акустика / gan_ws_acoustical_imaging_techniques_and_applications_for_en

7.8Electronic Circuits of Acoustical Microscope

7.8.1Gated Signal and Its Use in Acoustical Microscope

As the theory of the acoustical microscope [10, 11] is built on a monochromatic or single frequency concept, it is therefore necessary to understand the relationship between the frequency domain and the time domain. An acoustic signal may be described in terms of the components of each frequency present, known as the frequency domain, or in terms of the time domain, which shows the signal being oscillatory, as seen on the oscilloscope. These two domains can be related by a Fourier transform as

−∞

From the properties of the Fourier transform, it follows that if a pulse is of finite duration, then it cannot have a single frequency but rather consist of a finite spread or spectrum of frequency components. An ideally monochromatic signal would have only a single frequency present, and therefore would have to be of infinite duration. For instance, if the envelope of a pulse is of rectangular form, then in the frequency domain it will have the Fourier transform of a rectangular function (or a sinc function, defined as sinc(x) = sinx/x). For a rectangular pulse of length to, the width of the central maximum in the frequency spectrum is 2/t0. This gives a measure of the spread of frequencies present.

The convolution of two functions of the same variable, G( f ) and H( f ) can be written as

−∞

The convolution operation is a way of describing the product of two overlapping functions, integrated over the whole of their overlap for a given value of their relative displacement. The convolution theorem states that the Fourier transform of the product of two functions is equal to the convolution of their separate transforms

where F denotes the Fourier transform and denotes convolution.

If we take a pulse as the output of a monochromatic oscillator of amplitude A0 and apply to it a rectangular gate of width t0, the resulting spectrum will be the convolution of the spectrum

If the pulses are repetitive, with a repetition frequency f1, then the gated signal is convolved in the time domain with a comb function (a comb function is a series of delta functions at constant spacing). This means that the Fourier transform of a single-gated pulse is multiplied by the Fourier transform of the pulse repetition which is, in turn, a comb function starting at the origin and repeating at intervals of f1. Thus, the frequency spectrum of a series of gated

pulses is the Fourier transform of the envelope of an individual pulse, centred at the frequency of the oscillator, and composed not of a continuous distribution but of a series of discrete spikes (that is, delta functions) within that envelope.

In the acoustic microscope, the required signal can be selected not only in the time domain but also in the frequency domain. It is then possible to select the specimen echo and separate it in time from the unwanted lens echo over the basis of the design consideration of the focal length of the lens, and hence the resolution is available. Smaller lens reverberations are always present that cannot be separated in time from the specimen’s echo. Moreover, even if such a reverberation could be eliminated, there could still be a problem from the fact that different parts of the acoustic wave from the specimen may be reflected with different time shifts. This could occur, if the specimen has two closely spaced layers, each of which reflects some energy, or if some of the energy is reflected back after coupling into surface waves. If the signal is measured by a peak detector circuit, a reasonable value will be obtained when the interference is constructive, but when it is destructive the value will be quite wrong, corresponding simply to the largest component present. If very long duration pulses could be used, it might be possible to measure the middle where the overlap is adequate, but this is not practicable when there are constraints on the pulse length – as there are in all high-frequency microscopes.

Acoustic microscopy involves the interference of an incident wave, a reflected wave and a refracted wave and the interference theory is built on the assumption that the microscope is perfectly monochromatic. This is especially so for the theory of the V (z) technique, studying how the contrast varies with defocus. The monochromatic theory could be summed over a frequency spectrum that is actually used in a given system, but would be almost impossible to invert when interpreting measured results. For much of qualitative imaging the narrow band detected signal may be adequate.

For more accurate measurements, the heterodyne circuit is used. An example of a heterodyne circuit is shown in Figure 7.14 [15].

If the bandwidth of the detector system can be narrowed to a fraction of the spacing between adjacent spikes, it is possible to select one of them and to reject all other signals at spacings of multiples of the pulse repetition frequency. In this way, it is possible to isolate and measure a single-frequency component and then achieve a measurement that is monochromatic, subject only to the phase noise of the signal source. Here the local oscillator is phase-locked to the signal source and has a frequency that differs from the signal source by some small amount [12, 13].

In the simple heterodyne circuit shown in Figure 7.14, and is used in most imaging microscopes, the pulse length is defined by the switch S1. As the speed of this switch determines the minimum pulse length and, hence, the minimum lens focal length, it also determines the highest frequency of the microscope. Thus the limit to the resolution is ultimately determined by the highest useful speed of the switch. S2 is the single-pole double-throw SPDT) switch and A1 the low-noise preamplifier. The mixer is a device that takes two inputs: the radio frequency signal and the local oscillator signal and gives outputs as the sum and different frequencies of these two [14]. The local oscillator frequency is chosen so that the different frequency is in the middle of the pass band of the narrow band filter, which is placed in the circuit at the intermediate frequency output of the mixer. Gating of the preamplifier output is achieved by gating the local oscillator of the heterodyne circuit.

(a)lens

Signal Acoustic monitor

lens

(b)

Figure 7.14 Schematic radio frequency (r.f.) systems: (a) simple heterodyne circuit, S1 determines the pulse length, S2 switches the lens from transmit to receive, and A1 amplifies the reflected signal;

(b) quasi-monochromatic circuit; the two oscillators and the pulse repetition frequency are phase-locked, and the final signal is lock-in detected (Weaver [15])

7.8.2Quasi-Monochromatic Systems

For quantitative acoustical microscopy, that is, the V (z) curve measurement, the quasimonochromatic circuit of Figure 7.14(b) is more accurate [15].

The basic principles of this circuit are similar to those of Figure 7.14(a) but there are some important differences. The radio frequency (r.f.) oscillator and the local oscillator are two frequency synthesizers that are phase-locked to one another to give a difference frequency of precisely defined phase. This difference frequency is very much lower than in the simple heterodyne circuit in order to make it comparable with the pulse repetition frequency.

In order for the system to behave as truly monochromatic, it is important that the receiver gate should not introduce any distortion of the frequency spectrum of the reflected pulse. The

reflected pulse will be multiplied in the time domain by the receiver gate, and that corresponds in the frequency domain to a convolution with the (repetitive) pulse gate transform.

After the output of the mixer has been amplified and low-pass filtered, it may be fed to a lock-in amplifier. This is a phase-sensitive detector performs at near-audio frequencies, rather as a mixer does at radio frequencies but with more sophisticated controls.

With a dual-phase lock-in amplifier, the in-phase and quadrature components, or equivalently the module and phase, can be measured simultaneously. If only the module of the detected component is required, then a readily available alternative to the circuit illustrated in Figure 7.14(b) is to use a spectrum analyzer with a measurement output in place of the heterodyne detector system in Figure 7.14(a), with its own tracking generator as the r.f. oscillator and the swept frequency range set to zero [16].

The quasi-monochromatic system has great advantages in terms of SNR, dynamic range and linearity over the quasi-continuous wave (qcw) system. It also allows the effect of the troublesome lens reverberation that occurs within the time gate to be at last eliminated. Since this also appears now as a monochromatic contribution, it can be removed by subtracting a uniform signal of compensating amplitude and phase at the reference frequency from the input to the lock-in amplifier. But most important of all, it allows measurements to be made at, effectively, a single frequency, so that they can be analyzed accurately in terms of the monochromatic theory of V (z) (the video signal as an explicit function of defocus).

7.8.3Very Short Pulse Technique

For some purposes, it may be necessary to have accurate frequency definition; for others, a good time discrimination is useful. Because of the Fourier relationship between frequency and time, the more precisely the time of a signal is known, the greater is it necessary to know the bandwidth of frequencies. Approximately, the time resolution τ is the reciprocal of the

bandwidth Bw that their product Bwτ = 1.

The design of a system for working with short pulses follows the same principles as other pulsed ultrasonic systems, such as ultrasound flaw detectors, but it is necessary to achieve very much great stability and high bandwidth.

In Sections 8.3, 9.2 and 9.3, the techniques and applications of time-resolved quantitative measurements will be given in which impulse excitation is essential. But many uses of acoustic microscope call primarily for an image, and for that purpose conventional gated continuous wave electronics are quite adequate and indeed are to be preferred because of the good signal strength that they give for obtaining pictures at a reasonable speed with good contrast.

References

[1]Korpel, A., Kessler, L.W. and Palermo, P.R. (1871) Acoustic microscope operating at 100 MHz. Nature, 232(5306), 110–111.

[2]Hoss,¯ A., Ermert, H., el Gammal, S. and Altmeyer, P. (1989) A 50 MHz ultrasonic imaging system for dermatologic application. IEEE Ultrasonics Symposium Proceedings, pp. 849–852.

[3]Crocker, R.L., Gray, N.J., Phillips, R.B. and Chivers, R.C. (1989) High frequency ultrasonic B-scanner.

Ultrasonics International 89 Conference Proceedings, pp. 578–583.

[4]Nakamura, M.N., Obara, K. and Segawa, M. (1976) The strong piezoelectricity in polyvinylidene fluoride (pvdf). Ultrasonics, 14, 15–23.

[5]Passmann, C. and Ermert, H. (1995) Adaptive 150 MHz ultrasound imaging of the skin and the eye using an optimal combination of short pulse mode and pulse compression mode. Proceedings IEEE Ultrasonics Symposium, Seattle, USA, 1995.

[6]Passmann, C. and Ermert, H. (1995) In vivo imaging of the skin in the 100 MHz region using the synthetic aperture concept. Proceedings IEEE Ultrasonics Symposium, Seattle, 1995.

[7]Pollakowski, M. (1993) Ein Beitrag zur Anwendung der Pulskom-pressionstechnik in der Zerstorungsfreien¨ Werkstoffprufung¨ mit Ultraschall. Ph.D. thesis, Ruhr-Universitat Bochum, Shaker, Aachen.

[8]Fowle, E.N. (1961) A general method for controlling the time and frequency envelopes of FM signals. Technical Report 41G-0008, Massachusetts Institute of Technology (MIT), Lincoln Laboratory, Lexington, Mass., June 1961.

[9]Loupas, T., McDicken, W.N. and Allan, P.L. (1989) An adaptive weighted median filter for speckle suppression in medical ultrasonic images. IEEE Trans. Ultrason. Ferroel. Freq. Control, UFFC-36(1): 129–135.

[10]Briggs, A. (1992) Acoustic Microscopy, Clarendon Press, Oxford, pp. 64–78.

[11]Atalar, A. and Hoppe, M. (1986) High-performance acoustic microscope. Rev. Sci. Instrum., 57, 2568–2576.

[12]Liang, K.K., Bennett, S.D., Khuri-Yakub, B.T. and Kino, G.S. (1985) Precise phase measurements with the acoustic microscope. IEEE Trans., SU-32, 266–273.

[13]Liang, K.K., Bennett, S.D. and Kino, G.S. (1986) Precise phase measurements with short tone burst signals in acoustic microscopy. Rev. Sci. Instrum., 57, 446–452.

[14]Henderson, B.C. (1990) Mixers in microwave systems. Watkins-Johnson Company Tech-notes, 17(1), 1–15; 17(2), 1–13.

[15]Weaver, J.M.R. (1991) An optimal R.F. system for quantitative acoustic microscopy. IEEE Trans. Ultrason. Ferroel. Freq. Control. UFFC.

[16]Kushibiki, J. and Chubachi, N. (1985) Material characterization by line-focus-beam acoustic microscope. IEEE Trans., SU-32, 189–212.