# Why do sensors that emit higher frequency signals give more accurate data?

I am doing a technical presentation about RADAR and LiDAR. I understand that LiDAR is several times more accurate and capable of producing really detailed 3-D maps of their surroundings, while RADARs tend to lag behind in accuracy.

Several sources indicate that the shorter wavelength signals from LiDAR contribute to its higher accuracy, but they don't really explain why.

This webpage explains that higher frequency signals yield more accurate data in RADARs, but does not really explain why either: http://www.radartutorial.eu/07.waves/Waves%20and%20Frequency%20Ranges.en.html

There are some posts that mention the Heisenberg Uncertainty Principle, but I don't think an explanation at the atomic level is really relevant nor required to explain this phenomenon.

Can anybody give an equation or state a scientific concept as to why sensors/apparatuses that use higher frequency signals yield more accurate data?

• REVISION: As somebody pointed out in comments, I actually mean to ask why image RESOLUTION is better, not accuracy. Oct 30 '18 at 1:34
• I think this explains it much better, the role of wavelength and all, in the comparison, robotsforroboticists.com/lidar-vs-radar Oct 30 '18 at 5:30

High frequency sensing gives a better resolution. The resolution is naturally limited by the wavelength. That being said, the propagation of your signal is also very important. A high frequency signal may have a smaller range or may have a smaller penetration depth, for example through clouds or vegetation. You have to pick the frequency that gives you optimal contrast for the signal that you are after.

• "High frequency sensing gives a better resolution. The resolution is naturally limited by the wavelength." The OP is asking for an explanation to see why this is the case. Oct 28 '18 at 23:25
• Resolution is not accuracy. Accuracy is the ability to measure in noise, resolution is the ability to discriminate one coherent signal from another in noise. (Coherent signals in the sense that there are multiple overlapping reflections from multiple sources in noise.) Oct 28 '18 at 23:37

This has nothing to do with Heisenberg or his uncertainty principle. To measure range both radar and lidar measure time of arrival for both assume that propagation velocity is known and is the same in all directions and all weather, etc. Timing measurement is, therefore, the measurement of rise time of a pulse in noise; measurement accuracy is defined as the statistical dispersion = standard deviation = jitter and is given by: $$\sigma_t \approx k_0\frac{t_r}{\sqrt{SNR}}$$ where $$t_r$$ is the rise-time, $$\frac{1}{2} < k_0 <2$$ is a number that depends on the details of the pulse and signal processing, and SNR is the effective signal to noise ratio. You can think of $$\sqrt{SNR}$$ in the denominator as representing the result of averaging across the pulse by the noise filter.

The rise time is $$t_r \approx \frac{k_1}{B}$$ where $$B$$ is the band width and $$k_1$$ is a number that depends on the details of the pulse. In other words $$\sigma_t \approx k_0k_1\frac{1}{B\sqrt{SNR}}$$ As you can see the jitter is inversely proportional with the signal bandwidth and is independent of the carrier frequency. But note that higher the carrier frequency the wider the signal bandwidth can be! In practice a laser pulse can easily be made a nanosec or shorter while radar bands are constrained both by FCC regulations and by electronics.

There is a similar result for angle measurement accuracy $$\sigma_\phi \approx k_2\frac{1}{D\sqrt{SNR}}$$ Here $$D$$ is the effective diameter of the antenna (lens) and $$0.5 < k_2 <2$$ is a number dependent on the illumination details. This is the so-called diffraction limited case.

In the article that anna v mentioned: