Читать книгу The Physics and Technology of Diagnostic Ultrasound: A Practitioner's Guide - Robert Gill - Страница 18

In this chapter we have implicitly assumed that the ultrasound wave is continuous (i.e. it goes on for ever). This is referred to as "continuous wave" ultrasound. Later we will see that diagnostic ultrasound actually uses short "pulses" of ultrasound (although there is one situation where continuous wave ultrasound is used – "continuous wave Doppler").

A continuous wave is the purest form of oscillation. It is often found in nature, e.g. in the motion of a plucked guitar string or of a clock pendulum. Mathematically it is referred to as a "sinusoidal" wave because it can be described by the sine function. For example, the mathematical expression for the pressure at a point as a function of time (as shown in Figure 2.2) is:

pressure = A × sin(2πft)

where f is the frequency of the wave and t is time.

The sinusoidal wave is also useful as the building block for more complex waveforms. Any form of repetitive function can be broken up into the sum of a number of sinusoidal waves of different frequencies. This process is referred to as "frequency analysis". Thus, for example, a continuous triangular wave can be broken up into the sum of a number of sinusoidal waves of different frequencies, as shown in Figure 2.4.

Figure 2.4 A non-sinusoidal waveform (like this triangle waveform) with frequency f can be broken up into the sum of sinusoidal waves of different amplitudes and with frequencies f, 2f, 3f, .... etc.

Note that there are frequency components at the repetition frequency of the wave and at integer multiples of it ("harmonics"). We will return to this concept in chapter 12 when we discuss Harmonic Imaging.

Similarly a pulse (i.e. a wave that lasts just a short time) can be broken up into the sum of many different waves with different frequencies. This will be discussed further in chapter 3.