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1、3D Synthetic Aperture Techniquefor Ultrasonic ImagingAbstract3D Synthetic Aperture Technique for UltrasonicImagingThe group for non-destructive testing at Uppsala University has recently implementedthe phase shift migration method, which is a method to focus images acquiredunfocused using ultrasound
2、. However, their work has been limited to 2D data, whilefor many applications the gathered data is 3D. This project has extended the oldimplementation to 3D data. The new implementation has been done in two differentways, giving one algorithm that works fast but needs much RAM, and one algorithmthat
3、 takes long time but works on smaller computers, not demanding as muchmemory. The fast algorithm works faster than the time it takes to acquire the rawdata, which makes real-time use realistic. To test the performance of the twoalgorithms with respect to image improvement, both against each other an
4、d againstthe previous 2D implementation, a number of experiments were carried out, whichshowed that, apart from processing time, the two new algorithms were equal inperformance. The experiments also showed that the obtained resolution in both x-and y-directions matched the theoretical discussion.Con
5、tentsContents1 Introduction1.1 Background . . . .1.2 Ultrasonic Imaging1.3 Project description1.3.1 Goals . . .12352 Theory72.1 2D Time Domain SAFT . . . . . . . . . . . . . .2.2 Frequency Domain SAFT: Phase Shift Migration2.2.1 3D Phase Shift Migration . . . . . . . . .2.2.2 Aliasing . . . . . . .
6、. . . . . . . . . . . .2.2.3 Implementation . . . . . . . . . . . . . . .2.2.4 Computational complexity . . . . . . . . .2.3 Resolution . . . . . . . . . . . . . . . . . . . . . .799121519193 Experiments213.1 Needle target . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2 Contact testing
7、of a copper block with side drilled holes . . . . .3.3 Immersion testing of a copper block with side drilled holes . . . .3.4 Immersion testing of an aluminium block with at bottom holes3.5 Immersion testing of a copper block with at bottom holes . . .3.6 Aliasing . . . . . . . . . . . . . . . . . .
8、 . . . . . . . . . . . . . .3.7 Computational complexity . . . . . . . . . . . . . . . . . . . . . .4 Discussion and conclusionsBibliographyA Matched lteri.232934384145485559i151CONTENTSB EnvelopeC Neareld/FareldList of Symbols and AbbreviationsList of FiguresList of Tables63656871ii67Chapter 1Intro
9、duction1.1BackgroundIn the eld of ultrasonic nondestructive testing (NDT), the objective is to allowan object to be examined internally without damaging or putting any stress on thematerial, which can be highly useful e.g. when searching for cracks in welds. Oneapproach to the problem is to transmit
10、 ultrasonic signals into the object and recordthe echoes that comes back from discontinuities inside. A picture of the object isthen built by scanning an area and placing the recorded echoes from each positionin that area in a matrix. Doing this with an unfocused beam will give a picture withpoor re
11、solution, dicult to interpret, and one way of improving the resolution couldbe to use a focused beam. However, if using a focused beam, focus can only beachieved in one depth at the same time, blurring the rest of the image. Thereforeother techniques need to be used.One possible option is synthetic
12、aperture imaging (SAI), a technique based oncoherent summation of ultrasonic signals received by a transducer in dierent loca-tions in order to mimic a physical lens. There are many areas in which SAI, rstdeveloped in the 1950s in radar systems, is useful, e.g. medical diagnostics, seismicexploratio
13、n and nondestructive testing.In the eld of NDT, SAI was rst investigated in the 1970s and 80s, and showedpossibility to improve NDT applications. The technique was an implementation ofthe synthetic aperture principle succesfully used in radar and sonar.The simplest version of synthetic aperture imag
14、ing is known in NDT as SAFT- Synthetic Aperture Focusing Technique - which uses delay-and-sum techniques tomimic a physical lens. One of the advantages of SAFT is that it can achieve focusingin all points simultaneously.Even though SAFT theory has been known for a number of years in NDT, andhas been
15、 applied since the late 80s, it is still interesting, for as the modern comput-1CHAPTER 1. INTRODUCTIONFigure 1.1: The ultrasonic transducers used in the project. The left is an immer-sion transducer, and the right is a contact transducer.ers grow more powerful, so does the practical use of real-tim
16、e SAI implementations.There are still problems within SAFT that can be developed with further research,such as dealing with a layered structure in the object under examination. This hastraditionally been done in the time domain, but interest has recently turned to meth-ods of solving the problem in
17、the frequency domain instead, which is what this projectis adressing.Section 1.2 will give a brief description of the transducer used for transmittingand receiving ultrasonic pulses, as well as dierent ways of presenting ultrasonic data.Further on in section 1.3, the project will be presented, with
18、the goals set up. Chapter2 will give a review on the theory for time-domain SAFT and frequency-domainSAFT, known as phase shift migration. In chapter 3, a series of experiments will bepresented, and nally in chapter 4, the conclusions are summarized and discussed.1.2Ultrasonic ImagingTo be able to t
19、ransmit and receive the ultrasonic pulses, an ultrasonic transducer canbe used. The transducer transforms electrical signals into ultrasound waves duringtransmission, and during reception it does the opposite, and transforms ultrasoundwaves to electrical signals that can be handled in a computer. In
20、 this project, twodierent types of ultrasonic transducers have been used; the immersion transducer,and the contact transducer, see gure 1.1.In the so called monostatic case of ultrasound imaging, a single transducer is usedto scan an area of interest. There are dierent ways of representing the gathe
21、reddata, as seen in gure 1.3. At each point in the scanning area, the transducer sendsout an ultrasonic wave pulse, and receives the echoes from scatterers and reectors21.3. PROJECT DESCRIPTIONFigure 1.2: Setup for the immersed transducer.within the region of interest (ROI) below the transducer, gur
22、e 1.2 shows the setupfor the immersed transducer. For every such measurement the received amplitudecan be plotted against time resulting in what is called an A-scan1, an example ofwhich is shown in gure 1.3(a). Figure 1.3(b) shows the envelope of the same A-scan2. When scanning the transducer horizo
23、ntally along the x- or y-axis and puttingthe A-scan from each transducer position in a matrix, with the amplitude coded asintensity, a B-scan image is obtained (gure 1.3(c), and if instead using envelopeA-scans, an envelope B-scan is obtained, see gure 1.3(d). Envelope B-scans wereused to present th
24、e results in this project, since it can be more dicult for a user tovisually interpret the B-scan in gure 1.3(c) than the one in gure 1.3(d). Finally,gure 1.3(e) shows a C-scan which is created by scanning in both x- and y-directionand taking the maximum value of the received, enveloped, A-scans in
25、a time-frame5.1.3Project descriptionIn NDT, SAFT algorithms are commonly implemented in the time domain. How-ever, when investigating objects immersed in water, or objects that have a layeredstructure, refraction of the ultrasound signals impose problems when calculating prop-agation delays necessar
26、y in the processing, that are dicult to solve. There are time-domain techniques that adress and solve this problem, but recently there has beenan increased interest for techniques that implement SAFT in the frequency domaininstead. If implemented in the frequency domain with the use of a technique c
27、alledphase shift migration, the problem with inhomogeneities can be handled in a straight-The A is short for AmplitudeFor a more detailed discussion on envelope, see Appendix B.312CHAPTER 1. INTRODUCTION(a) A-scan(c) B-scan(b) envelope A-scan(d) envelope B-scan(e) C-scanFigure 1.3: Dierent ways of p
28、resenting data in ultrasonic imaging.forward way. The phase shift migation method has recently been implemented, butlimited to 2D data, and this project aimed at extending the implementation to 3Ddata. The implementations were evalutated both in terms of imaging performanceand computational eciency.
29、 The experimental data was collected from metal sam-ples using contact tests as well as using an immersion setup.Also, a time-domain SAFT algorithm was implemented with the intention ofrunning time-domain SAFT on the 2D frequency-domain processed data to obtain(quasi) 3D processed data, and compare
30、with the results from 3D frequency-domain41.3. PROJECT DESCRIPTIONSAFT processing. That idea was abandoned in an early stage, due to issues with thetime-domain implementation.1.3.1GoalsIn summary, the goals of this project were to:1. Implement an algorithm for time-domain SAFT with the intention to
31、run it ondata already processed with 2D frequency-domain SAFT in order to get quasi3D processed data.2. Extend 2D phase shift migration to 3D, and implement 3D phase shift migra-tion. Two ways of doing this were considered:a) one brute force implementation for fast processing on powerful computers,a
32、ndb) one slower but more memory ecient implementation that works on com-monly available computers.3. Compare the performance of the dierent implementations with respect toimage quality and computational eciency.5Chapter 2TheoryThis chapter will give a derivation of the theory for basic 2D time domai
33、n SAFT,that cannot handle any changes in the speed of sound, thus restricting us to tests onhomogeneous isotropic objects. Then a derivation for 3D frequency domain SAFT, amethod called Phase Shift Migration, is given. This method allows for dierent speedsof sound, as long as the boundary between tw
34、o regions with dierent speed of soundis in the same plane as the transducer. The problem of spatial aliasing that comeswith the Fourier transforms is adressed, and the two algorithms for implementing thefrequency domain theory that has been developed is presented. Finally, a discussionis given of th
35、e resolution that can be expected in the nal results.2.12D Time Domain SAFTFigure 2.1 illustrates the formation of a B-scan in the case of a single point scatterer.The transducer is scanned in the x-direction, and because of the width of its mainlobe, it will receive echoes from the scatterer at oth
36、er positions than directly aboveit. The point scatterer will give rise to a hyperbolic pattern in the B-scan, due to thedierence in time the pulse echoe has to travel to reach the transducers dierentpositions during the scan, and the fact that, in the B-scan, all echoes appears as ifthey are coming
37、from directly beneath the transducer. The deeper the scatterer isbelow the transducer, the wider the hyperbolic pattern. The width of the pattern willalso be dependent on the main lobe width of the transducer. The SAFT algorithmtake these hyperbolic patterns into account when reconstructing an image
38、. Basicallywhat it does is that it goes through all the pixels in a B-scan image and calculateshow the hyperbolic pattern would look if the pixel were to contain a scatterer. Thenthat pattern can be compared to the corresponding surrounding pixels, to determineif there is actually a scatterer there.
39、7CHAPTER 2. THEORYFigure 2.1: When a transducer scans over a point scatterer, the scatterer will besmeared out into a hyperbola in the B-scan, due to the dierence in travelingtimes for the transmitted pulses at dierent locations.This discussion of time-domain SAFT will be conned to the xz-plane, sho
40、wn ingure 2.2, and under the assumption that the size of the transducer is innitesimal 7,the wavefronts will be circular. First, we consider the case when the ROI contains onepoint scatterer, located at spatial coordinates xp = (xp, zp). When the transducertransmits a pulse at position xn = (xn, 0),
41、 the transmitted pulse will reach the pointscatterer and be backscattered, the echo reaching the transducer after a time2tp(xn) = |xp xn| =czp + (xn xp)2,(2.1)Figure 2.2: Geometry of the synthetic aperture822c2.2. FREQUENCY DOMAIN SAFT: PHASE SHIFT MIGRATIONwhere c is the speed of sound. If the tran
42、smitted pulse is g(t), and assuming thatthe scattered wave is nothing more than a scaled and delayed copy of the originalpulse, then the received echoed signal isr(t, xn) = pg t tp(xn) = pg t zp + (xn xp)2 ,(2.2)where p is the backscattering coecient. Now, by neglecting all secondary andhigher order scattering, the received signal at transducer position xn, when the ROIcontains a collection of point scatterers, becomesr(t, xn) =pg t zp + (xn xp)2(2.3)The reconstructed image that is focused at all poi
