New Electronic Components and Software for Single and Multi-Channel Ultrasonic Inspections of Piping and Components

NDTnet 1998 May, Vol.3 No.5 The Hardware Concept of a new Digital Ultrasonic NDE System
L.Svilainis and V.Puodziunas; Kaunas Lithuania *

TABLE OF CONTENTS

Abstract
Introduction
Transducer excitation
Transducers
Receiver/preamplifier
Filtering
Main amplifier
Scanner
A/D conversion
Sampling in ultrasonic system
Conclusions
Acknowlegements
References

Abstract

Because of arising number of components with digital parameters control, ultrasonic systems receive large impulse for further development and parameters improvement with simultaneous size and price reduction. Ultrasonic active investigation systems are offering some advantages over conventional acquisition systems if proper care is taken during the design process. Jitter of conventional systems can be eliminated completely in ultrasonic systems, equivalent time sampling and system synchronization are more feasible. Digital TVG and gain implementation together with automated calibration allow for dynamic range of system improvement and flexible signal gating. Despite A/D conversion sampling rate can be chosen slightly lower than required limit, care must be taken for possible artifacts. Transducer parameters control is available when using generator pulse width adjustment. Preamplifier input clamping and generator and transducer matching into excitation channel still remain the problem to be solved properly.

Introduction

Fig. 1. Ultrasonic NDT system equipment diagram

The ultrasonic transducer is excited by generation of electrical pulse and transmits the pressure (ultrasonic) pulse to the media under investigation. The ultrasonic pulse travels in the material and is reflected, refracted, scattered or transmitted through its' inhomogeneities. The affected signal is picked by same (transceiver mode) transducer or separate transducer and is converted to the electrical signal. This signal then is amplified (the amplifier block), filtered and converted to the digital form. If necessary, signal is stored on disk. Latter digital signal pre-processing (averaging, smoothing), post-processing or just real - time presentation on screen is performed as A-scan, B-scan or other appropriate image. The transducer can be positioned on the material in any position on the material surface (or in water if the immerse scanning is used) using coordinate scanner.

Transducer excitation

Fig.2. Common exciting pulse shapes

Fig.3. Spectral density of common exciting pulse shapes.

All pulses presented above have same maximal amplitude and 0.5 level duration (which differs from the duration definition, used in signals theory) of 200ns. If such pulse is used for 2.5MHz transducer excitation best energy feed is achieved but bandwidth is reduced. Positive pulse edge is exciting the transducer and negative edge is working at the same phase. In case negative edge is positioned to be in opposite to excited transient, ringing time can be significantly reduced but energy feed will be sacred. Therefore pulse generator with variable pulse width is very suitable for pulse bandwidth programming. If pulse duration can be digitally controlled and is stable, repeatability of measurement results is increased. It must be noted here that stable duration is of great desire, because even slight variations of pulse width, if it is adjusted for improved bandwidth generation, can cause rapid changes in generated pulse energy. This will definitely lead to the unwanted artifacts. When avalanche devices are applied for sharp front pulses generation, the avalanche creation uncertainty can lead to such problems. Same situation can occur if RC circuitry or IC ramp generator is used for duration formation with no special precautions taken for add-on noise. Turning back to pulses presented above, it should be noted that all these have same maximal amplitude. From the electronical point of view such pulses generation circuitry's must have same chances, since higher working voltage of active device implies larger volume of semiconductor which itself leads into higher charge accumulated in volume. Best spectra would answer the pulse shape choice question. For this reason we have presented the absolute spectral densities of pulses shown in Fig.3.

By investigating the spectral densities of pulses mentioned, comes the conclusion that rectangular pulse is best matching the bandwidth and efficiency requirements for 2.5MHz transducer (2.5MHz transducer frequency implied 200ns pulse duration choice T=1/(2f)). Triangular and cosine pulse has smaller slew rate requirements so in some cases might be more attractive. It must be noted that sharp pulse transition time limitations will add additional decay 1/fon all power spectra. Bearing this in mind and also taking on account that much wider exciting pulse frequency range might be necessary, voltage step function comes out as a possible candidate. For comparison, 20ns duration exponential and rectangular pulse spectra is presented in Fig.3. Step function (or exponentially decaying pulse) is easy to generate. It can be generated using one active element with sufficiently high speed and there will be no necessity to care about active element saturation. Therefore, rising edge will be much sharper. In case of rectangular pulse, active elements saturation is limiting the switching speed - care must be taken to saturate the switching element in order to be able to switch it off immediately. In our discussion group we often see the requests of students to present excitation circuitry for ultrasonic transducers. Fig.4. is demonstrating single stage capable of excellent performance for excitation of transducers of up to 100MHz. It must be noted that all the components are recommended to be surface mounted type, low inductance and sufficient ground plane on PCB must be produced.

Fig.4. Simple exciting pulse generator

The schematics presented suffers the energy given into transducer, since is driven by step function. As can be seen from Fig.3. voltage step spectra is smooth so it might be attractive to be employed for wide bandwidth transducers excitation. But short duration rectangular pulse is capable to produce the sufficient bandwidth with higher efficiency (note the spectra for narrow rectangular pulse in Fig.3.). Generator presented at Fig.4. with proper application of voltage follower after it and some minor changes of components, can be used to generate the rectangular pulses. To conclude, pulse generator, producing rectangular pulses design looks as follows: last stage contains two switches, one responsible for fast pull-up and another push-down of output voltage. In order to achieve high slew rates, generator output impedance is kept as low as possible. This induces other problem :

the impedance of cable, connected to transducer usually is 50 Ohm so impedance mismatch will be causing multiple reflections in cable, especially if transducer impedance is not matched into cables;
after exciting pulse has been sent into cable, if same transducer is used to excite and receive the signals, it is desirable to disconnect a generator from line, because low output impedance will be damping the received pulses. Despite multiple attempts to employ the 50Ohm RF amplifiers, special switching networks etc. which were more or less successful, we consider this problem still open.

As separate case, special waveform generation circuits can be mentioned [1,2,3]. These are employed because of two possible reasons.

If high pulse energy is required, then complex signals are of good choice. For instance, phase manipulated signal will pertain high energy, inherent from CW signals, but will maintain the excellent temporal resolution, obtained after signal compression. Especially attractive in air-matched ultrasound applications, where high surrounding noise level and large attenuation are present. High signal-to-noise ratio (SNR) can be achieved.
Using signal post-processing, signal bandwidth/ temporal resolution can be improved. But because of insufficient signal level at frequencies to be restored, noise becomes prevailing here so unwanted artifacts are created. If exciting signal is precompensated for frequencies, missing in at the received signal, better SNR is achieved. Possibility to generate any shape exciting signal offer even more sophisticated solution - instead of doing signal deconvolution after receiving it, exciting signal can constructed to have such frequency and phase content, that received signal is already deconvolved. Such approach allows to save the processing time and improve SNR.

Additional advantages offer the possibility to have the programmable exciting pulse delay. The closest application for such feature is the electronical steering of ultrasonic beam, when ultrasonic transducer array is used [3,4]. Another application, offering improvement in sampling rate will be discussed further.

Transducers

Special attention must be drawn to unfocussed transducers. Because of wide wave front these require sufficient shielding and matching coil to reduce the noise level at high gains which are usual for such applications. Passing the cable through the high permeability ferrite bead can also reduce the induced noise level significantly. Also, special precautions on preamplifier shielding construction must be taken here.

Receiver/preamplifier

if transceiver mode is used, is to cope with high excitation voltage;
usually, preamplifier is placed closer to the transducer than the rest of the system, so it has to have low noise level and after preamplifying the signal 6-20dB signal can be sent further;
it has to filter the noise at the frequencies which are definitely out of employed frequency range. Conventional circuitry applied for high voltage coping is two opposite diodes clamping into ground, preceded with 100-300 Ohm resistor. Sometimes, small inductance can be applied here and capacitor connected in parallel with the diodes.

Such circuit has two main disadvantages :

due to the large exciting pulse energy, diodes accumulate a large charge amount, which latter is stuffing the channel;
because of nonlinear character of the diodes, they distort the useful signals too, what later is causing additional artifacts in signal processing;
if high efficiency transducer is used, it can produce the voltages greater than diode threshold voltage.

Employment of fast switching SCR/diode based circuitry with adjustable threshold solve the problems at acceptable level. Attractive choice is two-terminal circuit protectors offered by MAXIM. Placed in series with signal lines, each two-terminal device guards sensitive circuit components against voltages near and beyond the normal supply voltages. These devices are voltage-sensitive MOSFET transistor arrays that are normally on when power is applied and normally open circuit when power is off. When signal voltages exceed the threshold the two-terminal resistance increases dramatically, limiting fault current as well as output voltage to sensitive circuits. The protected side of the switch maintains the correct polarity. There are no "glitches" or polarity reversals going into or coming out of a fault condition. Unfortunately, available versions offer just > 40V operating range.

Still, the impedance mismatch caused ringing problem remains which can not be solved by such circuits. If low impedance switch is connected near transducer, after exciting pulse has fed into transducer pulse bouncing in the cable and transducer reverberation can be canceled by opening this switch. As it was mentioned above, exciting generator can be designed to have low output impedance. So, this impedance, after exciting pulse has been sent, can be employed as dampening switch. Just after desired time has passed, generator low impedance has to be disconnected from transducer (if transceiver mode is used) in order to let the reflected signals pass to the preamplifier.

Filtering

The filters block is used to adopt the system bandpass range to the frequency of transducer used, to lower the system noise and to meet the Nyquist sampling criteria. There is no single recipe what filters should be applied here - it depends on application. In case phase sensitive processing is to be used, filter should have as flat phase spectra in bandpass region as possible so the Bessel and Butterworth filters are closest candidates. But this implies less steeper frequency response of filter. If phase information can be compensated during processing (which is easily implemented in digital systems) or phase response is not of much importance Chebyshev or Elliptic filters can be applied in order to have better frequency response steepness at cutting frequencies. Switched capacitance filter are not recommended here. Active RC filters offer smaller and cheaper schematics, but are of limited frequency range. LC filters offer better SNR, but have higher dimensions and require woven elements. Combination of RC at low frequencies and LC filters- at higher frequencies can be of possible choice. From the user point of view digitally programmable filters are of great profit - signal bandwidth can be adjusted by software for best match. Then question of possible frequency steps available is of another order - as smaller is the step as more accurate adjustment can be.

Main amplifier

We distinguish two amplifier types - static and dynamic amplifier. Static amplifier gain remains stable during one A-scan acquisition or even whole scan time. The possibility of digital gain control allows for signal dynamic gain compression as it will be discussed further. Dynamic gain amplifier gain is varied during A-scan acquisition time as is called TVG amplifier (time variable gain). Thanks to digital TVG control, gain for every time instant can be known, so later, if necessary can be removed in order to get proper signal processing results. Dynamic gain is mostly dedicated for signal decrease versus depth compensation. Decrease can occur because of various reasons - mostly beam spreading is influencing it, but attenuation in material is not of least importance too. In composite materials scattering is the prevailing reason of signal level degradation. Signal amplitudes can vary in a 90...120 dB range.

Table 1 Number of bits required for A/D conversion
Input signal dynamic range (dB) Number of A/D converter bits
20
40
60
80
100
120 5
8
11
15
18
21
The frequency range used in conventional NDT usually varies from 0.1 MHz to 25 MHz. In digital NDT systems, such ultrasonic signals must be sampled and digitized. This requires high sampling frequency and a large number of quantization levels of A/D converters. The instrumentation used for such purposes cannot usually satisfy both requirements at the same time. On the other hand, due to the finite linear range of amplifiers, detectors and other analog electronic units, the signal amplitude must not exceed the maximum allowed level. On the contrary, it can cause an overload of amplifiers and a significant loss of information.

Usually, the levels of the received signals are not known in advance. Therefore, each time when starting NDT of a new object, it is necessary to adjust the amplitude range of received signals to the linear range of the instrumentation. Usually this is done manually by performing multiple scans of the object. It is a time-wasting and boring procedure for an operator. When an inspection is performed in a dangerous environment, for instance in nuclear power plants, the time needed for testing should be as short as possible. So, it is highly desirable to develop an automated NDT procedure which will allow, in the ideal case, to obtain 2D ultrasonic images during a single scan without a priori knowledge about the features of the object under investigation.

Adaptive gain control we've developed and implemented in our systems offers signal dynamic range compression which allows for employment of smaller bit number A/D converters (refer to [8] for more details). The essence of the method is based on the assumption that ultrasonic signal level is not changing rapidly from one scanning step to another. In order to satisfy Nyquist sampling criteria for spatial information sampling scanning system must stick to this requirement. Bearing this in mind, one can predict the next step amplitude basing the previous steps measurement. In case digital gain control is incorporated in system, gain correspondence to the control code can be easily established. Then, by knowing the previous measurements amplitudes and the gain level they were obtained, one can predict the absolute value next measurement. Of course, it will be the rough approximation, but sufficient in order to set the gain before next measurement is performed. Gain is set at such level, that A/D converter dynamic range is exploited the best way - i.e. maximal amplitude of predicted signal is set to be close to A/D conversion range top. If signal is stored on disk or other media, together with samples of A/D converter, current gain level is stored. So, when data is restored after measurement for post-processing or imaging, it can be restored to the absolute signal values by taking current gain values into account. Restored with higher accuracy as it was sampled with gain not being adaptively controlled. In addition, signal measurement can be performed in one shot, so multiple scans and gain adjustments chain is not necessary. Accuracy and the time is the profit here.

Also, digital gain control allows for interactive gain setup if adaptive gain control is not used. User can see the immediate result on ultrasonic signal obtained after gain change. Major work here, to introduce this feature attractive and user-friendly is the corresponding software development if the necessary hardware control is incorporated in system.

Scanner

1. Automated scanner.
Transducer is positioned into desired position automatically, using analog, step or piezo motor drivers. The track of it's position is either measured counting driving pulses, supplied to step or piezo driver or measured using any or wide variety of available position tracking devices (GPS, unfortunately, is not suitable here at it's stage of development, but who knows...). Separate case is electronical beam steering, either using linear or two dimensional arrays. Especially interesting is FUSIS ultrasonic camcoder introduced by Bob Lasser [11] to us. Chip is presenting the ultrasonic field distribution at chosen depth as video output.

2. Manual scanner.
Position of transducer is chosen by operator by moving it manually into desired position. Position readout varies from optical tracing, introduced by Sonomatic Ltd. to special wheels or belts systems offered by Panametrics or robotics arm follower employed by ALOCA.

We do not plan to present the coverage of scanning methods or variety of equipment. We just mention some important features the acquisition point of view. In order to obtain high measurement speed, especially if large volumes have to be covered, transducer positioning from one desired position to another should be as fast as possible. But this automatically implies the positioning error occurrence. Stepwise movement should suggest higher achieved accuracy, especially if step motors are applied. Step motors also offer better efficiency of driving circuitry because of simple construction of driver. But using step motors implies discrete noise in position determination. Therefore the quality of positioning system as resonant contour should be kept as low as possible. Usually, this is done by using high hold torque motors or applying the gearbox. Also, post-scanning delay should be introduced in order to let the scanning head to settle down. Implementation of gearbox is implemented to reduce the step size and increase the moving torque too. But gearbox can implement hysteresis between movement back and forward. Besides, such useful feature of step motors as hold-off is no longer available then. Applying hold-off, step motor driving current is removed. Then, scanner head can be positioned manually into desired position. This approach offers more natural positioning interface for small systems, when initial positioning is applied. By counting the pulses induced on step motor output track of manually adjusted position can be tracked. In case just relative scan position is important it's not necessary. Since step motors offer limited single step angle, gearbox application for step size reduction seems self evident. In case strong torque is not necessary there is a way to reduce the step size without gearbox. We have implemented gearbox-free driver for step motors. Instead of applying 4 phase bipolar control of step position, we supply the sin/cos stepwise current function into driving coils. If number of steps on sin/cos function is 4, then such driver does not differ from conventional step motor driver. If number of steps is greater by 2ⁿ step size is reduced by the same number. Of course, same approach can be used even is step motor has a gear box.

From the acquisition speed requirement scanner controller design should take all the responsibility and functions of scanner positioning, position tracking and even data acquisition. In such case host computer can perform more general tasks, like signal processing (some can be moved to preprocessing DSP), defects position calculation, decision making, imaging, user interface service and data storage.

A/D conversion

shah

where is the Dirac function and T is the sampling period. The Fourier transform of this function is also shah function

Bearing in mind that multiplication in time domain corresponds to convolution in frequency domain, one can see, that sampled signal spectra will be periodical with period of sampling frequency harmonics. Furthermore, because of discrete presentation of spectra in computer adaptation of Fourier transform (DFT), the signal investigated using the DFT (actually FFT) is also interpreted as periodical. Periodical character car turn out when doing the signal processing. For instance, multiplication in frequency domain with filter function correspond to convolution time domain, so unwanted influence of signal tail will occur in signal head which might cause confusing results. And opposite - at first glance non-harmful multiplication with some sort of compensation function in time domain might cause the frequencies mix in frequency domain because of circular convolution.

Everything said above puts some limits when setting the sampling interval. It must be chosen to have sufficient zero-padding at the beginning of the gate and at the end. As we have noted, sampling usually is performed at some particular depth, therefore we've introduced the possibility to shift the A/D converter buffer memory address to any depth. Such concept allows to sample virtually any depth of material, using relatively small capacity (4-32kb) buffer memory. For analog gating, if necessary, TVG generator code sequence can be programmed accordingly if digital TVG control is used. For further processing, in order to avoid the circular convolution influence in time domain, artificial zero- padding can be added to sampling array.

Choice of sampling frequency is the question always arising during signal acquisition. One can always direct us to Nyquist criteria or Kotelnikov sampling theorem. But all these gentleman are using the maximal frequency still present in signal spectra. Usually transducer central frequency is best known, because this signal is large and easy detectable or can be calculated even from time domain signal presentation. If to go into further measurements, noise will be hiding the maximal frequency. The easiest approach is to apply anti-aliasing filter with sufficient attenuation in order to satisfy this criteria. We have ended at such considerations:

since signal is being amplitude quantized too, maximal frequency level below A/D converter dynamic range is of no longer interest;
despite wide frequency range, virtually every ultrasonic transducer signal is decreasing as frequency increase;
noise signal influence can be eliminated using data averaging if it has random distribution, despite it will be aliased averaging will still work;
once transducer reflection from acoustic mirror is matching the sampling criteria, there should be no more higher frequencies during whole measurement process except the noise (see point 3).

Basing the ideas above, we decided to play around with some experimental work.
We have sampled 2MHz central frequency wide bandwidth transducer reflection in water from polished steel surface. Pulse duration was chosen in such way, that first spectral zero was at 2MHz. In such way transducer bandwidth was artificially increased. Matching coil was removed, so we also had second and third harmonics present. Large number (1024) of A-scans were obtained in order to have good noise reduction. Every A-scan was stored on disk separately. After collection, same time position samples were averaged. Such approach allowed us to increase signal to noise ration, keeping the quantization noise low. Such averaged A-scan was Fourier transformed and amplitude spectra calculated in dB of central frequency amplitude. Basing these calculations, signal bandwidth at -6dB level was calculated and 8bit A/D converter dynamic range levels based maximal frequency extracted. By investigating the figures obtained (Fig 5, Fig 6 and Fig 7 are presenting the spectra obtained with slightly varied pulse duration), one can see that despite bandwidth variations maximal frequency in spectra has not changed and is 7.2MHz. Using the assumptions made above, 8bit converter should use 14.8MHz sampling frequency (2x7.2MHz).

Fig.5. Amplitude spectra of 2MHz transducer reflection from steel mirror (@Tpulse=500ns-5%)

Fig.6. Amplitude spectra of 2MHz transducer reflection from steel mirror (@Tpulse=500ns)

Fig.7. Amplitude spectra of 2MHz transducer reflection from steel mirror (@Tpulse=500ns+5%)

Fig.8. Time domain presentation of error signal (zoomed to highest deviation area)

Usually, sampling frequency is chosen to be about 4 times higher the transducer central frequency. We have chosen 10MHz sampling frequency and resampled same original A-scan (signal s_o(nt_s40)) with this frequency, by taking just every 4-th sample. In some processing algorithms (e.g. Wiener deconvolution, autoregresive spectral extrapolation, L1 norm deconvolution) higher sampling rate is required in order to avoid large interpolation between samples. We decided to experimentally verify the errors introduced by zero padding of slightly undersampled signal. Since chosen sampling frequency was lower than required, 3-rd harmonic was aliased into signal spectra. Signal, sampled at 10MHz was transformed into frequency domain, zero padded at higher frequencies in order to obtain 40MHz equivalent sampling and then transformed back into time domain. After DC removal and normalizing of both original (signal s_o(nt_s40)) and resampled signal (signal s_r(nt_s40)), new signal s_r(nt_s40)) was examined for errors from original s_o(nt_s40). Fig.8. is presenting the error signal (s_err(nt_s40)=s_o(nt_s40)-s_r(nt_s40)) in percent from original (s_err(nt_s40)/max(abs(so(nt_s40))). For better comparison, original signal s_o(nt_s40) is presented on same picture.

Two relative error evaluation criteria were chosen:

1. normalized average absolute difference, the L1-norm:
;

2. the normalized standard deviation, L2-norm:

For signal presented on Fig.5. above, L1-norm value was 11% and L2-norm was 9.2%. Dashed line on Fig.5. indicates the place from which the circular aliasing occurred which, consequently, caused the errors mentioned. Here can be noted, that the place for "maximal" frequency in such case was -30dB below the central frequency amplitude. Still, in some cases such ratio of sampling frequency can be acceptable, just one has to bear in mind possible artifacts caused by circular aliasing. Of course, one would have had much lower errors if sampling frequency was chosen for the limit below -42dB, that is, at ratio of 8 or even 10 of central frequency.

Sampling in ultrasonic system

In conventional acquisition systems sampling process in synchronized using external trigger or using particular input signal level and front. Since the time of signal arrival in not known in priori this seems natural. In ultrasonic systems with active excitation time of arrival can be predicted, since the exciting pulse emission time is deciding the necessary event to expect some signal. In such case, exciting pulse generator signal can be used to synchronize the acquisition process.

But one has to bear in mind that sampling process has discrete character. This means, that despite trigger signal has arrived into sampling block, it has to wait for synchronization period front. If no special precautions are taken here, acquisition of repeated ultrasonic signals (for instance for averaging purposes) will contain a jitter noise which can significantly distort the measurement results. Furthermore, even during scanning process, the front of reflections from smooth surface will have stairs on it. If all system blocks are "in one hands", synchronization process here can be reversed upside down. The sampling block can initiate the exciting pulse generation trigger signal, synchronized to it's internal clock. in such case, there is virtually no jitter in received signals.

Some commercial A/D conversion cards offer internal trigger function. If digital oscilloscope (DSO) is used, this feature implementation is more complicated. In addition to the profit mentioned one can go even further. As it was mentioned above in discussion about exciting generators design, generator can have the possibility to vary the exciting pulse shift relatively to start trigger signal. If adjustment step is stable enough, equivalent time sampling (ETS) can be obtained here.

If in conventional acquisition systems special synchronization schemes are employed in order to have good synchronization with signal arrival time in order to produce ETS phase shift, active excitation ultrasonic system can have the ETS at virtually no cost, if corresponding generator design is present. Furthermore, if sampling block is taking care of trigger, same sampling frequency and trigger, distributed over whole system can ensure the stability of generator, TVG or other devices.

Conclusions

Acknowlegements

We would like to thank the Dr.Vytas Dumbrava for his notes and co-operation and Prof.R.Kazys and Prof.R.Krivickas for encouragement and useful literature support.

References

Ohta K. and Watanabe Ultrasonic flaw detection using a synthetic waveform generator and finite impulse response filter (FIR-filter), T.NDT & E International Vol 30, 6, 1997 p405

Grimaldi U. and Parvis M. Enhancing ultrasonic sensor performance by optimization of the driving signal Measurement Vol 14, 1995 p219-228

Sukhorukov V., Vainberg E., Kazys R. Non-destructive testing. Imaging and automation of testing Vol 5 (Vysshaja shkola) Moscow (1993) Ch 5

Lovejoy A., Pedrick P. et all A novel 8-bit ultrasound phased-array controller for hypertermia applications. Ultrasonics Vol 33 1995 p.69-73

Fitting D.W., Adler L. Ultrasonic spectral analysis for non-destructive evaluation. Plenum Press, New York (1981)

Armitage A.D., Scales N.R et. all An integrated array transducer receiver for ultrasound imaging Sensors and Actuators A: Physical Vol 47, 1995 p542-546

Hughes D.I. and Duck F.A. Automatic attenuation compensation for ultrasonic imaging Ultrasound in Medicine & Biology Vol 23, 1997 p 651-664

Kazys R. and Svilainis L. Analysis of adaptive imaging algorithms for ultrasonic non-destructive testing. Ultrasonics 1995. Vol 33, No1. p.19-30.

Bracewell R.N. The Fourier transform and it's applications. 2-nd ed., revised, McGraw-Hill, (1986)

Vaitkus N., Svilainis L., Dumbrava V. General purpose scanning unit for NDT ultrasonic systems. // Proc. of higherschools of Lithuania, Ultragarsas, 1993, vol.25. p.p.88-97.

Lasser M., Harrison G., Real time, large area ultrasound imaging system using two-dimensional array technique.

F - A
NDTnet Journal, http://www.ndt.net, Vol. 3 No. 3 (March 1998)

Svilainis Linas, Analysis and Optimization of Ultrasonic Imaging Methods for Inhomogeneous Structures.

F - A
NDTnet Journal, http://www.ndt.net, Vol. 2 No. 5 (May 1997)

Authors

L.Svilainis and V.Puodziunas

Dr.Linas Svilainis

svilnis@tef.ktu.lt

http://vingis.sc-uni.ktu.lt/ultrasound/index.htm

Ultrasound Research Center on NDTnet

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Table 1 Number of bits required for A/D conversion
Input signal dynamic range (dB)	Number of A/D converter bits
20 40 60 80 100 120	5 8 11 15 18 21