Real-time full matrix capture with auto-focussing of known geometry through dual layered media

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1 Real-time full matrix capture with auto-focussing of known geometry through dual layered media Mark Sutcliffe, Miles Weston, Ben Dutton and Ian Cooper TWI NDT Validation Centre Heol Cefn Gwrgan, Margam, Port Talbot, SA1 6ED Kelvin Donne Swansea Metropolitan University Mt Pleasant, Swansea, SA13 EZ, UK Abstract A full matrix capture technique is presented that allows for real-time imaging through a non-planar surface where the geometry is known. For an identified geometry the point of incidence at the refractive interface is calculated using Fermat s principle and iterative techniques for each possible transducer position which is pre-processed ahead of the inspection. This information is combined with the transducer s encoded position during the inspection process with post-processing of ultrasonic data performed over the graphic processing unit. This is shown to allow for rapid imaging of ultrasonic data by firstly reducing the need to auto-focus through the media, and secondly by exploiting the parallelisation power of the graphic card. To demonstrate this, a linear array transducer was mounted to a Perspex wedge where the technique was applied to generate ultrasonic imagery of side drilled holes through a curved surface. This is shown to offer significant performance over traditional full matrix imaging with low implementation and development costs. 1. Introduction Ultrasonic array imaging is a useful inspection technique for the identification and classification of defects within solid structures and is routinely used within a wide range of site and lab based applications. When imaging of complex geometries is required, coupling of a rigid linear array transducer to a non-planar surface can prove problematic where direct contact is not always possible, and is often overcome by coupling through an intermediate medium such as a shoe or a fluid as in the case of immersion testing. With the introduction of advanced ultrasonic imaging techniques such as Full Matrix Capture (FMC), the Total Focusing Method (TFM) (1) and Sampling Phased Array (SPA) (), imaging through a non-planar surface is a computationally intensive task, where it is necessary to calculate the time of flight from each transmit / receive element combination to a given pixel region of interest through the refractive boundary. While extensive investigation has been undertaken in the efficient imaging of such data (3), it is often applied during post-processing sometime after the inspection has been undertaken. This in part is due to the much larger datasets associated with FMC, but also due to the

2 number of calculations required to effectively image ultrasonic data for a non-planar surface. This paper describes a method that allows for real-time inspection of FMC acquired data for a non-planar surface applicable to immersion testing. A technique was explored that generated the focal calculations ahead of the inspection in relation to the position of the transducer along the length of the geometry. This information was stored to file for later retrieval based on the encoded transducer position at time of the actual inspection, and was combined with post-processing of the FMC imaging algorithm over the Graphic Processing Unit (GPU) to allow for rapid inspection. This was shown to provide an effective approach for a non-planar surface through dual media given that the geometry was well known and calculated ahead of time.. Theoretical Background.1 Full Matrix Capture Imaging FMC is a data acquisition technique that allows for the complete time domain signal to be captured from every element of a linear array probe. A technique first introduced to NDT by Holmes et all in 005 (1), and extensively explored for use with medical ultrasound for many years prior to this (4). Data is acquired using a transmit on one and receive on all data capture approach, with the first element initially acting as transmitter, with every element (n) acting as receiver. The process repeats until all elements have transmitted; generating a complete set of time domain signals containing n A-scans. Since the energy in the material at any moment is generated from only a single element, the technique is often referred to as a sequential data acquisition method. Imaging of FMC data is commonly achieved through the Total Focussing Method (TFM), where a grid of pixels representative of the region of interest is defined with relevant amplitude information from the full matrix of data being extracted, allowing every pixel in the image to be treated as a focal point allowing for fully focused imagery of the region-of-interest to be rendered. The algorithm used to image this data is generated through a standard sum and beam-forming approach as expressed in equation 1 (1) ; where I is the intensity value for pixel location x,z, which is determined from the time of flight calculations from each transmit (tx) and receive (rx) pair to the pixel region of interest (x,z) with c being the velocity in the medium. A Hilbert transform (h) is used to convert the real time domain signal into complex form allowing the signal magnitude (envelope) to be found. I( x, z) = h tx, rx (x tx x) z (xrx x) z c...(1) Where the transducer is placed normal to the surface this technique proves effective. However when dealing with a non-planar surfaces such a curved geometry with

3 immersion testing or imaging through a wedge it is necessary to introduce the velocity of this interface medium and the refractive boundary into the algorithm. This is commonly achieved by exploiting Snell s law and Fermat s principle..1 Snell s law and Fermat s Principle The direction of a beam at an interface point between two media of acoustic velocities ci and c can be calculated using the well-known Snell s law, and is expressed here in its most common form in equation where φ i and φ R represent the angle of incidence and the angle of refraction respectively. This equation is often used for angle beam inspection to determine the path ultrasonic energy will take as it leaves the transducer and propagates through the refractive interface into the second medium. With the equation holding true for both longitudinal and shear wave modes, setting φ R equal to 90 o for a refracted longitudinal wave mode, the first critical angle can be determined. Beyond this angle no longitudinal wave mode exists and shear wave mode will be the dominant mode of propagation. sin( φ i ) sin( φr ) =...() ci c px ci pz qx qz c... (3) It can be shown that Snell s law is derived from Fermat s principle of least time (5). Expressed here in figure 1 and equation 3; where px, pz is the location of point source P, and qx,qz is the location Q within the material. The point along the refractive interface at which the least travel time is determined is the point at which the maximum ultrasonic energy will be transmitted from the interface material into the test material. By adopting an iterative approach along this refractive interface the path from which the ultrasonic source is emitted to a given pixel region of interest can be determined for both a planar and non-planar surface. In the case of a non-planar surface, the angle of incidence from the point source P is of importance as mode conversion is a consideration..1 Focusing through dual media Expanding equation 1 to account for focusing through a refractive interface leads to equation 4, and is illustrated for a non-planar surface in Figure ; where I is the intensity value for pixel location x,z, which is determined from the time of flight calculations from each transmit (tx) and receive (rx) pair to the pixel region of interest (x,z) via the point at which the ultrasonic energy passes through the refractive interface (x txi, z txi for transmit and x rxi, z rxi for receive) to the pixel location. The velocity in the medium is c and the velocity though the interface material is ci. 3

4 Figure 1. Fermat s principle; where the time to get from point P to point Q will take the path of least time through the refractive interface. Figure. Fully focused imaging of FMC data where every pixel acts as a focal point with intensity values calculated from the summed contribution from all elements. I( x, z) = h tx, rx (x (x tx txi - x txi - x) ) z txi ci z ( z z ) (x - x) ( z z ) txi (x c rx - x rxi rxi ) rxi rxi...(4) 4

5 Determining the point of incidence from a transducer element through the refractive interface for a given pixel may be solved analytically for a planar surface, but for nonplanar surfaces it is necessary to solve this using a numerical or iterative approach. For computational simplicity an iterative approach has been explored for the work in this paper. Each focal calculation for each pixel was pre calculated and stored for later retrieval; this provided the benefit of computational efficiency during the inspection process, with additional gains made through parallelisation of the summation of data through the graphic processing unit.. The graphic processing unit CUDA is a parallel programming model first introduced in 006 by NVIDA to allow for complex computational problems to operate over its GPU architecture. It is built around a scalable array of multithreaded streaming multiprocessors that are designed to execute hundreds of threads concurrently, with thread management controlled by the Single Instruction - Multiple Thread (SIMT) architecture. A technique based on the supercomputers of the 1970 s, it is an architecture that is not suitable for general purpose threading (where there is a dependency between threads). Thread execution is performed in groups of 3 parallel threads referred to as warps, with each GPU having a limited amount of memory which is managed independently of the CPU. Implemented as a subset of the C programming language, each CUDA kernel is capable of executing only a limited amount of code. Originally developed for speeding up graphic operations, the GPU has evolved to allow for a high level of parallelisation where a single operation is required. An example of this would be in the case of 3D computer animation, where a typical data-set would be the vector information for objects within the virtual world, and an operation involving the rotation of all objects along a specific axis. As each vector may be rotated in isolation of all other objects a single instruction is executed against all vectors in memory in parallel. While the CPU offers greater flexibility in its parallel processing and threading architecture, it typically contains a smaller number of processing cores than that of the GPU. While a typical CPU may have 4-8 cores, it is common for an entry level GPU to have in excess of 96 cores. Furthermore due to the simplified threading architecture, issues of thread concurrency and thread management are less of an issue with the GPU. Given that the TFM algorithm has no internal dependency on data, it is an ideal candidate for post-processing over the GPU, as each calculation may be performed in isolation. 3. Experimental configuration A data acquisition and post-processing system was assembled for this work consisting of a Micropulse 5PA array controller. Data was acquired using the half matrix FMC technique and processed by the TFM algorithm using a desktop computer with two quad core 3GHz CPUs and 48GB of RAM with a NVDIA GTX 560TI 380 CUDA core graphic card. The maximum data transfer rate of this acquisition system was 5

6 approximately 7 MB/s. The transducer used was a GE 3 element linear array probe with 1 mm pitch and 5 MHz central frequency. This was attached to a single axis encoder with a resolution of 1 cycles per mm to record its position relative to the test specimen. A low carbon steel block containing 5 horizontal side drilled holes with a curved profile was used, which was attached to a custom made Perspex shoe for ease of inspection, and is illustrated in figure 3. Figure 3. Experimental configuration allowing for encoded tracking of transducer movement. Focal calculations were performed ahead of the inspection by simulating the transducers location relative to the curved refractive boundary in software at 1 mm increments. This information was stored for use during the inspection where the data was linked to the transducers encoded position. For the experimental configuration calculation of this data for the entire test specimen took approximately 65 minutes to complete. During the inspection process these calculations were retrieved with post-processing against the FMC acquired data performed over the graphic card. 4. Results The focusing algorithm was simulated in software to map a region of interest -15mm to 15mm horizontally and 15mm to 35mm vertically relative to the transducer for the experimental configuration described in section 3. The transducer was simulated to move over the entire width of the test specimen with focal calculations stored as separate files for each transducer location. The experimental configuration allowed for the tracking of the transducer locations during the inspection through the use of a wheel encoder. The use of this encoded information allowed for the retrieval of the appropriate focal calculations to be copied to memory. As looking up pre-calculated values is more computationally effective than calculating the time of flight calculations as needed imaging of the raw data was completed in a time-efficient manner. 6

7 The image was rendered at a resolution of 0.5mm per pixel producing an image of 10x80 pixels. The fully focused image of this test specimen is shown in figure 4, where each side drill hole is clearly visible at its correct location. Specifically each side drill hole is seen to lie on a horizontal axis, showing correct focussing through the curved interface. Imaging of this data was done live during the inspection with results provided in table 1, where the approach was shown to provide a real-time method of inspection for a complex surface if prior knowledge of the geometry is known. Figure 4. Actual imagery acquired from experimental system demonstrating accuracy of the focusing algorithm. Table 1. Time taken to generate imagery with and without pre-calculating the focal data required for the inspection (all times in milliseconds) Pre-calculated Non pre-calculated Task Time Get data 13 Load focal calculations 30 Render 6 TOTAL 49 Task Time Get data 13 Generate focal calculations 49,300 Render 6 TOTAL 49, Conclusions and Further Work An algorithm was presented to allow for focussing through non-planar geometry for FMC acquired data where there is prior knowledge of the geometry. Based on Fermat s principle an iterative solution was found whereby focal calculations were performed 7

8 ahead of the inspection. This when combined with post-processing over the graphic hardware was shown to allow for real-time inspection through a non-planar surface. The ability to perform analysis in real-time during the inspection makes the solution suitable for automated or repeated inspection on a number of components of an identical geometric configuration. A limitation of the algorithms presented here is that they do not take into account mode conversions that can occur where the geometry causes the ultrasound to deviate from the calculated path. However, this can be accounted for by adopting a technique allowing for multi-mode focussing of FMC data (6). Further efficiency gains may also be exploited by optimising the focal calculation algorithms. With FMC being a popular topic within NDT at present this illustrated focussing of FMC data through complex geometry can be accomplished at frame rates comparable to existing phased-array and traditional ultrasonic inspection techniques, with low implementation costs. Acknowledgements This work was completed in partnership with TWI NDT Validation Centre (Wales), Swansea Metropolitan University, the University of Wales and the Prince of Wales Innovation Scholarship scheme (POWIS). References and footnotes 1 C. Holmes, B. Drinkwater, and P. Wilcox, Post-processing of the full matrix of ultrasonic transmit receive array data for non-destructive evaluation, NDT & E International, vol. 38, no. 8, pp , Dec P. Arrays, Sampling phased array a new technique for ultrasonic signal processing and imaging, Insight, vol. 50, no. 3, pp , A. J. Hunter, B. W. Drinkwater, and P. D. Wilcox, Autofocusing ultrasonic imagery for non-destructive testing and evaluation of specimens with complicated geometries, NDT & E International, vol. 43, no., pp , Mar J. A. Jensen, S. I. Nikolov, K. L. Gammelmark, and M. H. Pedersen, Synthetic aperture ultrasound imaging, Ultrasonics, vol. 44, K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical Methods for Physics and Engineering. Cambridge University Press, 00, p J. Zhang, B. W. Drinkwater, P. D. Wilcox, and A. J. Hunter, Defect detection using ultrasonic arrays: The multi-mode total focusing method, NDT & E International, vol. 43, no., pp , Mar