Radar and lidar are remote sensing technologies that measure distance, speed, direction, and object shape using reflected waves. Radar uses radio or microwave signals, while lidar uses laser light. This cheat sheet helps engineering students connect wave physics with real sensor design.
It focuses on the formulas and rules used to interpret echoes, estimate range, and compare system performance.
The most important idea is time of flight: a signal travels to a target and returns, so distance equals wave speed times round-trip time divided by 2. Radar often uses electromagnetic wave speed c, while lidar also uses c in air for most high school engineering calculations. Doppler shift connects frequency change to radial velocity, and resolution depends on pulse width, bandwidth, beam angle, and wavelength.
Power loss, reflectivity, and noise determine whether the returned signal is strong enough to detect.
Key Facts
- Two-way range is R = vΔt/2, where v is wave speed and Δt is the measured round-trip time.
- For radar and lidar in air, use c ≈ 3.00 x 10^8 m/s unless a different propagation speed is given.
- Radar Doppler shift for a target moving directly toward or away from the sensor is fd = 2vr/λ, where vr is radial velocity and λ is wavelength.
- A positive Doppler shift usually means the target is moving toward the sensor if the system defines approaching motion as positive.
- Range resolution for a pulse system is ΔR = cτ/2, where τ is pulse duration.
- For a bandwidth-limited radar, range resolution is approximately ΔR = c/(2B), where B is signal bandwidth.
- Angular resolution improves when beamwidth θ is smaller, and a useful diffraction estimate is θ ≈ 1.22λ/D for a circular aperture.
- Signal-to-noise ratio is SNR = signal power/noise power, and detection becomes more reliable as SNR increases.
Vocabulary
- Radar
- Radar is a sensing system that uses reflected radio or microwave waves to find the range, speed, or direction of a target.
- Lidar
- Lidar is a sensing system that uses reflected laser light pulses to measure distance, shape, or surface properties.
- Time of flight
- Time of flight is the travel time between sending a signal and receiving its reflection from a target.
- Doppler shift
- Doppler shift is the change in received frequency caused by relative motion between the sensor and the target.
- Range resolution
- Range resolution is the smallest separation in distance that allows two targets along the same line of sight to be distinguished.
- Signal-to-noise ratio
- Signal-to-noise ratio compares useful received signal power with unwanted noise power.
Common Mistakes to Avoid
- Forgetting to divide by 2 in range calculations is wrong because the measured time is usually a round trip from sensor to target and back.
- Using the speed of sound for radar or lidar is wrong because both systems use electromagnetic waves, not acoustic waves.
- Using total target speed instead of radial velocity in Doppler calculations is wrong because Doppler shift depends only on motion toward or away from the sensor.
- Confusing range resolution with maximum range is wrong because resolution describes separation between targets, while maximum range describes how far the system can detect.
- Assuming a stronger transmitted signal always guarantees detection is wrong because noise, reflection strength, spreading loss, and atmospheric attenuation also affect the returned signal.
Practice Questions
- 1 A lidar pulse returns after 80 ns. Using c = 3.00 x 10^8 m/s, what is the target range?
- 2 A radar has wavelength 0.030 m and measures a Doppler shift of 2,000 Hz for a target moving directly toward it. What is the radial speed?
- 3 A pulsed radar has pulse duration 20 ns. What is its approximate range resolution using ΔR = cτ/2?
- 4 Explain why a lidar may give better shape detail than radar at short range, but radar may perform better through fog, dust, or rain.
Understanding Radar & Lidar Reference
A sensor does not receive a clean copy of the pulse it sends. A real echo is weakened, delayed, spread out, and mixed with unwanted signals. The outgoing beam expands as it travels.
Only a small part reaches the target, and only a small part of the scattered energy returns toward the receiver. This is why distant targets are much harder to detect than nearby ones. In a simple radar model, received power can fall roughly with one over distance to the fourth power.
The path out causes loss, then the return path causes more loss. Target material matters too. Metal surfaces often give strong radar echoes.
Dark, rough, or angled surfaces may send less energy back. Lidar reflectance depends strongly on colour, surface texture, and the angle of the laser beam.
Pulse timing has practical limits. After transmitting a strong pulse, a receiver may briefly be unable to hear weak echoes. This creates a minimum measurable range.
The sensor cannot reliably detect a target that is too close during this recovery time. There is often a maximum unambiguous range as well. If the next pulse is sent before an earlier echo returns, the system can assign that echo to the wrong pulse.
Engineers choose the pulse repetition rate carefully. A faster rate can update measurements more often, but it reduces the distance that can be measured without confusion. This tradeoff appears in weather radar, aircraft tracking, and automotive sensors.
Doppler measurements describe only motion along the line from sensor to target. A car crossing directly in front of a roadside radar can move quickly while producing little Doppler shift at the instant it is side on. Its radial speed is then close to zero.
This matters when interpreting speed cameras, airport radar, and robot sensors. Doppler systems can face aliasing too.
If the true frequency shift is larger than the system can sample correctly, a fast target may appear slower or even moving in the opposite direction. Repeated measurements, known sensor motion, and data from several viewing angles help reduce these errors.
Resolution is not the same as detection. A sensor may detect a large object at a long distance but still be unable to separate two nearby objects. Short pulses or wider bandwidth improve separation in range, though they can require more complex electronics.
A larger antenna or optical aperture narrows the beam, which improves direction finding. Narrow beams demand careful alignment and stable pointing. Atmospheric conditions add further limits.
Rain can weaken some radar bands. Fog, dust, snow, and heavy rain can strongly reduce lidar returns because light scatters from the particles before reaching the intended target. When studying measurements, check the units, confirm whether a value is one way or round trip, and consider noise, target angle, weather, and sensor alignment before trusting a result.