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Parabolic Stereo

by Ron Ward

For every adage there is an equally apt one saying the opposite; for example, many hands make light work - unless they happen to be cooks! So it is with parabolic stereo - to divide or not, to use two reflectors, or to use a Siamese twin version of the very same thing. It is true that there has been much work and experiment put into this problem, but a certain mystique has developed in this area and the real issues have become obscured. It is felt, therefore, that in order to understand the complexities involved it might be useful if we went back to basic principles and examined the way in which a parabolic reflector works, and the pros and cons of the various methods advocated for stereo.

The principle of a parabola

Figure 1: The principle of a parabola. Parallel incoming waves all converge at a focal point

A parabolic reflector is constructed to the formula y2 = 4ax, 'x' and 'y' being the two axes and 'a' the focal point. The parabola has the property that whatever the ang1e 'ba' makes to the axis 'x', 'cb + ba' is a constant. Thus, sound waves travelling as a plane wave will, after reflection, arrive at the focal point at the same instant, i.e. in phase. The position of the focal point will determine the shape of the reflector - the shorter the focal length, the deeper the dish. When using a parabolic reflector for reflecting sound, the reflector does not behave in quite the same way as one used for reflecting light or radio waves. Because the sounds we wish to record range from 100Hz to 20,000 Hz, a range of 200 : 1, at some frequencies the wave length can be equal to the diameter of the reflector, or the microphone, or have a relationship to the focal length of the reflector. This can cause interference or cancellation problems. This effect does not occur with light or microwaves since the range of frequencies, and therefore the wavelengths, is of the order of about 2 : 1, and are very small compared with the dimensions of the reflector[1]. Another property which occurs when using sound reflectors is that of foreshortened perspective. The reflector acts in much the same way as a telephoto lens so that sounds that are more distant than the subject, if they are on the same axis, are brought forward, and if they are already at a high level they can overpower the recording of the subject. This compression can usually be overcome by the choice of a different recording position so that the unwanted sound is well off axis.

Mono recording with a parabolic reflector

If one supposes that the purpose is to single out one sound, say for example, a thrush singing his Spring song, with the exclusion or suppression of other sounds, then if it is not possible to get close enough to the subject with a conventional microphone, a reflector of suitable size and shape coupled with a matching microphone is an appropriate way of achieving that. A reflector will convert a relatively cheap omni-directional microphone into a highly directional and sensitive transducer with a forward gain possibly better than a more expensive gun microphone. Why? Well, size and shape of reflector are factors - the bigger your ears, the better you hear. what one is in fact doing is collecting sound along a 'beam' from a 'sound stage' consisting of a circle the same diameter as the reflector. The singing bird is a point source, and sounds outside the circle of maximum sensitivity may be heard but not with the same strength. The collected sound is focussed on to the microphone by the reflector. Collecting power in terms of surface area of the reflector compared with cross-sectional area of the microphone explains where the gain is obtained, and the benefit is that recording levels need not be set at maximum thus reducing HISS.

The response curve of a typical omni-directional microphone such as the Grampian DP6 in a 24 inch reflector with a focal length of 7 inches is shown in figure 2. The frequency response of the microphone itself has been subtracted, so the change in gain achieved by the reflector is shown.

response curve of an omni-directional microphone in a 7-inch focal length reflector

Figure 2: The response curve of an omni-directional microphone in a 7-inch focal length reflector with the sound source on-axis.

response curve of an omni-directional microphone in a 7-inch focal length reflector 10deg off axis

Figure 3: The response curve of an omni-directional microphone in a 7-inch focal length reflector with the sound source 10 degrees off-axis

When the test sound source is shifted 10 degrees off axis the result is as in figure 3, and illustrates just how directional the reflector is, particularly at higher frequencies. Both diagrams show one of the problems mentioned earlier; the dip in response between 500 Hz and 1000 Hz ( i.e. between one and two octaves above middle 'C' ), is thought to be ,due to cancellation of the reflected wave by the direct wave, since the omni-directional microphone will receive both. The reflected wave arrives at the microphone a little later than the direct wave, and the distance involved, twice the focal length, corresponds to half a wavelength at around those frequencies. This problem is aggravated further as the diameter of the reflector is reduced., indeed below 19 inches the curve dips progressively below the zero gain axis to a negative value, thus causing the microphone to perform less well in the reflector than out of it. Audiospectrograms, or Sonagrams, of the calls of many birds contain elements within this suppressed range, so their calls will sound not quite natural. A deeper reflector, i.e. with shorter focal length, appears to go some way towards overcoming this problem. Figure 4 is the response curve of the same test - a DP6 microphone in a 24 inch reflector but with a focal length of 4 inches. The dip should now occur at about 900 Hz. It does, but is not very pronounced, and apart from a more uniform response, the deeper reflector goes someway towards protecting the microphone from the effects of the wind and from sounds coming from behind the reflector.

response curve of an omni-directional microphone in a 4-inch focal length reflector

Figure 4: A reflector with a shorter focal length does not have the dip in signal characteristic of the longer focal length parabola shown in Figures 2 and 3

Microphones - omni or cardioid?

An omni becomes very directional when used in a reflector, except at the lower frequencies, and if the reflector is deep enough, it will, as just mentioned be shielded to a degree from sounds behind the reflector. A cardioid, on the other hand, is directional to start with - but in the wrong direction in this instance, since to mount it in a reflector it has to face to the rear, and it will pick up low frequencies (breathing, coughing, motor noise, etc.) better in that direction than via the reflector! Also, a glance at figure 5 will show the steep curve, which means that when setting the recording level to achieve good results in the mid-range of frequencies, there is a real danger of over-modulation at the top end - those 'sudden high transients.

response curve of an cardioid microphone in a 4-inch focal length reflector

Figure 5: The response of a cardioid microphone in a parabola gives an even greater emphasis to the higher frequencies

stereo mics in a parabolic dish
Roger Boughton with his stereo parabolic rig made
along the general principles of this article

Stereo

It cannot be done with reflectors! At least, not without some modification. Consider what we said about mono - the sound stage is a circle the same diameter as the reflector, and maximum signal from that circle along a parallel 'beam'. If we use two reflectors, and try to cover a reasonable field of view, we shall end up with two unconnected mono images - hardly satisfactory. What if we could find a way of enlarging the two sound stage circles from a pair of reflectors, each to cover a group of subjects instead of a single one, and then arrange these two circles horizontally side by side, so that they overlap to give a good centre image? The' beam of receptivity' can be made to diverge by moving the microphone head away from the focal point towards the reflector. If we could determine the amount of divergence required to obtain a given amount of combined spread to cover a reasonable field of view at a given distance, and provided there was an overlap of circles, we would get a stereo image which did not suffer from the Polo effect. There is a loss in gain, of course, for you never get owt for nowt, and the reflectors are now not so sharply directional as they were previously, but for this application that is an advantage. A recording in one of the recent circulating tapes was made with two reflectors, and the stereo was favourably commented upon. Somebody else is also having a go! However, there can be phase cancellation problems if the left and right channels are combined for a mono playback, because the microphones are so far apart.

Research has established that to overcome phase cancellation, the microphones for stereo should coincide, but since that is physically impossible, a compromise position vertically one above the other, angled left and right, provides an acceptable solution. Unfortunately this is not convenient in a reflector. One system that does seem to work, is to place the heads of the microphones close together in the reflector, and to separate them with a baffle plate, figure 6a & 6b. Each microphone receives a reflected signal via the baffle plate and reflector, the left half of the reflector and the left microphone receiving signals from the right, and vice versa. Again, owt for nowt comes into play, for there are three disadvantages with this system. First, the two reflector principle described earlier has been used, but each reflector has been cut in half, baffled, and joined to its opposite number in order to get the two microphones as coincident as possible. The result is that each microphone can only receive sound from half the reflector surface, so the gain is halved and recording levels have to be turned up. Second, the dividing baffle itself masks out some of the desired sound, (Figure 7) causing a further reduction in gain due to the reduced reflecting surface. Third, weight and bulk have been increased.

response curve of an omni-directional microphone in a 7-inch focal length reflector

Figure 6: (a) Side view showing microphone next to the central baffle (b) Plan view showing positions of the stereo pair of mics

response curve of an omni-directional microphone in a 7-inch focal length reflector 10deg off axis

Figure 7: Masking of the reflector surface reduces the gain provided by the reflector

A further solution presents itself. Taking the example of the car headlamp, which uses a parabolic reflector, it is possible to get two diverging beams from the same reflector, each going in different directions, without using a divider. Also, if one considers how close together the two filaments are in the head lamp bulb, it will be realised that accurate positioning is essential. Accordingly, two omni-directional microphones were positioned with the centres of the heads one inch apart on either side of the focal point (4") of a 24 inch reflector. The result was a very confused 'stereo' image. On analysis, by reconstructing this on the drawing board, and working backwards. from the position of the microphones, it was found that the two 'beams', whilst going in the correct direction left and right, were not themselves even parallel. They each converged to points some distance in front of the reflector, and then spread out again, in other words each became laterally inverted - no wonder the stereo image was confused, with the ears and brain working overtime trying to make sense of it! After further experiment. it was found that by repositioning the microphones one inch closer to the reflector, i.e. at a 'focus' of 3 inches instead of 4 inches, with centres still one inch apart, two diverging beams were obtained, giving a total horizontal spread of 25 degrees with 6 degrees of overlap in the centre.

stereo mics in a parabolic dish
detailed view of mics

The results were very encouraging, and a further series of tests will determine the optimum position. With reflectors of different focal lengths it is felt that a good basis for experiment would be to place the microphones at 75% of the focal length. Considerations of weight and bulk give this system distinct advantages over other systems, but the main advantage is that of GAIN; each microphone uses the whole reflector surface, so the gain is doubled.

Some researchers advocate cutting off the top and bottom of a divided reflector. It is understood that this is to eliminate some of the top and bottom sound, presumably to improve separation? Would they then fit horizontal baffles to cut off some of the top and bottom sound reaching a pair of guns or cardioids? So what is so different about a telephoto version of the same thing?

Acknowledgements and Bibliography

  1. 'Wildlife Sound Recording' David Tombs WSRS
  2. 'Microphone Reflectors'G. N. Patchett - University of Bradford
  3. Published in 'Wireless World', June 1973 (Photocopies probably available from your Ref. Library)
  4. 'Birds of North America' Robbins, Bruun and Zim, Golden Press, New York

Editors note: This article by Ron Ward appeared in Wildife Sound in the early 1980s. Gerry Patchett's article also appeared in Wildlife Sound No6 Sept 1972

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  1. To complicate matters further, sound waves are an example of longitudinal propagation, as opposed to electromagnetic waves which are an example of transverse propagation. Analysis of one mode can not neccesarily be applied directly to the other, and much more work has been done on light and radio reflection with parabolic dishes than has been done with sound reflection.

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