The Wave Physics behind LiDAR, RADAR, Infrared (IR), SONAR, & Ultrasonic Sensors

Sensors are devices that measure and collect data about the environment. They are employed in a variety and range of different applications, such as in autonomous vehicles, drones, smart watches, smart phones, household appliances, and more.

A common technique for sensors to measure their environment is to shoot outgoing waves and wait for them to return. The outgoing waves will return if they hit something in the environment and are deflected back to the sensor. Based on the time it took for the return wave to come back as well as the speed of the wave, approximate distances between the sensor and the objects can be determined. Typically, in this setup, the sensor will have a transmitter that is sending outgoing waves and a receiver that is collecting return waves.

This technique is used by LiDAR, RADAR, Infrared (IR), SONAR, & Ultrasonic sensors. In this article, we will overview the physics behind using waves in this fashion and provide some general characterizations of these sensors.

Note: these characterizations are not exhaustive or universal. There’s a lot of variation, nuance, and innovation in these sensor technologies and how they leverage waves.

The Kinematics of Using Waves

So far, we’ve established that we have a transmitter emitting an outgoing wave and a receiver receiving a return wave if an object is present. This allows the sensor to detect objects in their environment. However, how does the sensor then approximate the distance from the detected object?

Well, the sensor keeps track of the time between the wave being emitted and returning.

In this setup, we’ll know the speed of the wave used by the sensor, which we will denote as v, and the time between being transmitted and received, which we will denote as t. From kinematics / physics, we have that distance, which we will denote as d, is speed multiplied by time. Thus, we can determine the total distance travelled by the wave by multiplying the speed of the wave by the time taken. Since the wave had to first travel to hit the object and then return back, we actually need to halve the total distance to get the actual distance between the sensor and the object. Thus, we can describe the dynamics for such a sensor by this formula:

The Speed of the Wave

Let’s dive deeper into understanding the speed of a wave. Different waves have different speeds. For example, sound waves and light waves will travel with different speeds.

The speed of a wave is affected by the physical properties of the medium it travels in. For example, sound waves travel at ~343 meters per second in air versus ~1,480 meters per second in water. Light travels at ~300,000,000 meters per second versus ~225,000,000 meters per second in water.). Researchers and scientists will typically collect and maintain records of the speed of different types of waves in different mediums (an example of this can be found here).

Furthermore, while in a constant medium (i.e., the wave doesn’t change mediums), the speed of the wave is constant. This is a very useful characteristic because it means we only need to deal with one value for the speed, v, in our above formula (as we usually design for our sensor to be contained within one medium).

Frequency & Wavelength

Beyond speed, wavelength and frequency are important characteristics of a wave. The speed, wavelength, and frequency are all connected and defined by this formula:

Waves oscillate, meaning that they move in repeatable, predictable patterns. The wavelength of a wave is the amount of distance before the wave repeats itself. The frequency of a wave is how often a wave repeats itself within some fixed period of time. Typically we use Hertz, which measures the number of cycles / repetitions per second.

The longer the wavelength, the more the wave has to travel before it repeats a cycle, meaning it covers less cycles within a given time frame, thus having lower frequency. Conversely, the shorter the wavelength, the less the wave has to travel before it repeats a cycle, meaning it covers more cycles within a given time frame, thus having higher frequency. We can also draw similar conclusions relating the frequency to wavelength. The key takeaway is that longer wavelength implies lower frequency (and vice versa) and shorter wavelength implies higher frequency (and vice versa). The relationship between wavelength and frequency is inversely related.

The inverse relationship can also be seen from the formula relating wave speed, wavelength, and frequency:

Since the speed of a wave is constant, an increase in either wavelength or frequency has to cause a decrease in the other to maintain the above equation (assuming the medium that the wave is traveling in doesn’t change). Moreover, knowing either wavelength or frequency usually informs us about the other characteristic, since we’ll typically also know the speed of the wave (based on the type of wave and the medium its traveling in). Therefore, we can describe a wave with either wavelength or frequency, as the other characteristic can be determined by the above formula. This can carry over to the world of sensors as sensors may sometimes be described by either wavelength or frequency, such as high frequency radar or long-wavelength LiDAR.

The Role of Frequency & Wavelength for Sensors

The frequency / wavelength plays an important role in a sensor’s capabilities. Generally speaking, a sensor that uses higher frequency waves will provide better resolution of the environment. Intuitively, since the wave is oscillating more, it has a greater chance of hitting objects in the environment and detecting them, thus providing much better resolution. Another consequence of a higher frequency is being able to detect smaller objects, as there’s more opportunity for the wave to collide into it. This can be very advantageous for situation were detailed information about environment is needed, such as with self-driving cars.

However a downside of higher frequency waves is that they lack range. Lower frequency waves have a longer wavelength, enabling them to travel farther and cover more distance. Going back to the autonomous vehicle example, lower frequency waves can provide information further away from the car and enable more time for the autonomous vehicle to process and react.

Another limitation of higher frequency waves is that they generally need more energy. This can be a constraint in situation where access to power or energy is limited (such as in sea or in space) or when energy capacity is low (such as with drones which have small batteries), making low frequency waves more preferable.

Thus, there’s no one frequency that fits all situations. The frequency used will depend on the context / objective of the task and the trade-offs between low and high frequencies. For example, different frequencies of sounds are used for SONAR, with low frequencies being used for deep water exploration while high frequencies being used for more shallow, but detailed search. Another example is with many current autonomous vehicle solutions, which will leverage both RADAR (lower frequency wave) and LiDAR (higher frequency wave) sensors in tandem — doing so allows for higher resolution for near objects with LiDAR and awareness of far objects with RADAR.

Other Wave Properties & Characteristics

There are other attributes to consider in fully capturing a wave’s behavior. We won’t go further into them, but it is worth highlighting, as these are also considerations when designing and building with sensors (note: this list isn’t exhaustive):

• Wave absorption: energy from the wave being absorbed by the medium, affecting the sensor’s performance
• Human sensory range: for sound and light waves, using frequencies in the ranges that humans can hear or see, respectively, for sensors is deemed undesirable and intrusive
• Wave type: waves can refer to both physical and electromagnetic waves, which exhibit different properties

Conclusion

Waves play a crucial role in LiDAR, RADAR, Infrared (IR), SONAR, and Ultrasonic sensors, enabling them to detect objects and determine distances. The physics behind how we translate the data from these sensors to distances is informed by kinematics and properties of the wave, such as constant speed in a fixed medium. Furthermore, we explored how changing other characteristics of the wave, such as wavelength or frequency, impacts the performance and capability of the sensor.