8.2.1 Achieving true stereo sound reproduction
When we listen to stereo recordings through headphones, each ear hears exactly what it should: the left ear receives only the sound from the left headphone, and the right only that from the right. If the recording has been mixed correctly, then the listener will hear an accurate representation of the spatial distribution of the original sources, which the brain infers from the relative intensities and timings of the sounds as they arrive at the ears.
If, as is perhaps more common, we listen to recordings through a pair of loudspeakers, then the effect is imperfect, for each ear hears sounds originating at both loudspeakers. It may be, of course, that the left loudspeaker is better heard by the left ear, but in general there will be considerable cross-talk. The result is that, although a degree of stereo imaging persists, the effect is far less pronounced than when using headphones; in general, sources that with headphones appeared to be spread all around the listener now seem all to be located between the two loudspeakers.
Fig.
Cross-talk compensation in stereo audio systems.
Interference allows this defect, at least in principle, to be corrected, for we can use the principle of Young’s double-slit fringes to achieve a cancellation of the sound from the left channel that reaches the right ear, and vice versa. We achieve this, as illustrated in Fig. 8.2, by feeding the left channel to both loudspeakers – just as in Young’s experiment the same wave arrived at both slits – but we introduce a phase shift, whose effect is to shift the fringe pattern to the left or right, so that a node in the interference pattern coincides with
the position of the right ear. The left channel is thus heard only by the left ear. The converse arrangement similarly limits the right channel to the right ear.
Sound, of course, comprises a range of frequencies, each of which requires the appropriate phase difference for this effect to work. Fortunately, the principle can be understood equally simply for arbitrary signals: our phase shift is actually a delay, sufficient to cancel out that with which simultaneous sounds would arrive at the right ear, together with an inversion (multiplication by −1). Sound from the left channel therefore reaches the right ear via both loudspeakers at the same time, but with opposite signs, cancelling out
identically. The right channel is then added, processed in the same way with a delay and inversion before it is fed to the left-hand loudspeaker. The result is that the left ear is positioned at a node for the right channel, and the right ear at a node for the left channel.
There are, of course, some disadvantages to this trick. First, there is a slight delay between the two versions of the left channel heard by the left ear: not sufficient to be apparent as an echo, but enough to disturb the purists. More critical is that the head must be positioned precisely with respect to the loudspeakers. For these reasons, most implementations attenuate the correction, achieving a smaller but still significant enhancement over a wider range of conditions. This is the mechanism behind the ‘wideness’ or ‘surround’ setting on portable ‘ghetto-blasters’, and was the starting point behind more recent developments in ‘surround-sound’ technology.
8.3 Wavefront dividers
Young’s double slit effectively produced two sources from the same wavefront,
by sampling it spatially at two different points. This method of producing multiple sources is traditionally referred to as division of the wavefront, and the resulting interference is the phenomenon of diffraction – the subject of the next chapter. It is also possible to produce two waves from a single wavefront by division of amplitude by using devices that reflect a fraction of the wave while transmitting the remainder. The distinction between these two processes is neither absolute nor important, but rather indicates a pragmatic classification
of traditional interference geometries. We shall make little further reference to these distinctions but, since they are referred to in many textbooks, the following brief explanation is offered.
Interference by division of the wavefront is regarded as a method for comparing different parts of the wave at a given time: the sampling points are reached simultaneously by the wavefront, but are displaced in a direction transverse to thewave propagation. For stable fringe patterns to be observed, the two samples must have a fixed phase relationship, or coherence. Instruments that use division of the wavefront are therefore sensitive to the transverse (or spatial) coherence of the wave: the extent to which laterally separated
points maintain a fixed relative phase, which may be shown to depend upon the
shape and size of the wave source. It follows that interference between sources
generated by division of the wavefront may be used to measure the size of a source – as in the Michelson stellar interferometer or, arguably, any imaging system including telescopes and microscopes.
Interference by division of amplitude, on the other hand, is generally used to compare parts of the wave that are separated in their times of arrival at the same point in space – that is, they are displaced in the longitudinal direction, but not in the transverse. Instruments that employ this process are therefore sensitive to the longitudinal (or temporal) coherence of the wave – the extent to which longitudinally separated points maintain a fixed relative phase. The longitudinal coherence of a wave may be shown to depend upon the wave spectrum. Division of amplitude is therefore used to determine the
spectral properties of a source, in optical instruments such as the Michelson interferometer, Fabry–Perot ´etalon and interference filter.
Although the distinction between these two categories of beamsplitter is therefore of practical significance, examination of the detailed mechanisms may sometimes render the separation rather less clear: diffraction gratings, for example, may fall into either category, and almost all interference is to some extent affected both by the spectrum and by the size of the source. Fundamentally, however, this is of no great significance, for in all cases we are
simply sampling and comparing parts of the wave motion at different points in space.
8.4 The Michelson interferometer
To illustrate interference through the division of amplitude, and its use in investigatingthe spectral properties of a wave source, we consider the Michelson
interferometer – an optical instrument, shown in Fig. 8.3, that is commonly used to investigate narrow-band emissions in the visible and infrared regions of the spectrum. The heart of the interferometer is a beamsplitter, typically comprising an optically flat plate of glass on which has been deposited a layer of metal that is sufficiently thin to be partially transmitting. Incident light strikes the beamsplitter at an angle of ; part of the light is transmitted, while the remainder is reflected sideways at
The transmitted and reflected beams subsequently strike the mirrors A and
B, which reflect them back upon themselves towards the beamsplitter where, as before, they may be transmitted or reflected. The result is that incident light may travel through the interferometer via either mirror A or mirror B. The wave therefore has two routes to reach P from S, and the total wave amplitude at P is given by the phasor sum of the components emerging from each of these routes. If the times taken to follow the two routes were equal, then the corresponding wave components would always arrive at P with the same phase and we should find nothing remarkable; the Michelson interferometer therefore works by introducing a difference between the two path lengths