Topic 11.  Reflections, part 2.  Radar and Sonar

If the velocity of propagation of a wave is known, the time it takes the reflected wave to return to the source is a measure of the distance between the source and the object that produced the reflection. This is the basis for radar, sonar and time domain reflectometry (TDR), all of which measure the distance between a transmitter and a reflector using the time it takes the echo of a pulse to return to the sender.

In order for radar and sonar to be useful, the system must operate in the limit where geometrical optics is valid. In other words, these methods will only “see” an object if its size is considerably larger than the wavelength that is used, so that the ratio of l/D is less than 1. For example, if a bat is to detect an insect whose size is about 6 millimeters in diameter (about 0.25 inches), the bat must use a sound wave whose wavelength is significantly smaller than this value. The velocity of sound in air is about 335 m/s. If we take a wavelength of 3 mm as just barely satisfying the criterion of being not larger than the object that is to be detected, the frequency of the sound wave must be at least

n = c/l = 335/3x10-3 ~ 112 kHz

This is in fact about the frequency that bats use. It is much higher than we can hear. Shorter wavelengths (that is, higher frequencies) allow the bat to detect smaller objects or to see the structure of a larger object.

Note that we use the symbol “c” for the velocity of sound in air (rather than “v”) to avoid confusing it with the frequency n.

Time domain reflectometry is often used to detect the location of a broken power cable in a remote region. When a pulse of voltage is applied to one end of the cable, the broken end of the cable causes a reflection to be sent back to the transmitter. The time it takes the pulse to return gives the approximate location of the break. The same technique is used to detect the location of a break in an underground telephone cable.

Unlike our eyes or our cameras, which are simply receivers that detect objects using reflected light that is produced by some external source, radar and sonar systems also must include an active transmitter. They are therefore both more complex and more versatile – they can detect objects even in the absence of ambient light, but they must include a separate transmitter to make this possible.

The range of radar and sonar systems is limited by two factors. The maximum range is determined by the amount of power that the transmitter can produce and by the sensitivity of the receiver that is used to detect the echo. The minimum range is given by the timing resolution of the receiver – that is, by the ability of the receiver to distinguish between the original transmitted pulse and the (usually much weaker) reflected echo. When the range to the target is too small, the echo can arrive so quickly that the transmitted pulse has not yet died away.  The goals to be able to detect objects that are very far or very close to the transmitter using a single system conflict with each other to some extent. The maximum range of an echo system is increased by increasing the transmitted power, but this increase will saturate the receiver for a longer period of time and make it more difficult to detect an object that is very nearby. Radar systems have clever pulse shapes (called chirps) that attempt to minimize this conflict. Bats use the same techniques.