# How can light be timed?

There are measuring instruments that measure distance by measuring the time a lightbeam takes to come back. An example is a LICA scanner, that uses this tecnology to make 3D models of objects using laser beams.

Question is: How is it possible to measure how long light takes to get from point A to point B and back if light travels so fast? Isn't electronics too slow to measure such tiny time differences? What about the time electronic components need to change its state?

• Google the term "interferometry" Nov 14, 2016 at 10:26
• @PlasmaHH: 3D scanners are not generally interferometric. Nov 14, 2016 at 10:37
• @AndreasH.: the majority of precision laser ranging is done that (or similar) way though. Going through the product palette of Leica provides a nice overview Nov 14, 2016 at 10:39
• @PlasmaHH: True, but LEICA was just an example. The question is about measurement of time differences in context of optical measurements. Interferometry is just one specialized method (only) for high precision. Rangefinding works well without interferometry Nov 14, 2016 at 10:45
• check out the principles of LIDAR Nov 14, 2016 at 10:56

In general such systems do not use time of flight measurements, at least not directly. Light is just too fast for current systems, if you want better repeatability than a few meters for a cost effective system. There are a few things you can do: geometric measurement, interferometry, modulation.

The simplest thing you can do is to use triangulation. This is how the cheap distance measurement equipment used in construction works. You shine a beam, it reflects, and you pick it up from a different sensor near the receiver. Measure the angle, and you can get a relatively coarse repeatability in the 10's of mm range.

If you need better repeatability, you can use interferometry. You simply measure the difference in phase shift. This can get you to um repeatability. The problem here is that the wavelength changes with atmospheric conditions e.g. 0.1 K rise in temperature generates a 1ppm change. You need to compensate for temperature, pressure, humidity etc. Furthermore, this will give you incremental readings. You need to combine this with the former method.

A relatively new method is to send a modulated waveform. When you receive it back you can use the fact that you know its shape. This then reduces to an optimization problem. A convex optimization problem to be precise. The main disadvantage here is that there is a relationship between bandwidth, and time: the uncertainty principle. But you can get very accurate results.

• You can get timers with a resolution of about 20ps that results in a resolution of 3mm. They aren't even that expensive. Sure to get stable results you have to consider some things, but light is not too fast. Nov 14, 2016 at 12:06
• @Arsenal the problem is not the timer. It is the sampling. The timers are level triggered, which is fine when your SNR is good. However, as you start moving away you may actually need an ADC in order to do some DSP. I would admit it depends on the technology, and it is quite difficult to have a general discussion on the subject. For some applications a timer works fine. But keep in mind that it is far cheaper to get a line camera and use triangulation, than it is to generate accurate clocks for the timer. If you are measuring 20ps you are in atomic clock territory. Nov 14, 2016 at 12:17
• Well your light isn't going to take a day to travel the distance you want to measure, and if it does, you don't care about 3mm I guess. Short term stability is what is important and that you can get a lot cheaper. acam.de/products/time-to-digital-converters Sure building the opto-electronical front-end won't be easy, but doable. Nov 14, 2016 at 12:30

Light covers 1 metre in 3.33 ns. That 3.33 ns (if it were a waveform) would have a frequency of 300 MHz so, if you had an oscillator running at 10 GHz you'd have a distance resolution of 3 cm. If you had a higher frequency you'd get a better distance resolution.

I'm not saying that these sorts of circuits are trivial but they do exist.