Sunday, March 15, 2020

How do laser distance measures work?

I recently bought a laser tape measure; it's pretty great.  One button to turn it on, then it gives you instant distance measurements to wherever you point the laser.  There are more expensive ones that do further distances, but the one I got was $30 and goes up to 65 feet.  I compared it to a normal tape measure and it was accurate and repeatable to an eighth of an inch.  I was pretty impressed with it, and it was a great toy to add to my collection of measuring devices.

However, I began to wonder how it worked, especially since it worked so well, and was so cheap.

How laser distance measures don't work

In principle it would be simple.  Light has a very well known speed, so all you have to do is measure how long it takes for the light to go out and reflect back.  Distance = speed x time.  You could encode a binary number in the laser, just a counter incrementing and resetting when it runs out of numbers.  Measure what number is being reflected back and how long ago you sent that number out and you know how long it took to come back.

However, the devil is in the details, and getting that time precise enough to measure an 1/8th of an inch is going to be hard.

An 1/8th of an inch is 3.175 mm.  The speed of light is 299,792,458 m/s.  Or 299,792,458,000 mm/s.  3.175 mm / 299,792,458,000 mm/s = 1.059066002254133e-11 seconds.  Which is about 10.59 picoseconds.  Take the inverse of that and it's 94.42 Gigahertz.  I'm going to go out on a limb and assume that the $30 laser tape measure I have in my pocket doesn't have a 100 GHz clock inside of it.

How do they actually work?

Instead of transmitting a counter, just send an alternating pulse.  It doesn't have to be very fast, a MHz would be enough.  Then your reflected pulse is the same wave, but delayed slightly.  You only care about measuring the difference in time of the leading and falling edges of the two waves, or delta.  This means you can just compare the two waves using an XOR gate, which is just a fancy way of saying "tell me whenever these waves are different".

Here's an example

Where the top red line is the original signal, and the second blue line is the reflected version.  Then the third green line is the XORed delta of the two.

When you measure something slightly further away the reflected wave gets more delayed and the delta version gets a longer pulse.

Are logic gates fast enough? 

Logic gates like these are cheaper and faster than the circuitry you'd need for a timer.  However, they still aren't quite fast enough for the precision we see in these tools.  Luckily though, a delay doesn't really impact the measurement.  As long as it's a consistent delay on both the rising and falling edges of the two waves.

All you end up with is a slightly offset delta signal.

Who will measure the measurer?

It might seem like we're back to square one here, with the need to precisely measure the time of that pulse, but we actually just need take the average of that signal.  There are a variety of ways we can do this, but as a proof of concept, imagine the delta signal is charging a capacitor, which is simultaneously being drained by a constant resistor.  You'd end up with a level of charge in the capacitor which would translate into what percentage of time the delta single is high.

Now, all you have to do is measure the charge in the capacitor and turn that into a measurement you display.  Let's review what we need:
  • Laser transmitter and optical sensor.
  • MHz clock to turn laser on and off.
  • XOR circuit to compare the two transmitted and received signals.
  • A capacitor and resistor circuit to find average of the digital signal.
  • A way to measure the charge in the capacitor.
  • Something to take that measurement and convert it into the distance.
  • A display.
None of this is very expensive.  I'm pretty amazed they can combine them for less than $30, but at that point, you'd be losing money not to buy one.

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