorption and because of the downloading effect induced by antenna-ground coupling.
Actually, to extend the conclusions derived from fig.7 to the orthogonal direction, i.e., to the distance between parallel profiles, we should consider a more general situation where the rebars are not orthogonal to the profiles. Thus, the experiment was repeated by rotating 45o the profile direction with respect to the rebar orientation. The final result validates the above conclusions (fig.9).
Summarizing, the result from the laboratory experiment discussed above is that the setup of a 3D acquisition performed with a good positioning system, i.e., a positioning system that can ensure an accuracy of 1 cm in a 1 m2 area and can preserve the correct orientation of the antenna, can be designed according to the lowest spatial sampling intervals required by the theory. As an example, a 1GHz antenna survey can be designed on a grid size ranging from 2.5 to 5 cm depending on the medium velocity and absorption. This means that half an hour can be enough to survey a 1 m2 area, provided that the positioning tool does not require a complex and long installation. If these requirements are satisfied, 3D surveys are successful and cost effective. On the contrary, if the accuracy of the data position and the correct orientation of the antenna are not ensured, 3D surveys are not going to be rewarding and the benefit of the 3D migration of the data will be lost due to traveltime and amplitude effects induced by position and orientation errors respectively (Groenenboom et al., 2001; Reppert et al., 2002).
According to the above results, data density can be reduced to the minimum if the positioning systems is accurate. But an additional problem must be solved: how to ensure a regular distribution of the measurement points. In other words, there are probably more than one good solutions that can fulfill the accuracy requirement but that practically does not allow a reduction of data density during acquisition since they do not force the antenna to follow a regular path. As an example, an optical mouse system (Doerksen, 2002) or any other system where the movement of the antenna is monitored but is totally free, is not a good candidate to solve simultaneously all the problems. The antenna must be triggered during the survey. Now, if triggering is time-controlled, the data volume will tend to be oversized to ensure that the spatial sampling requirement is satisfied even when the antenna is running faster. On the contrary, if triggering is space-controlled by the positioning system itself, in principle, the data volume can be kept to a minimum. Anyway, in both cases, a practical solution must be found to drive the operator in order to visit all the grid points of the survey area.
In conclusions, the optimal solution is a system that can ensure simultaneously position accuracy, constant antenna orientation and full coverage of a regular grid of measurement points. With such a system, the final quality is preserved and acquisition time, memory allocation and processing time are minimized.
Hints for improving the 3D reconstructions
In principle, 3D reconstructions can be produced by assembling radar profiles processed with a 2D processing software. Nevertheless, there are some processing steps that are more rewarding when they are applied in 3D mode.
An example is the subtraction of the background noise that is usually performed by subtracting the average trace. By implementing the algorithm in 3D mode, the estimate of the background signal is statistically more reliable and the final result is more effective.
Another important operation that can take benefit from a 3D approach is the focusing algorithm. A good solution to produce a 3D focusing code efficient and sufficiently flexible consists of the 2D-2step method originally proposed by Gibson et al. (1983) to process seismic data for geophysical exploration. This algorithm is based on two subsequent bidimensional migrations executed along orthogonal directions and is quite attractive because it dramatically reduces the computation time. Gibson et al. demonstrated that in a homogeneous medium this approach is exactly equivalent to a real 3D migration. In a non homogeneous medium the focusing operator is approximated but the deviation from the real 3D operator is of a negligible order compared to the inaccuracy in the definition of the operator resulting from the poor resolution normally experienced in velocity estimation.
The algorithm, as proposed by Gibson et al., is applicable to monostatic radar system. Anyway, it can be extended to GPR bistatic systems (Valle et al., 2000), provided that the acquisitions are executed with a constant azimuth of the TX-RX axis and that the first 2D migration step is performed in this direction. Assuming that this direction is the y direction and that a scattering target is located in x=0, y=0, z=Z, as shown in fig.10, then the diffraction surface observed by the bistatic system will have equation
where To=2Z/v, v being the velocity of the homogeneous medium. This diffraction surface can be migrated in the target position by migrating first in the y direction, according to
where t is the time in the original data volume and t0 the time in the partially migrated volume, and then in the x direction, according to
Whatever the focusing operator is, an approximate description of the antenna footprint should be always included to limit the migration aperture. This helps to reduce the clutter and to prevent migration artifacts especially for near-surface targets. A practical and convenient approach is to calibrate the operator aperture directly on the data by analyzing the lateral extension of the target diffractions. The option of defining a different aperture for the in-line and for the cross-line directions can be very useful for focusing linear targets (beams, tie-rods, etc.) and near-surface targets since the diffractions produced by these objects do not present a circular symmetry. This is quite obvious for linear targets that can be efficiently migrated by drastically reducing the aperture in the direction parallel to the target.
As a consequence, a good practice for producing optimal reconstructions of linear targets distributed along orthogonal directions (crossing beams, reinforcement mesh, etc.) consists of separately focusing the 3D data collected along the orthogonal directions using an unbalanced operator. The sum of the resulting volumes will produce a 3D reconstruction of the targets much more effective than the result achievable by summing the data before the 3D migration.
Fig.11 shows a result obtained with this procedure: the target was again a reinforcement mesh in a concrete floor. The reconstruction is quite effective, although the dimension of the rebars is overestimated for obvious resolution limits that can be removed only by using higher radar frequencies.
For near-surface targets, including scattering points, the asymmetric shape of the diffraction depends on the antenna separation, on the finite dimensions of the antennas and on their polarization. As an example, fig.12 compares the XT section with the YT section intersecting the diffraction produced by a cylindrical target embedded in a homogeneous medium at about 10 cm from the surface. The comparison demonstrates the asymmetry of the diffraction surface in the orthogonal directions. The diffraction curve predicted by equation (3) is also overimposed to show the deviation of the analytical description from the real diffraction surface as a result of antenna dimension and polarization. This suggests that an advanced software for focusing targets observed in the near-field should also include an appropriate correction of the diffraction equation to reduce these deviations.
The application of 3D reconstruction to some typical cases found in the preservation of Cultural Heritage, shows the importance of 3D for the solution of difficult problems, which sometimes were up to now approached only by destructive investigation.
The GPR 3D investigation seems to be successful particularly in the detection of the hidden structure of timber floors or roofs.
To cut the costs of 3D acquisitions and to ensure the quality of the results, new solutions are needed for the problem of antenna positioning. The positioning system should ensure simultaneously position accuracy (within 1 cm in a 1 m2 area), constant antenna orientation and full coverage of a regular grid of measurement points. With such a system, the final quality is preserved and acquisition time, memory allocation and processing time can be minimized.
An advanced software for 3D data focusing is also an essential tool to make 3D reconstructions effective and rewarding. The software should be based on an efficient scheme such as the 2D-2step algorithm to reduce the computation time. It must be flexible enough to accept a different aperture for the in-line and for the cross-line directions. Finally, the focusing operator should also include an appropriate correction of the diffraction equation to take into account the near-field effects associated with the antenna dimension and polarization.