Application of Arbitrary Position and Width Pulse Trains Signals in Ultrasonic Imaging : Correlation Performance Study

Ultrasonic imaging requires both the accuracy and the resolution. Conventional imaging systems use the pulse signals to accomplish the task. But the energy attainable with such signals is limited. Spread spectrum, compressible signals allow to achieve the wide bandwidth even using long durations. Conventional signals do not offer full flexibility or, like nonlinear frequency modulation signals, lack the ease of properties control. We suggest using novel spread spectrum signals generation technique: trains of pulses of arbitrary pulse width and position (APWP). It is expected that APWP should have properties similar to chirp (wide, controllable bandwidth) and both the single pulse (low correlation sidelobes) signals. Study presented here was aimed at evaluating the correlation properties of APWP signals. It indicates that application of APWP signals allows obtaining the properties better or close to those of the conventional signals. It can be concluded that APWP signals offer a new perspective in imaging applications. DOI: http://dx.doi.org/10.5755/j01.eee.19.3.2690


I. INTRODUCTION
Ultrasonic applications gained popularity thanks to small equipment size, environmental safety and cost-effectiveness.Ultrasonic imaging in medicine [1], [2] and non-destructive testing and evaluation [3]- [5] is the only technique offering the direct interaction with test media.While propagation time estimation accuracy depend on the signal energy, input noise and signal spectrum [6]- [8], imaging resolution depends on the envelope bandwidth [9]- [11].In order to obtain both the accuracy and the resolution, high energy and wide bandwidth signals are needed.Conventional imaging systems use the high voltage pulse signals to accomplish the task.But the energy attainable with such signals is limited by the excitation voltage, which in turn is defined by transducer construction or excitation electronics.Spread spectrum (SS), compressible signals [12]- [14] allow to achieve the wide bandwidth even using long durations.After compression in matched filter (correlation processing) signal duration in reduced and the energy is concentrate at one time instant [15], [16].Wideband signals can turn useful if applied for structural noise dispersion increase in composites imaging [17].Another advantage offered by SS signals is the simultaneous probing ability thanks to availability of the orthogonal signals [16], [20].Usually, linear frequency modulation (chirp) or arbitrary waveform signals are considered [4], [9] best candidates for SS.But chirp has rectangular spectrum which causes its correlation function to have large sidelobes [9].Arbitrary waveform signals are not easy to generate if large voltages are needed [13].Nonlinear frequency modulation (NFM) signals are gaining popularity thanks to the ability to control the shape of the spectrum [14] and the sidelobe level [15], [16].But there is no convenient procedure for frequency modulation function rectification from desired properties.Therefore, NFM studies are being carried out by manually assigning various functions and looking for desired performance.Pulse signal exhibits best correlation sidelobes properties but do not possess the high energy and orthogonality properties of SS.We suggest using novel spread spectrum signals generation technique [18]: trains of arbitrary pulse width and position (APWP) pulses.It is expected that APWP should have properties similar to chirp (wide, controllable bandwidth) and both the single pulse (low correlation sidelobes) signals.Study presented below was aimed at evaluating the correlation properties of APWP signals.

II. APWP SIGNALS
The novel spectrum spread technique did not receive the proper attention in ultrasound: trains of the arbitrary position and width pulses (APWP) [18], [19].Technique is using a chaotically placed train of square pulses with arbitrary position and width (Fig. 1).
width modulation (PWM) and the pulse position modulation (PPM).It is produced from the set of random duration pulses, where both pause and duration is guarded to be within the allowed range to construct the frequency components within desired range.

III. EXPERIMENT SETUP
Usual experimental setup would be expected to be carried out in real conditions.But in such case the variation of ultrasonic transducer of propagation media properties due to temperature would affect the transmission AC response.In addition, changing the excitation signal, upload to pulser memory and collection of new signals would take time.Therefore it was suggested to split the experiment into two parts: one was used for whole system AC response measurement, another was carried out numerically, using the former measurement results.Solid stainless steel block was placed into water tank and reflections of ultrasonic signals from the block were collected (Fig. 2).Wideband (86%) composite (48 dB sensitivity) ultrasonic transducer TF5C6N (supplied by Doppler Ltd.) with center frequency 4,61 MHz was used in pulse-echo mode.The received echo signal s R can be treated as carrying the information about the whole system (pulser, ultrasonic transducer and acquisition system) transmission properties where T P (t) is the transmission AC response of the pulser, T X (t) is the combined transmission AC response of the transducer in transmission, water path, reflection from interface and transducer in reception, T ACQ (t) is the transmission AC response of the whole acquisition system, including cables, preamplifier, filters and ADC response and n(t) is a non-correlated additive white Gaussian noise (AWGN).Then, using the excitation signal S T (ω) (obtained as Fourier transform of the mathematical representation of signal loaded into pulser memory) and the received echo signal S R (ω) (obtained as the Fourier transform of the signal recorded in acquisition system memory) transmission AC response T sys of the whole system can be obtained All the obtained system transmission AC responses were combined to produce a single AC response (solid line in Fig. 4) This AC response T sys was later used to obtain the received echo signal S R (ω) for any candidate signal which was described mathematically Signal in frequency domain S R (ω) was converted into time domain signal s R (t) using the inverse Fourier transform.
AC response analysis was used to establish the -6dB passband frequencies.From Fig. 4 data it was established that lowest passband frequency is 4.5 MHz and highest passband frequency is 8.1 MHz.
Three signals were used in succeeding experiments: square pulse, chirp and APWP (Fig. 1).The APWP signal was described as a sequence of the interleaving high and low level pulses of duration τ n ( ) ( ) ( ) ( ) ( ) ( ) Generation of durations τ n was done using Monte Carlo technique, using random generator with even distribution.Chirp signal was not optimized: it was assigned to span from 4.5 MHz to 8.1 MHz.Pulse signal was optimized by linearly varying the pulse duration and noting the best value of the convergence criteria.After optimisation procedure (1000000 Monte Carlo runs) signals (refer Fig. 5 for example signals after sidelobe energy optimisation) were submitted for further analysis.Three convergence criteria, reflecting different correlation function properties were used: i) maximum value of the sidelobe (max(SL)); ii) sidelobe energy (E(SL)); iii) mainlobe duration τ i (Fig. 6).These criteria were applied on autocorrelation function Maximum value was obtained by searching the maximum value to the left of the mainlobe (index 1 to m L ) and to the right where m L and m R are leftmost and rightmost positions index of the mainlobe and M is autocorrelation function length.Sidelobe energy was obtained by taking the L2 norm over the left side of the mainlobe (index 1 to m L ) and to the right Mainlobe duration was obtained as the difference between index m L and m R with subsample interpolation using linear approximation.

IV. EXPERIMENT RESULTS
Three Monte Carlo runs with different convergence criteria were run.Results for sidelobe peaks level (max(SL)) optimisation are presented in Table 1 and Fig. 7 and Fig. 8.It can be seen, that APWP signal outperforms the last two, has much better correlation properties.
Results for sidelobe energy (E(SL)) optimisation are presented in Table II and Fig. 9.It can be seen (Fig. 9), that though square pulse signal outperforms the last two, APWP signal has much better correlation properties than chirp signal.Again, chirp signal has shortest mainlobe width.Results for mainlobe width (duration τ i ) optimisation are presented in Table III and Fig. 10.Here, all signals have similar performance.Though, APWP signal has slightly better correlation properties than the other two.

V. CONCLUSIONS
A preliminary study indicates that application of APWP signals allows obtaining the properties better or close to those of the conventional signals.In case sidelobe of peaks level optimisation APWP signal outperforms the last two, has much better correlation properties.In case of the sidelobe energy optimisation, though square pulse signal outperforms the rest of the signals, APWP signal has much better correlation properties than chirp signal.In case of the mainlobe width optimisation all signals have similar performance.Though, APWP signal has slightly better correlation properties than the other two.It can be concluded that APWP signals offer a new perspective in imaging applications.

Fig. 3 .
Fig. 3. System AC response when measured with square pulse.

Fig. 4 .
Fig. 4. System AC response when measured with chirp and mean value of all measurement (solid line).

TABLE I .
RESULTS FOR SIDELOBE MAXIMUM OPTIMISATION.

TABLE II .
RESULTS FOR SIDELOBE ENERGY OPTIMISATION.

TABLE III .
RESULTS FOR MAINLOBE DURATION OPTIMISATION.