- Email: [email protected]
Application of digital signal processing techniques to synthetic aperture focusing technique images
Sensors and Actuators 76 Ž1999. 448–456 www.elsevier.nlrlocatersna
Application of digital signal processing techniques to synthetic aperture focusing technique images O. Martinez ) , M. Parrilla, M.A.G. Izquierdo, L.G. Ullate Instituto de Automatica Industrial (CSIC), La PoÕeda (Arganda del Rey), 28500 Madrid, Spain ´ Accepted 4 December 1998
Abstract Synthetic aperture focusing technique ŽSAFT. has become a popular alternative to transmission–reception focused arrays ŽTRFA. in order to reduce hardware complexity and cost associated to ultrasonic ŽUT. imaging systems. A shortcoming of SAFT processing is that it introduces artifacts that distort the images. However, as SAFT is sequential, efficient digital processing algorithms can be used to improve image quality. In this paper, several digital processing techniques are proposed including apodization, deconvolution, dynamic focusing, deflection and envelope extraction. A pipeline architecture which allows execution of these algorithms in parallel for real-time imaging is also proposed. q 1999 Elsevier Science S.A. All rights reserved. Keywords: SAFT; Pipeline architectures; UT images; Real-time digital processing
1. Introduction Ultrasonic ŽUT. arrays are formed by sets of transducers, which can be delayed electronically in emission and in reception to control the UT beam direction, thus allowing the space of interest to be scanned without mechanical motion. Echographic systems based on transmission–reception focused arrays ŽTRFA. are very usual for medical applications. As TRFA systems require a high degree of parallelism, they are usually based on analog techniques, which are more suitable for real-time imaging w1x. However, synthetic aperture focusing techniques ŽSAFT. are more adequate for non-destructive testing ŽNDT. applications where a reduction on complexity and costs are pursued. Conventional SAFT operate sequentially in two stages. First, each transducer element emits and receives an echosignal which is digitized and stored. Then, digital signal processing ŽDSP. is applied to generate the scanning lines, which form the UT image w2x. SAFT images have fairly good lateral resolution, but present several disadvantages
)
Corresponding author. Tel.: q34-1-871-1900; Fax: q34-1-871-7050; E-mail: [email protected]
in processing speed for image compounding, SNR, and even in image quality due to grating and side lobes. However, SAFT allows an efficient use of digital processing algorithms to improve image quality. Previous works have been mainly addressed to improve delays management, i.e., for dynamic focusing which improves lateral resolution and side lobes level w2x, or sub-sampling techniques which reduce phase aberration effects w3x. Other techniques based on complex aperture functions and multiplying the number of shots per element have been proposed to reduce side and grating lobes w4,5x. Side lobes may also be reduced by analog apodization which is easy to implement w6,7x. This work presents a processing method that includes a set of algorithms, some of them mentioned above, i.e., sub-sampled dynamic focusing processing and apodization. and, additionally, deconvolution that improves axial resolution and reduces grating lobes, and real-time envelope extraction that smoothens the image. The main problem is to design a simple processing system fast enough to execute all the above algorithms in real-time. To this purpose, an architecture is proposed which is based on the SENDAS approach w8x. This is a modular-pipelined architecture able to execute complex digital processing algorithms at 10 Msamplesrs. In addi-
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 0 2 8 - X
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
tion, the use of binomial approximation for dynamic focusing will allow to further reduce the architecture complexity, with little alteration of the image quality.
2. Theory background SAFT can be used to emulate TRFA. However, while TRFA is a two-way focusing technique, SAFT only focuses in reception. For a N-element array, like that shown in Fig. 1, the differences between both approaches may be analyzed by means of the continuous wave point spread function ŽPSF. w5x, which shows the acoustic lateral profile for the focal line. Assuming a dynamic focus, the PSF at any given depth for TRFA is: sin2
k
ž
Nd sin Ž u . 2 PSF Ž u . A k sin2 d sin Ž u . 2
ž
/
Ž 1.
/
and for SAFT: PSF Ž u . A
sin Ž kNd sin Ž u . . sin Ž kd sin Ž u . .
Ž 2.
where k s 2prl, d is the element spacing and u is the deflecting angle. From both expressions three important differences between SAFT and TRFA imaging must be highlighted. Ža. The ratio from signal to grass noise decreases in SAFT. The quadratic terms of Eq. Ž1. produce an increment in main-to-side lobe ratio ŽMSLR. that is not achievable with SAFT. Žb. The lateral resolution doubles with SAFT. Žc. Grating lobes with SAFT are greater and nearer to the main lobe than with TRFA. In TRFA the angular distance between grating lobes and main lobe is u s arcsinŽ lr Ž Nd .., but in SAFT it decreases to u s arcsinŽ lr Ž2 Nd ... That makes SAFT more sensitive to grating lobes. These effects, described for the far-field, can also be
449
shown in the near-field. Fig. 2 shows the PSF computed for a 16-element Ž8 mm high. linear array with d s 0.5 mm, l s 0.43 Žwe shall use this configuration as reference array in this work., focused at z s 50 mm. The acoustic field has been modelled using the exact algorithm given in Ref. w9x. It can be observed that lateral resolution and the level of side lobes and grating lobes are very much affected by SAFT.
3. Signal processing The object of the front-end signal processing is to improve UT image quality by decreasing the effects of side and grating lobes while maintaining system resolution with optimal specifications. Different strategies have been developed by several authors w5x, but most of them increase hardware volume and complexity. The purpose of this paper is to introduce a set of digital processing algorithms at the two stages of SAFT image formation, which are executed sequentially over the traces in a pipeline arrangement.
3.1. Dynamic focusing Dynamic focusing is based on the spatial diversity that characterizes transducer arrays. The objective is to add in phase the signals, which arrive at every element with different delays, for every field point. Cylindrical focusing applied to a spatial point P Ž R f , u . for a N-element linear array, requires to delay the signal received at the i-element Ž i s 0, . . . , N y 1. by an amount T Ž i .:
T Ž i. s
(
2
R f y R 2f q Q Ž i . y 2 R f Q Ž i . sin u c
Ž 3.
where QŽ i . s id y Ž N y 1. dr2 is the distance from the ith element to the center of the array aperture, R f is the depth of the focus lens, u is the steering angle and c is the sound propagation velocity. For a given steering angle u , varying the focus R f as the pulse propagates Ž R f s tr2 c . performs dynamic focusing. For the points where R f 4 D, the binomial approximation of Eq. Ž3. w10x can be applied:
T Ž i. f
Fig. 1. Linear array configuration.
Q Ž i . sin u c
y
QŽ i.
2
2 Rf c
Ž 4.
which has two terms: the first term is a linear function of the element position QŽ i . and the steering angle u and may be considered as deflecting delays; the second term is
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
450
Fig. 2. Near-field of a linear array of 16 elements spaced 0.5 mm, focused at Z s 50 mm. TRFA processing in dotted line. SAFT processing in solid line.
a quadratic function of the element position QŽ i . and implements dynamic focusing for every range R f ŽFig. 3.: Q Ž i . sin u Tu Ž i . s , Ž 5. c Tf Ž i . s y
QŽ i.
sense the array can be considered as a spatial filter whose characteristics Žresolution, main lobe to side lobe ratio, etc.. can be studied in the spatial frequency domain w11x. The spatial filter is described as:
2
2 Rf c
.
Ž 6.
Focusing has been divided into two different operations which is very useful for the hardware implementation. The validity of this approximation can be observed in Fig. 4 where the array acoustic field in the case of dynamic focusing at u s 208 has been modelled w9x. 3.2. Apodization The diffraction lobes produced by the array aperture can be reduced by controlling the channel gains w6x. In this
Ž Ny1 .
yw nx s
Ý
wi x i w n x
Ž 7.
is0
where x i w n x is the signal received from the ith channel and wi is the gain of that channel. Uniform apodization Ž w b w i x s 1, i s 0 . . . Ž N y 1.. describes the natural aperture behaviour, which has both maximum diffraction lobes and higher resolution. Other apodization functions ŽHanning, Hamming, Blackman, etc.. use gain values that smooth the aperture to decrease side lobes, reducing strongly the gain in the extreme elements.
Fig. 3. Time delay vectors focussing at the point P Ž R f , u .. On the left, time delays for the Fresnel approximation; on the right, exact cylindrical focusing delays.
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
451
Fig. 4. Acoustic field contour Žy3, y6, y12 and y18 dB. dynamic focussing a 16-element array at the steering angle u s 208: top, exact cylindrical focusing delays; bottom, Fresnel approximation.
To guarantee the condition of spatial diversity, some level of signal contribution per channel is required. Then, an interesting apodization function which takes into consideration an aperture exploitation degree a is the Generalized Hamming Window ŽGHW. which is defined as: wGH W w i x s
½
a q Ž 1y a . cos
2p
ž ž N 0,
iy
N y1 2
//
,
0 F i F Ž N y1. rest
Ž 8. where 0.5 F a F 1, and the minimum apodization value is 2Ž a y 0.5.. Fig. 5 that shows increasing a improves resolution, although MSLR is reduced. Therefore, a trade-off between resolution and side lobe reduction must be reached. It is possible to recognize three special cases: Ž1. for a s 0.5 GHW becomes the Hanning Window; Ž2. for a s 0.54 it becomes the Hamming Window, which achieves the greater MSLR and Ž3. for a s 1 it becomes the Boxcar Window, which achieves the best resolution. The grating lobes are a repetition of the aperture diffraction pattern in the direction u s arcsinŽ lrŽ2 Nd ... A drawback of apodization is that grating lobes are widened. This
characteristic is especially important for SAFT imaging where the use of apodization techniques may not be recommended for certain applications. Fig. 6 shows the PSF for values of a that make MSLR to be: 40 dB ŽHamming Window., 30 dBŽ a s 0.608., 20 dB Ž a s 0.76. and 13 dB ŽBoxcar Window.. Low values of a widens grating lobes as can be seen in Fig. 6. Due to the finite size of the array elements, the MSLR improvement is better than expected from the apodization filter. 3.3. DeconÕolution Deconvolution w12x is used to narrow the time domain UT pulse with the purpose of increasing axial resolution and reducing grating lobes. By the theory of linear systems, it is possible to describe a pulse–echo system as: U
y Ž t . s hŽ t . x Ž t .
Ž 9.
where y Ž t . is the received signal, x Ž t . is a band-limited signal that includes the two-ways response of the transducer and electronics, and hŽ t . represents the spatial impulse response of the studied object.
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
452
Fig. 5. Generalized Hamming Window, 0.5 - a - 1. Ža. MSLR; Žb. resolution, measured as resolutionŽ a s 1.rresolutionŽ a ..
To achieve narrow signals, an approximation of hŽ t . should be obtained from y Ž t . and x Ž t ., the latter being considered as a reference signal, measurable and invariant for any problem. The inverse filter is a good approach to deconvolution in real-time. In the frequency domain: Y Ž f . sX Ž f . HŽ f . ™HŽ f .s s Fy1
YŽ f .
½ 5 XŽ f .
.
YŽ f . XŽ f .
U
™
c s Ry1 Q
Ž 13 .
™ hŽ t .
Ž 10 .
The term cŽ t . s Fy1 1rX Ž f .4 yields the filter coefficients vector which allows to get hŽ t . directly by a convolution process: hŽ t . s y Ž t . c Ž t . .
whose band width is adapted to the UT pulse. The method gives the following values for the filter coefficient vector ™ c in discrete form:
where R is the autocorrelation matrix of x Ž n. and Q is the cross correlation vector of x Ž n. and dŽ n.. In a second stage, deconvolution is computed in real-time by executing Eq. Ž11. with the aid of a specific correlator. The desired
Ž 11 .
However, this is not quite a practical solution as outside the ideal conditions hŽ t . is very sensitive to noise. If we include noise in Eq. Ž10.: HŽ f . s
Y Ž f . qRyŽ f . X Ž f . qRxŽ f .
Ž 12 .
where R y Ž f . and R x Ž f . are noise spectral densities for y Ž t . and x Ž t ., respectively. It indicates that outside the frequency band of the UT pulse Žpoor SNR., the equation above yields H Ž f . f R y Ž y .rR x Ž f ., an indeterminate solution. There are different solutions for this problem, i.e., band pass filter, Wiener filter, shaping filter, etc. The last method has been used in this work. In a setup stage, the inverse filter coefficients are calculated to obtain an estimated impulsive response dŽ n.
Fig. 6. Acoustic field for SAFT processing with GHW apodization. Ža. a s 0.54; Žb. a s 0.608; Žc. a s 0.76; Žd. a s1.
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
453
4. System operation
Fig. 7. Diagram block of the receiving processing chain.
output dŽ n. has been approximated to a Gaussian pulse centered at the transducer frequency. 3.4. EnÕelope extraction DSP techniques frequently operate on RF signals. However, UT images improve using the trace envelope. By means of the Hilbert transform, conventional methods to compute the analytical signal have been derived. However, even using DSP, such methods are not fast enough for array imaging. Other methods, based on non-linear filtering which are executed in the time domain have been proposed. In this sense, an approach which computes a good approximation of the analytical signal magnitude at the required rate of 10 Msamplesrs has been presented in Ref. w13x.
This work proposes to introduce DSP at the two stages that constitutes a conventional SAFT. At the first one, where signals from the elements are digitized and stored, the following digital techniques are included: apodization, deconvolution and quadratic dynamic focusing. At the second stage, where the image lines are formed, steering and envelope extraction are performed ŽFig. 7.. The SENDAS architecture presented in Ref. w8x allows to develop this configuration in a pipelined arrangement. Dynamic focusing is a complex operation that requires high processing and storage capabilities w2x. However, using the Fresnel approach, the hardware complexity can be reduced. This can be explained with the aid of Fig. 8 for an array of N-elements, which store m samples per signal and forms L lines per UT image. For a conventional SAFT, memory for NmL data is required. Applying binomial approximation the memory requirements are lowered to Nm data for dynamic focusing, and NL for steering. For example, for N s 32 elements, m s 1000 samplesrtrace and L s 200 linesrimage, conventional SAFT requires 6.4 Mbytes, while the binomial approach needs only 38.4 kbytes. Dynamic focusing can be carried out by shifting the received UT signal from every transducer element. From the sampling period, the time delays T Ž i . for focusing may be expressed in number of samples. In order to increase the time resolution sub-sampling techniques by linear interpolation-processing may be employed. The focusing
Fig. 8. SAFT architectures. Ža. Based on exact focusing; Žb. based on binomial focusing.
454
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
Fig. 9. Steering images wy408, q408x following different processing algorithms: Ža. steering only; Žb. dynamic focusing; Žc. dynamic focusing and apodization; Žd. steering and deconvolution; Že. dynamic focusing and deconvolution; Žf. dynamic focusing, deconvolution and apodization.
sample index k of the ith transducer will be computed as: X i Ž k . s x i Ž Tf w i ,k x . q
x i Ž Tf w i ,k x q 1 . y x i Ž Tf w i ,k x . If w i ,k x
Ž 14 .
where x i Ž k . and X i Ž k . are the samples of the unfocused and focused signals, respectively, Tf w i,k x is the sample delay, and If w i,k x is the interpolation factor associated with the delay. Steering operation is carried out analogously. For a given angle u , the delay index is common for all the
Fig. 10. Lateral profile, degrees in horizontal axis and amplitude ŽdB s. in vertical axis, Ža. steering only; Žb. dynamic focusing; Žc. dynamic focusing and apodization; Žd. steering and deconvolution; Že. dynamic focusing and deconvolution; Žf. dynamic focusing, deconvolution and apodization.
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
455
Fig. 11. Axial profiles Ž Z Žmm. in abscissa and amplitude ŽdB s. in ordinates., Ža. steering only; Žb. dynamic focusing; Žc. dynamic focusing and apodization; Žd. steering and deconvolution; Že. dynamic focusing and deconvolution; Žf. dynamic focusing, deconvolution and apodization.
samples of ith trace, and is given by T w i, u x. For the index sample k: N
Xu Ž k . s
Ý is1
q
ž
x i Ž k q T w i ,u x .
x i Ž k q T w i ,u x q 1. y x i Ž k q T w i ,u x . I w i ,u x
/ Ž 15 .
Where Xu Ž k . and x i Ž k . are the samples of steered and unsteered in signals, respectively, and I w i, u x is the interpolation factor associated with the delay for the ith trace.
main-to-side and grating lobes. Lateral resolution is dramatically improved. However grating lobes can be still observed. Žb. The role of apodization is not as interesting as it was estimated by simulations. The main reason is the wide band width of the UT pulses. Therefore, side lobes reduction is not an important issue as long as wideband transducers are used. Furthermore, apodization widens the grating lobes. Žc. Deconvolution plays an important role on image quality. Among others, axial resolution is highly increased and grating lobes are strongly reduced. Lateral resolution is maintained at good level. 6. Conclusions
5. Experiments For the experimental procedure a SENDAS system was used. The system controls a 16-element linear array Ž8 = 8 mm., which emits wide band width Ž40%. pulses with a central frequency of 3.5 MHz. The effect of digital processing has been studied by changing the process chain for result comparing. The images correspond to a 0.5-mm diameter wire positioned at Ž X s 0.4 mm, Z s 23.8 mm.. Images have been formed by 81 steering lines Žwy408, q408x.. 5.1. Results Fig. 9 shows six B-scan images using different processing chains. The lateral and axial profiles can be observed in Figs. 10 and 11. In subfigures Ža., Žb. and Žc. deconvolution has not been applied yet, while subfigures Žd., Že. and Žf. show results after deconvolution. From these figures some relevant results may be highlighted. Ža. Dynamic focusing increases the ratio from the
A system based on digital processing to improve SAFT images has been presented. The processing chain is introduced in the two stages that constitutes a conventional SAFT. The digital processing chain includes apodization, deconvolution, dynamic focusing and envelope detection. This work also considers the problems associated with real-time imaging. In this sense, an architecture based in a pipeline configuration has been presented, which allows to achieve digital processing at low cost and complexity. In particular, the advantage of using the binomial approximation to reduce hardware complexity has been studied. Experiments show that focusing and deconvolution improve UT images, especially lateral and axial resolution and grating lobes. However, apodization techniques have little influence in the images. Acknowledgements This work has been supported by CICYT, grants TAP97-1128-C02-02 and TAP97-0662-C02-01 of the Spanish Ministry for Science and Education.
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O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
References w1x R. Delannoy, R. Torguet, C. Bruneel, E. Bridous, M. Rouvaen, H. LaSota, Acoustical image reconstruction in parallel-processing analog electronic system, J. Appl. Phys. 50 Ž1979. 3153–3159. w2x D.K. Peterson, G.S. Kino, Real-time digital image reconstruction: a description of image hardware and a analysis of quantization errors, IEEE Trans. Sonics Ultrason. 13 Ž4. Ž1984. 337–351. w3x T.K. Song, B. Park, Optimum focusing in an ultrasonic annular array imaging system using a non-spherical lens, Ultrasonic Imaging 11 Ž1989. 197–214. w4x M. O’Donnell, B.M. Shapo, M.J. Eberle, D.N. Stephens, Experimental studies on an efficient catheter array imaging systems, Ultrasonic Imaging 17 Ž1995. 83–94. w5x M. Karaman, M. O’Donnell, Synthetic aperture imaging for small scale systems, IEEE Trans. Ultrason. Ferroelectrics Frequency Control 42 Ž3. Ž1995. 429–442. w6x C.H. Frazier, W.D. O’Brien, Synthetic aperture techniques with a virtual source element, IEEE Trans. Ultrason. Ferroelectrics Frequency Control 45 Ž1. Ž1998. 196–207. w7x S.D. Silverstein, L.J. Thomas, Analytical comparison of sensor signal processing enhancements for NDT synthetic aperture ultrasonic imaging, IEEE Trans. Image Processing 2 Ž1. Ž1987. 60–67. w8x C. Fritsch, T. Sanchez, J.J. Anaya, A. Ibanez, L.G. Ullate, M. ´˜ Parrilla, M.A.G. Izquierdo, A pipelined architecture for high speed automated NDE, Proc. 1995 IEEE Ultrasonics Symposium, Seattle, WA, USA, November 7–10, 1995, pp. 833–836. w9x L.G. Ullate, J.L. San Emeterio, A new algorithm to calculate the transient near-field of ultrasonic phased array, IEEE Trans. Ultrason. Ferroelectrics Frequency Control 39 Ž6. Ž1992. 745–753. w10x A. Macovski, Ultrasonic imaging using arrays, Proc. IEEE 67 Ž4. Ž1979. 484–495. w11x L.R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1975, pp. 88–107.
w12x J.J. Anaya, L.G. Ullate, C. Fritsch, A method for real-time deconvolution, IEEE Trans. Instrum. Meas. 41 Ž3. Ž1992. 413–419. w13x C. Fritsch, A. Ibanez, ´˜ M. Parrilla, A digital envelope detection filter for real-time operation, IEEE Trans. Instrum. Meas., 1998, in revision. Oscar Martınez ´ was born in Valencia, Spain. He received a Telecommunication Engineering degree in 1995 from the Polytechnic University of Valencia. Since then he is at the Instituto de Automatica Industrial ´ ŽC.S.I.C.. in Madrid. He is involved with ultrasonic imaging, ultrasonic arrays, digital signal processing and real-time architectures. Currently, he is working on his PhD directed towards ultrasonic imaging. Monserrat Parrilla was born in Ciudad Real, Spain. She received a BTech degree on Informatics and the MS degree in 1990 and 1992, respectively, from the Universidad Politecnica of Madrid. She also graduated on ´ Informatics from the same university and is currently working on her PhD Thesis involving data reduction and 3D ultrasonic imaging. Her research interests include real-time digital signal processing, ultrasonic imaging and automatic defect detection and characterization. Miguel Angel Garcia Izquierdo was born in San Sebastian, Spain, in 1969. He graduated from the Universidad Politecnica de Madrid ŽUPM. ´ with a degree in Telecommunication Engineering in 1995. Currently, he is working on his PhD at CSIC ŽSpanish Research Council. Instituto de Automatica Industrial. His current interest is focused on ultrasonic signal ´ processing, particularly in scattering media. Luis Gomez-Ullate was born in Ciudad Real, Spain. He received a master’s degree in Industrial Engineering in 1968, and PhD degree from the Polytechnic University of Madrid in 1970. Since 1972 he is at The Instituto de Automatica Industrial, CSIC, where he worked in different ´ scientific areas relative to automatics and signal processing. Since 1985, his work has been related to ultrasonic, signal processing, ultrasonic imaging and diverse techniques for NDT applications.
Application of digital signal processing techniques to synthetic aperture focusing technique images O. Martinez ) , M. Parrilla, M.A.G. Izquierdo, L.G. Ullate Instituto de Automatica Industrial (CSIC), La PoÕeda (Arganda del Rey), 28500 Madrid, Spain ´ Accepted 4 December 1998
Abstract Synthetic aperture focusing technique ŽSAFT. has become a popular alternative to transmission–reception focused arrays ŽTRFA. in order to reduce hardware complexity and cost associated to ultrasonic ŽUT. imaging systems. A shortcoming of SAFT processing is that it introduces artifacts that distort the images. However, as SAFT is sequential, efficient digital processing algorithms can be used to improve image quality. In this paper, several digital processing techniques are proposed including apodization, deconvolution, dynamic focusing, deflection and envelope extraction. A pipeline architecture which allows execution of these algorithms in parallel for real-time imaging is also proposed. q 1999 Elsevier Science S.A. All rights reserved. Keywords: SAFT; Pipeline architectures; UT images; Real-time digital processing
1. Introduction Ultrasonic ŽUT. arrays are formed by sets of transducers, which can be delayed electronically in emission and in reception to control the UT beam direction, thus allowing the space of interest to be scanned without mechanical motion. Echographic systems based on transmission–reception focused arrays ŽTRFA. are very usual for medical applications. As TRFA systems require a high degree of parallelism, they are usually based on analog techniques, which are more suitable for real-time imaging w1x. However, synthetic aperture focusing techniques ŽSAFT. are more adequate for non-destructive testing ŽNDT. applications where a reduction on complexity and costs are pursued. Conventional SAFT operate sequentially in two stages. First, each transducer element emits and receives an echosignal which is digitized and stored. Then, digital signal processing ŽDSP. is applied to generate the scanning lines, which form the UT image w2x. SAFT images have fairly good lateral resolution, but present several disadvantages
)
Corresponding author. Tel.: q34-1-871-1900; Fax: q34-1-871-7050; E-mail: [email protected]
in processing speed for image compounding, SNR, and even in image quality due to grating and side lobes. However, SAFT allows an efficient use of digital processing algorithms to improve image quality. Previous works have been mainly addressed to improve delays management, i.e., for dynamic focusing which improves lateral resolution and side lobes level w2x, or sub-sampling techniques which reduce phase aberration effects w3x. Other techniques based on complex aperture functions and multiplying the number of shots per element have been proposed to reduce side and grating lobes w4,5x. Side lobes may also be reduced by analog apodization which is easy to implement w6,7x. This work presents a processing method that includes a set of algorithms, some of them mentioned above, i.e., sub-sampled dynamic focusing processing and apodization. and, additionally, deconvolution that improves axial resolution and reduces grating lobes, and real-time envelope extraction that smoothens the image. The main problem is to design a simple processing system fast enough to execute all the above algorithms in real-time. To this purpose, an architecture is proposed which is based on the SENDAS approach w8x. This is a modular-pipelined architecture able to execute complex digital processing algorithms at 10 Msamplesrs. In addi-
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 0 2 8 - X
O. Martinez et al.r Sensors and Actuators 76 (1999) 448–456
tion, the use of binomial approximation for dynamic focusing will allow to further reduce the architecture complexity, with little alteration of the image quality.
2. Theory background SAFT can be used to emulate TRFA. However, while TRFA is a two-way focusing technique, SAFT only focuses in reception. For a N-element array, like that shown in Fig. 1, the differences between both approaches may be analyzed by means of the continuous wave point spread function ŽPSF. w5x, which shows the acoustic lateral profile for the focal line. Assuming a dynamic focus, the PSF at any given depth for TRFA is: sin2
k
ž
Nd sin Ž u . 2 PSF Ž u . A k sin2 d sin Ž u . 2
ž
/
Ž 1.
/
and for SAFT: PSF Ž u . A
sin Ž kNd sin Ž u . . sin Ž kd sin Ž u . .
Ž 2.
where k s 2prl, d is the element spacing and u is the deflecting angle. From both expressions three important differences between SAFT and TRFA imaging must be highlighted. Ža. The ratio from signal to grass noise decreases in SAFT. The quadratic terms of Eq. Ž1. produce an increment in main-to-side lobe ratio ŽMSLR. that is not achievable with SAFT. Žb. The lateral resolution doubles with SAFT. Žc. Grating lobes with SAFT are greater and nearer to the main lobe than with TRFA. In TRFA the angular distance between grating lobes and main lobe is u s arcsinŽ lr Ž Nd .., but in SAFT it decreases to u s arcsinŽ lr Ž2 Nd ... That makes SAFT more sensitive to grating lobes. These effects, described for the far-field, can also be
449
shown in the near-field. Fig. 2 shows the PSF computed for a 16-element Ž8 mm high. linear array with d s 0.5 mm, l s 0.43 Žwe shall use this configuration as reference array in this work., focused at z s 50 mm. The acoustic field has been modelled using the exact algorithm given in Ref. w9x. It can be observed that lateral resolution and the level of side lobes and grating lobes are very much affected by SAFT.
3. Signal processing The object of the front-end signal processing is to improve UT image quality by decreasing the effects of side and grating lobes while maintaining system resolution with optimal specifications. Different strategies have been developed by several authors w5x, but most of them increase hardware volume and complexity. The purpose of this paper is to introduce a set of digital processing algorithms at the two stages of SAFT image formation, which are executed sequentially over the traces in a pipeline arrangement.
3.1. Dynamic focusing Dynamic focusing is based on the spatial diversity that characterizes transducer arrays. The objective is to add in phase the signals, which arrive at every element with different delays, for every field point. Cylindrical focusing applied to a spatial point P Ž R f , u . for a N-element linear array, requires to delay the signal received at the i-element Ž i s 0, . . . , N y 1. by an amount T Ž i .:
T Ž i. s
(
2
R f y R 2f q Q Ž i . y 2 R f Q Ž i . sin u c
Ž 3.
where QŽ i . s id y Ž N y 1. dr2 is the distance from the ith element to the center of the array aperture, R f is the depth of the focus lens, u is the steering angle and c is the sound propagation velocity. For a given steering angle u , varying the focus R f as the pulse propagates Ž R f s tr2 c . performs dynamic focusing. For the points where R f 4 D, the binomial approximation of Eq. Ž3. w10x can be applied:
T Ž i. f
Fig. 1. Linear array configuration.
Q Ž i . sin u c
y
QŽ i.
2
2 Rf c
Ž 4.
which has two terms: the first term is a linear function of the element position QŽ i . and the steering angle u and may be considered as deflecting delays; the second term is
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Fig. 2. Near-field of a linear array of 16 elements spaced 0.5 mm, focused at Z s 50 mm. TRFA processing in dotted line. SAFT processing in solid line.
a quadratic function of the element position QŽ i . and implements dynamic focusing for every range R f ŽFig. 3.: Q Ž i . sin u Tu Ž i . s , Ž 5. c Tf Ž i . s y
QŽ i.
sense the array can be considered as a spatial filter whose characteristics Žresolution, main lobe to side lobe ratio, etc.. can be studied in the spatial frequency domain w11x. The spatial filter is described as:
2
2 Rf c
.
Ž 6.
Focusing has been divided into two different operations which is very useful for the hardware implementation. The validity of this approximation can be observed in Fig. 4 where the array acoustic field in the case of dynamic focusing at u s 208 has been modelled w9x. 3.2. Apodization The diffraction lobes produced by the array aperture can be reduced by controlling the channel gains w6x. In this
Ž Ny1 .
yw nx s
Ý
wi x i w n x
Ž 7.
is0
where x i w n x is the signal received from the ith channel and wi is the gain of that channel. Uniform apodization Ž w b w i x s 1, i s 0 . . . Ž N y 1.. describes the natural aperture behaviour, which has both maximum diffraction lobes and higher resolution. Other apodization functions ŽHanning, Hamming, Blackman, etc.. use gain values that smooth the aperture to decrease side lobes, reducing strongly the gain in the extreme elements.
Fig. 3. Time delay vectors focussing at the point P Ž R f , u .. On the left, time delays for the Fresnel approximation; on the right, exact cylindrical focusing delays.
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Fig. 4. Acoustic field contour Žy3, y6, y12 and y18 dB. dynamic focussing a 16-element array at the steering angle u s 208: top, exact cylindrical focusing delays; bottom, Fresnel approximation.
To guarantee the condition of spatial diversity, some level of signal contribution per channel is required. Then, an interesting apodization function which takes into consideration an aperture exploitation degree a is the Generalized Hamming Window ŽGHW. which is defined as: wGH W w i x s
½
a q Ž 1y a . cos
2p
ž ž N 0,
iy
N y1 2
//
,
0 F i F Ž N y1. rest
Ž 8. where 0.5 F a F 1, and the minimum apodization value is 2Ž a y 0.5.. Fig. 5 that shows increasing a improves resolution, although MSLR is reduced. Therefore, a trade-off between resolution and side lobe reduction must be reached. It is possible to recognize three special cases: Ž1. for a s 0.5 GHW becomes the Hanning Window; Ž2. for a s 0.54 it becomes the Hamming Window, which achieves the greater MSLR and Ž3. for a s 1 it becomes the Boxcar Window, which achieves the best resolution. The grating lobes are a repetition of the aperture diffraction pattern in the direction u s arcsinŽ lrŽ2 Nd ... A drawback of apodization is that grating lobes are widened. This
characteristic is especially important for SAFT imaging where the use of apodization techniques may not be recommended for certain applications. Fig. 6 shows the PSF for values of a that make MSLR to be: 40 dB ŽHamming Window., 30 dBŽ a s 0.608., 20 dB Ž a s 0.76. and 13 dB ŽBoxcar Window.. Low values of a widens grating lobes as can be seen in Fig. 6. Due to the finite size of the array elements, the MSLR improvement is better than expected from the apodization filter. 3.3. DeconÕolution Deconvolution w12x is used to narrow the time domain UT pulse with the purpose of increasing axial resolution and reducing grating lobes. By the theory of linear systems, it is possible to describe a pulse–echo system as: U
y Ž t . s hŽ t . x Ž t .
Ž 9.
where y Ž t . is the received signal, x Ž t . is a band-limited signal that includes the two-ways response of the transducer and electronics, and hŽ t . represents the spatial impulse response of the studied object.
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Fig. 5. Generalized Hamming Window, 0.5 - a - 1. Ža. MSLR; Žb. resolution, measured as resolutionŽ a s 1.rresolutionŽ a ..
To achieve narrow signals, an approximation of hŽ t . should be obtained from y Ž t . and x Ž t ., the latter being considered as a reference signal, measurable and invariant for any problem. The inverse filter is a good approach to deconvolution in real-time. In the frequency domain: Y Ž f . sX Ž f . HŽ f . ™HŽ f .s s Fy1
YŽ f .
½ 5 XŽ f .
.
YŽ f . XŽ f .
U
™
c s Ry1 Q
Ž 13 .
™ hŽ t .
Ž 10 .
The term cŽ t . s Fy1 1rX Ž f .4 yields the filter coefficients vector which allows to get hŽ t . directly by a convolution process: hŽ t . s y Ž t . c Ž t . .
whose band width is adapted to the UT pulse. The method gives the following values for the filter coefficient vector ™ c in discrete form:
where R is the autocorrelation matrix of x Ž n. and Q is the cross correlation vector of x Ž n. and dŽ n.. In a second stage, deconvolution is computed in real-time by executing Eq. Ž11. with the aid of a specific correlator. The desired
Ž 11 .
However, this is not quite a practical solution as outside the ideal conditions hŽ t . is very sensitive to noise. If we include noise in Eq. Ž10.: HŽ f . s
Y Ž f . qRyŽ f . X Ž f . qRxŽ f .
Ž 12 .
where R y Ž f . and R x Ž f . are noise spectral densities for y Ž t . and x Ž t ., respectively. It indicates that outside the frequency band of the UT pulse Žpoor SNR., the equation above yields H Ž f . f R y Ž y .rR x Ž f ., an indeterminate solution. There are different solutions for this problem, i.e., band pass filter, Wiener filter, shaping filter, etc. The last method has been used in this work. In a setup stage, the inverse filter coefficients are calculated to obtain an estimated impulsive response dŽ n.
Fig. 6. Acoustic field for SAFT processing with GHW apodization. Ža. a s 0.54; Žb. a s 0.608; Žc. a s 0.76; Žd. a s1.
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4. System operation
Fig. 7. Diagram block of the receiving processing chain.
output dŽ n. has been approximated to a Gaussian pulse centered at the transducer frequency. 3.4. EnÕelope extraction DSP techniques frequently operate on RF signals. However, UT images improve using the trace envelope. By means of the Hilbert transform, conventional methods to compute the analytical signal have been derived. However, even using DSP, such methods are not fast enough for array imaging. Other methods, based on non-linear filtering which are executed in the time domain have been proposed. In this sense, an approach which computes a good approximation of the analytical signal magnitude at the required rate of 10 Msamplesrs has been presented in Ref. w13x.
This work proposes to introduce DSP at the two stages that constitutes a conventional SAFT. At the first one, where signals from the elements are digitized and stored, the following digital techniques are included: apodization, deconvolution and quadratic dynamic focusing. At the second stage, where the image lines are formed, steering and envelope extraction are performed ŽFig. 7.. The SENDAS architecture presented in Ref. w8x allows to develop this configuration in a pipelined arrangement. Dynamic focusing is a complex operation that requires high processing and storage capabilities w2x. However, using the Fresnel approach, the hardware complexity can be reduced. This can be explained with the aid of Fig. 8 for an array of N-elements, which store m samples per signal and forms L lines per UT image. For a conventional SAFT, memory for NmL data is required. Applying binomial approximation the memory requirements are lowered to Nm data for dynamic focusing, and NL for steering. For example, for N s 32 elements, m s 1000 samplesrtrace and L s 200 linesrimage, conventional SAFT requires 6.4 Mbytes, while the binomial approach needs only 38.4 kbytes. Dynamic focusing can be carried out by shifting the received UT signal from every transducer element. From the sampling period, the time delays T Ž i . for focusing may be expressed in number of samples. In order to increase the time resolution sub-sampling techniques by linear interpolation-processing may be employed. The focusing
Fig. 8. SAFT architectures. Ža. Based on exact focusing; Žb. based on binomial focusing.
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Fig. 9. Steering images wy408, q408x following different processing algorithms: Ža. steering only; Žb. dynamic focusing; Žc. dynamic focusing and apodization; Žd. steering and deconvolution; Že. dynamic focusing and deconvolution; Žf. dynamic focusing, deconvolution and apodization.
sample index k of the ith transducer will be computed as: X i Ž k . s x i Ž Tf w i ,k x . q
x i Ž Tf w i ,k x q 1 . y x i Ž Tf w i ,k x . If w i ,k x
Ž 14 .
where x i Ž k . and X i Ž k . are the samples of the unfocused and focused signals, respectively, Tf w i,k x is the sample delay, and If w i,k x is the interpolation factor associated with the delay. Steering operation is carried out analogously. For a given angle u , the delay index is common for all the
Fig. 10. Lateral profile, degrees in horizontal axis and amplitude ŽdB s. in vertical axis, Ža. steering only; Žb. dynamic focusing; Žc. dynamic focusing and apodization; Žd. steering and deconvolution; Že. dynamic focusing and deconvolution; Žf. dynamic focusing, deconvolution and apodization.
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Fig. 11. Axial profiles Ž Z Žmm. in abscissa and amplitude ŽdB s. in ordinates., Ža. steering only; Žb. dynamic focusing; Žc. dynamic focusing and apodization; Žd. steering and deconvolution; Že. dynamic focusing and deconvolution; Žf. dynamic focusing, deconvolution and apodization.
samples of ith trace, and is given by T w i, u x. For the index sample k: N
Xu Ž k . s
Ý is1
q
ž
x i Ž k q T w i ,u x .
x i Ž k q T w i ,u x q 1. y x i Ž k q T w i ,u x . I w i ,u x
/ Ž 15 .
Where Xu Ž k . and x i Ž k . are the samples of steered and unsteered in signals, respectively, and I w i, u x is the interpolation factor associated with the delay for the ith trace.
main-to-side and grating lobes. Lateral resolution is dramatically improved. However grating lobes can be still observed. Žb. The role of apodization is not as interesting as it was estimated by simulations. The main reason is the wide band width of the UT pulses. Therefore, side lobes reduction is not an important issue as long as wideband transducers are used. Furthermore, apodization widens the grating lobes. Žc. Deconvolution plays an important role on image quality. Among others, axial resolution is highly increased and grating lobes are strongly reduced. Lateral resolution is maintained at good level. 6. Conclusions
5. Experiments For the experimental procedure a SENDAS system was used. The system controls a 16-element linear array Ž8 = 8 mm., which emits wide band width Ž40%. pulses with a central frequency of 3.5 MHz. The effect of digital processing has been studied by changing the process chain for result comparing. The images correspond to a 0.5-mm diameter wire positioned at Ž X s 0.4 mm, Z s 23.8 mm.. Images have been formed by 81 steering lines Žwy408, q408x.. 5.1. Results Fig. 9 shows six B-scan images using different processing chains. The lateral and axial profiles can be observed in Figs. 10 and 11. In subfigures Ža., Žb. and Žc. deconvolution has not been applied yet, while subfigures Žd., Že. and Žf. show results after deconvolution. From these figures some relevant results may be highlighted. Ža. Dynamic focusing increases the ratio from the
A system based on digital processing to improve SAFT images has been presented. The processing chain is introduced in the two stages that constitutes a conventional SAFT. The digital processing chain includes apodization, deconvolution, dynamic focusing and envelope detection. This work also considers the problems associated with real-time imaging. In this sense, an architecture based in a pipeline configuration has been presented, which allows to achieve digital processing at low cost and complexity. In particular, the advantage of using the binomial approximation to reduce hardware complexity has been studied. Experiments show that focusing and deconvolution improve UT images, especially lateral and axial resolution and grating lobes. However, apodization techniques have little influence in the images. Acknowledgements This work has been supported by CICYT, grants TAP97-1128-C02-02 and TAP97-0662-C02-01 of the Spanish Ministry for Science and Education.
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References w1x R. Delannoy, R. Torguet, C. Bruneel, E. Bridous, M. Rouvaen, H. LaSota, Acoustical image reconstruction in parallel-processing analog electronic system, J. Appl. Phys. 50 Ž1979. 3153–3159. w2x D.K. Peterson, G.S. Kino, Real-time digital image reconstruction: a description of image hardware and a analysis of quantization errors, IEEE Trans. Sonics Ultrason. 13 Ž4. Ž1984. 337–351. w3x T.K. Song, B. Park, Optimum focusing in an ultrasonic annular array imaging system using a non-spherical lens, Ultrasonic Imaging 11 Ž1989. 197–214. w4x M. O’Donnell, B.M. Shapo, M.J. Eberle, D.N. Stephens, Experimental studies on an efficient catheter array imaging systems, Ultrasonic Imaging 17 Ž1995. 83–94. w5x M. Karaman, M. O’Donnell, Synthetic aperture imaging for small scale systems, IEEE Trans. Ultrason. Ferroelectrics Frequency Control 42 Ž3. Ž1995. 429–442. w6x C.H. Frazier, W.D. O’Brien, Synthetic aperture techniques with a virtual source element, IEEE Trans. Ultrason. Ferroelectrics Frequency Control 45 Ž1. Ž1998. 196–207. w7x S.D. Silverstein, L.J. Thomas, Analytical comparison of sensor signal processing enhancements for NDT synthetic aperture ultrasonic imaging, IEEE Trans. Image Processing 2 Ž1. Ž1987. 60–67. w8x C. Fritsch, T. Sanchez, J.J. Anaya, A. Ibanez, L.G. Ullate, M. ´˜ Parrilla, M.A.G. Izquierdo, A pipelined architecture for high speed automated NDE, Proc. 1995 IEEE Ultrasonics Symposium, Seattle, WA, USA, November 7–10, 1995, pp. 833–836. w9x L.G. Ullate, J.L. San Emeterio, A new algorithm to calculate the transient near-field of ultrasonic phased array, IEEE Trans. Ultrason. Ferroelectrics Frequency Control 39 Ž6. Ž1992. 745–753. w10x A. Macovski, Ultrasonic imaging using arrays, Proc. IEEE 67 Ž4. Ž1979. 484–495. w11x L.R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1975, pp. 88–107.
w12x J.J. Anaya, L.G. Ullate, C. Fritsch, A method for real-time deconvolution, IEEE Trans. Instrum. Meas. 41 Ž3. Ž1992. 413–419. w13x C. Fritsch, A. Ibanez, ´˜ M. Parrilla, A digital envelope detection filter for real-time operation, IEEE Trans. Instrum. Meas., 1998, in revision. Oscar Martınez ´ was born in Valencia, Spain. He received a Telecommunication Engineering degree in 1995 from the Polytechnic University of Valencia. Since then he is at the Instituto de Automatica Industrial ´ ŽC.S.I.C.. in Madrid. He is involved with ultrasonic imaging, ultrasonic arrays, digital signal processing and real-time architectures. Currently, he is working on his PhD directed towards ultrasonic imaging. Monserrat Parrilla was born in Ciudad Real, Spain. She received a BTech degree on Informatics and the MS degree in 1990 and 1992, respectively, from the Universidad Politecnica of Madrid. She also graduated on ´ Informatics from the same university and is currently working on her PhD Thesis involving data reduction and 3D ultrasonic imaging. Her research interests include real-time digital signal processing, ultrasonic imaging and automatic defect detection and characterization. Miguel Angel Garcia Izquierdo was born in San Sebastian, Spain, in 1969. He graduated from the Universidad Politecnica de Madrid ŽUPM. ´ with a degree in Telecommunication Engineering in 1995. Currently, he is working on his PhD at CSIC ŽSpanish Research Council. Instituto de Automatica Industrial. His current interest is focused on ultrasonic signal ´ processing, particularly in scattering media. Luis Gomez-Ullate was born in Ciudad Real, Spain. He received a master’s degree in Industrial Engineering in 1968, and PhD degree from the Polytechnic University of Madrid in 1970. Since 1972 he is at The Instituto de Automatica Industrial, CSIC, where he worked in different ´ scientific areas relative to automatics and signal processing. Since 1985, his work has been related to ultrasonic, signal processing, ultrasonic imaging and diverse techniques for NDT applications.