DOPPLER2 (Раздаточные материалы), страница 6

(i) Basic Principles and Analysis

The principles of non-coherent demodulation for the CW case are illustrated in Fig. 2.21. The clutter signal A might originate not only from stationary targets but also from direct leakage of electrical and ultrasonic energy between the adjacent transmitting and

receiving transducer elements. Whatever its source, the clutter signal A is usually much larger than the echo B backscattered by blood. The two components combine as ultrasonic echoes (in the schematic "ultrasonic combination" stage of Fig. 2.21) to produce

the resultant C detected at the receiver. The Doppler shifted components beat with the clutter-based reference producing amplitude variations in the received signal. These modulations can be extracted by rectifying the signal D and smoothing the output to produce the Doppler difference waveform E.

Non-coherent demodulation can be analysed using the vector analysis shown in Fig. 2.22. The vector A (of amplitude A) represents the clutter and rotates at an angular frequency w₀ about the origin. The Doppler shifted component is similarly represented by the much smaller amplitude vector B which rotates at an angular frequency (w₀ + w_d). For convenience the vector B is located at the tip of A so that the resultant received signal is represented by the vector sum R of the clutter and Doppler components. Because vector B is rotating at a slightly different frequency to vector A, the amplitude of the resultant R will vary at the Doppler difference frequency w_d. (In practice the echo received at the transducer is the real part of R which is described by the projection or component of R along the horizontal axis.)

In order to proceed with a mathematical analysis of non-coherent demodulation, the received echo R(t) given by Eqn (2.49) has first to be written into the more useful and meaningful form

(The details of the rather tedious mathematical procedure leading from Eqn (2.49) to Eqn (2.53) have been relegated to Appendix B.) Equation (2.53) can be interpreted to mean that so long as the clutter is much greater in amplitude than the blood echo, the combined received signal R(t) is essentially the clutter component modulated in both amplitude and phase by the Doppler shifted returns. Thus the simple amplitude detection system shown on the left of Fig. 2.21 which consists of half- or full-wave rectification followed by low-pass filtering to remove the carrier will extract the Doppler component, B sin (w_dt+ Æ_d). Notice also that the frequency of the Doppler signal is equal to the difference in frequency between the clutter and blood echoes, The significance of this is discussed in Section (ii) below.

More basic types of CW Flowmeter still incorporate this rather straightforward method of non-coherent demodulation, using transmitter-receiver breakthrough as the dominant source of reference signal. The system works well for non-directional demodulation but cannot be used when directional processing is required (see Section 2.4e).

(ii) Comparison with Coherent Demodulation

Initially, it might seem that non-coherent modulation could have advantages over coherent demodulation when used in range discriminating flowmeters. The reference signal would then be generated solely by "stationary" structures within the sample volume. If these clutter-providing targets are moving slowly, for example during respiration, then the Doppler difference waveform will indicate the velocity of the blood relative to its surroundings rather than the absolute velocity relative to the transducer which is extracted by coherent demodulation. Furthermore, the clutter signal itself is not subject to coherent demodulation and so small movements of, for example, vessel walls do not tend to produce such large amplitude low frequency variations in the Doppler difference waveform as those resulting from coherent demodulation, Although a rigorous treatment is outside the scope of this text, it would seem that clutter amplitude fluctuations should occur at lower frequencies than clutter components generated by coherent demodulation. Evidence for this rather intuitive statement is provided in Section 1.3b where it is shown that, for a random distribution of point scatterers, the echo amplitude fluctuations occur on the scale of a pulse length rather than on the scale of a wavelength as they would do if the returning echo were coherently demodulated. Since the clutter-producing targets considered here are much larger than red cells, the analysis of a blood target is perhaps not directly applicable although an analogous treatment would probably produce similar results.

It therefore seems that non-coherent demodulation (which is essentially envelope detection) should result in a wider separation of clutter and blood Doppler frequency bands. This in turn should allow more effective frequency filtering than would have been possible after coherent demodulation. These aspects are discussed in more detail by Atkinson and Follett (1975).

The problem with non-coherent demodulation in range discriminating flowmeters is that the sample volume has always to contain a target which provides an adequate clutter signal to generate the reference waveform. Absence of sufficiently strong clutter returns will cause Doppler signal drop-out. This is perhaps why non-coherent demodulation is rarely incorporated into range discriminating instruments, even as a switchable option, although the concept was mentioned by Baker (1970) over ten years ago.

2.4d Non-linear Reception

As a footnote to demodulation it is worthwhile mentioning how distortion in the receiving preamplifiers can affect demodulator performance, The radiofrequency (RF) preamplifier is used to boost the received signal from the transducer before it enters the demodulator. One common type of distortion produced in the RF preamplifier is limiting which can occur

either inadvertently during overload, or which can be introduced intentionally to reduce noise. Gardner (1967) has described how the signal-to-noise ratio of even wideband signals can be improved by hard limiting. However, it has been shown (see Atkinson and Follett, 1975) that hard limiting of an ultrasonic signal containing both clutter and Doppler components can produce spurious Doppler outputs. Although Peronneau et al. (1974) recommend the use of limiting preamplifiers in pulse Dopplers where clutter can be reduced by range gating, it is usually advisable to avoid using non-linear receivers in Doppler systems.

2.4e Directional Doppler Demodulation

It is often clinically useful (see Chapter 4) to monitor not only the velocity of blood flow but also its direction, that is, whether the component of movement is towards or away from the transducer. However, it was shown in Section 2.4b that straightforward demodulation techniques destroy the directional information by shifting both upper and lower Doppler sidebands into the same region of the base-band. Separation of upper and lower sidebands is a problem which is commonly encountered in the field of general communication theory. This section will investigate several of the solutions which have been developed for communication applications and subsequently adapted for directional Doppler demodulation.

(i) Single Sideband Filtering

The most direct method of directional demodulation (illustrated in Fig. 2.23a) is to separate the Doppler sidebands at the ultrasonic frequency using precisely tuned radiofrequency filters. This method has been developed by both De Jongh et aI. (1975) and Sato (1974). The raw ultrasonic echo is fed to high- and low-pass filters which are designed to pass only that signal in the upper and lower Doppler sidebands respectively. These sidebands can then be coherently demodulated in separate channels to give independent forward and reverse Doppler difference signals. This frequency separation process is illustrated in Fig. 2.23b which shows the filter characteristics and their effect on the echo spectrum.

The disadvantage of this conceptually simple approach is that the fillers have to be precisely set up and remain highly stable, Because the filters have to pass one sideband and stop the other and since the frequency spread of the sidebands is typically four to five orders of magnitude smaller than the frequency of the carrier, the Q-factor of the filer

(which controls the rate of roll-off) must exceed about 10⁵ and should preferably approach 10⁶ for acceptable channel separation. The only practical method of producing adequately high filter performance is to use multistage crystal filters and although the practical design is difficult it is apparently not insuperable since an instrument using single sideband filtering operating at an ultrasonic frequency of 5 MHz is commercially available. This device also uses a crystal-controlled master oscillator to ensure that the transmitted frequency does not drift into the passband of either filter. If precise frequency stability were not maintained then the transmission frequency could drift into the receiving frequency passbands and cause crosstalk between the forward and reverse flow channels. For example, if the transmission frequency drifted into the upper sideband, then some negative Doppler shifts from receding targets would still lie in the passband of the high-pass filter and thus falsely contribute to the forward flow channel.

(ii) Heterodyne Demodulation

Coherent demodulation destroys directional information because both upper and lower Doppler sidebands are shifted into the same region of the base-band. Figure 2.24a indicates the frequencies of the ultrasonic echoes returning from three targets: A, stationary; B, approaching the transducer at velocity v, (corresponding to a Doppler shift ¦_f); and C, receding from the transducer at velocity -v_r (Doppler shift -¦_r). lt. is assumed that v_¦ = v_r. Although the Doppler shifted echoes are separated in frequency, it can be seen from the illustration that, following demodulation, the Doppler difference spectra from advancing and receding targets have superimposed. The reason for this is that echo from the stationary target A demodulates to zero Doppler frequency and, since a negative frequency has no practical meaning, any movement either towards or away from the transducer must produce the same (positive) Doppler difference frequency component. Suppose however that the transducer was itself moving say towards the target as shown in Fig. 2.24b. The echo from the stationary target is Doppler shifted by a positive frequency ¦_h proportional to the transducer velocity. Target movement towards the transducer increases the Doppler shift frequency still further because the relative velocity has increased whereas target movement away from the transducer reduces the Doppler shift frequency. Thus, by moving the transducer, the Doppler baseline corresponding to zero target velocity can, in effect, be offset to what is commonly known as a "heterodyne" frequency ¦_h. Directional information is contained in the Doppler sidebands which now lie on either side of this new "zero-velocity" baseline. Furthermore, coherent demodulation of the signal into the base-band retains this offset so that the Doppler difference signals lie on either side of the heterodyne frequency as shown in Fig. 2.24b. An important point to note is that the transducer velocity must be greater than any encountered target velocity. This ensures that all targets are effectively closing toward the transducer. If a target were to move away at such a rate that it actually receded from the transducer, then the Doppler shift frequency would again become negative and the demodulated (positive frequency only) waveform would be ambiguous.