How can a lidar achieve cm-level resolution?

Question

In order to achieve cm-level resolution, it seems like a lidar would need to have extremely high sampling rates. Here's my thinking:

Light travels at roughly 3·10⁸ m/s, or 3·10¹⁰ cm/s. We need to sample at double this rate (Nyquist frequency), so the sampling rate has to be 6·10¹⁰ Hz, or 60 GHz, which is super fast. I'm sure these ADCs would be pretty hard to find...

Am I missing something? Are there other techniques lidars use to avoid the need to sample super quickly?

Answer 1

Your question affects all time of flight systems, not just LIDAR. What you are missing is that we do not measure the time in the naive way with a counter.

What we do is we sent a modulated signal. It is common to use a linear FM chirp of the form \$f = f_0 + f_1 t\$ in radar, but we obviously cannot do that in lidar. However, we can transmit an AM modulated signal.

After we receive the echo we apply a matched filter to our input. A matched filter gives us the best signal-to-noise ratio in an additive white Gaussian noise (AWGN) channel.

The additional benefit of the filter is that during the detection process we convolve the time reverse complex conjugate version of the transmitted pulse. In effect we slide the pulse in the time domain until we obtain the maximum power, which will give us the time of flight information we are after.

source

In the above animation the red pulse is our template and the blue pulse is the received signal. Remember that we can compute the value of the received echo at any point in time. We are not limited by the sampling rate as shown by the Nyquist-Shannon sampling theorem, i.e. we can use interpolation.

Answer 2

sampling with an ADC seems indeed impossible. However, there is no need for it.

The trick for such fast event is to deal with them at a much lower level, that doesn't involve a microprocessor or an ADC, but outputs a signal that can then be measured by an ADC or a micro-controler.

I don't know how it is really done, but there is one way one might achive it :

• there is a signal to trigger the measurement (that one can come from the micro-controler)
• this signal also enables the charging of a capacitor (that is initially empty)
• a phototransistor (or any other sensor detecting the return of the ligght beam) stops the charging of the capacitor
• it is then enough to read the voltage of the capacitor with an ADC, this time, there is plenty of time to do so (if you lidar makes measurement at 10 kHz, you get nearly 100µs for the conversion)
• you empty the capacitor

Basically, micro-controlers, microprocessors (and ADCs) are quit slow, but can do a lot of different things, and it's cheap to develop a new function. Then you have FPGA (field programable gate arrays, logic gates you can "connect" in software and discreat analog circuits, that are faster, but more complicated to design. Finaly, you get specialized integrated circuits (digital and/or analog) that are extremly fast, but it takes tens of thousands of dollars (if not more) for R&D and launching production.

So if you need something really fast, you will have to go away from the slow universal circuits (micto-controles, ADC, ...) and go into highly specialized circuits, that are much faster

Answer 3

In order to achieve cm-level resolution, it seems like a lidar would need to have extremely high sampling rates.

For direct time domain resolution, this is true. However most lidar systems do not have centimeter (or even meter) resolution. Instead they have cm or meter accuracy.

These are fundamentally different things. Resolution is the ability to resolve two reflectors with a given separation. Accuracy is the ability to measure the distance to a single reflector. Most lidar systems cannot resolve two perfectly coaxial detectors at all. Instead they just measure the distance to the first reflector and ignore the second. Such systems have no axial resolution at all because they cannot distinguish between one or two reflectors. If you're willing to give up on high resolution you can simply count until you get a reflection. The number will be proportional to distance, potentially with very high accuracy.

If you actually want 1 cm resolution (for example to measure how thick a plate of glass is), you have a number of options. The highest resolution can be obtained with interferometry, in which case you detection bandwidth can be hundreds of THz, giving resolutions in microns or less (and accuracies in nano or picometers). If lower resolution is acceptable, you can use time correlated single photon counting (TCSPC), which can time resolve down to tens or hundreds of picoseconds and thus obtain millimeter or better resolution.

Answer 4

You are ignoring the bandwidth required to attain a certain range resolution.

One approach is looking at the traditional definition of range resolution which is given as $$ \Delta R = {c \; \tau \over 2}$$ Where:
\$ \tau\$ = pulse width
\$ c\$ = speed of the signal (for light & RF, about 3e8 m/s)

For a 0.1m range resolution, you need a pulse width of about 667 ps which requires a bandwidth of approximately \$ 1/ \tau\$, in your case about 1.5 GHz. Thus, you need a sample rate of at least double the bandwidth, or > 3 GHz per your example. This gives a nice A-scan representation where point targets are moderately crisp.

You can fudge range resolution, as is done in some systems, and give range resolution as $$ \Delta R = {c \over {2 \; f_s}}$$ Where \$ f_s\$ is the sample rate of the ADC.
Thus, your example's sample rate is 1.5 GHz. In sonar systems, the A-scan looks noticeably worse using the slower sample rate (closely spaced targets in range start looking like one blob), however, it is sufficient to give accurate range information.

You still need a pretty fast A/D converter.