Lidar measures distance by bouncing light off objects-but there’s more to how light travels in the first place.
To be honest: I didn’t know the iPhone could do lidar scans. (the iPhone 12pro, 13pro, and iPad Pro all do it.) When I found out my phone could do it, I became obsessed with scanning things.
Lidar is useful as long as you need to know the shape of an object or surface. It is used in self-driving cars to identify road edges and detect people and cars. You can put lidar on an airplane and look down at the Earth’s surface to get mapping data that is useful for both agriculture and archaeology, such as looking for lost buildings. It is also well suited for surveying an area to obtain a three-dimensional map of a beautiful building.
This is a structure I recently scanned in the local downtown area.
LIDAR is an acronym for“Light Detection And Ranging.”. It’s basically like a tape measure — except it uses the speed of light to measure distance, not physical objects.
To help you visualize how it works, let’s consider a different measurement system — I’ll call it spherical radar. Here’s the thing. I found a tennis ball that I can throw continuously at a speed of 20 meters per second. Next, I threw the ball against the wall. It bounced off me and I caught it. I measure the time it takes the ball to go from my hand to the wall to the wall — we call it a second.
Since I know the velocity (v) and the time interval (ΔT) of the ball, I can calculate the total distance (s) as.
But since this uses the ball’s total time of flight, it gives the ball’s total distance from the wall to the wall. If you divide this distance by 2, you get the distance from my hand to the wall. In this case, it would be 10 meters.
I like the BALLDAR method because you can easily imagine throwing the ball and measuring the time. But lidar is essentially the same idea: instead of a ball moving back and forth, Lidar uses light. This is the“Good” part of LIDAR.
In theory, you could create a DIY version of lidar with a flashlight or even a laser pointer. Just Point the laser at an object and, once you turn it on, start the stopwatch. The light travels outward, hits the wall, and then bounces back. Once you see the laser spot on the wall, stop the stopwatch. Then you just need to calculate the distance using the speed of light.
There is, of course, a practical problem. Light travels very fast. Its speed is 3 x 108 meters per second. That’s over 670 million miles per hour. If you were to measure a distance of 10 meters (as in the BallDAR example) , the flight time would be about 0.00000067 seconds, or 67 nanoseconds.
If you want lidar to work, you’ll need a very fast stopwatch. Galileo actually tried to use his experiment to determine the speed of light, like this. Sure, he doesn’t have a laser, or even a fancy stopwatch, but that doesn’t stop him from trying. He couldn’t actually get a measurement.
Most versions of lidar use a single laser with a detector. When a short pulse is emitted, a computer measures the time it takes for the signal to return to the device. Then, with a simple calculation, we get the distance that the light has traveled.
But that’s just measuring a single distance. It is not enough to produce a three-dimensional lidar surface image that shows the shape of the object. To get this, you need more data.
If you know where the laser is pointing, you can get a distance and an orientation, which gives you a point on the surface. Next, you simply repeat the process when the laser is pointed in a slightly different direction, usually with a rotating mirror. Keep doing this and you’ll get a whole bunch of points. After you have collected thonds of dots, the dots merge into an image that looks like the surface of the object you are scanning.
But mirrors that use lasers and spins are not only expensive, they are also too bulky to fit on your phone. So how does lidar work on the iPhone? I want to say, “That’s amazing”– because that’s what it looks like to me. What I do know is that instead of measuring distance with a beam of light, the iPhone uses a grid of dots in the near-infrared wavelength emitted by the phone (like the light from your infrared TV remote control) . These multiple beams are due to an array of vertical-cavity surface-emitting lasers, or VCSELs. It’s basically a bunch of lasers on a chip, which is what makes it possible to put lidar in a smartphone.
In addition, the iPhone uses its accelerometer and gyroscope to determine the position and direction of the lidar sensor. This means you can get fairly accurate scans even when you’re moving your phone.
Lidar and refractive index
We like to say that the speed of light is constant at 3 x 108 meters per second. But that is not entirely true. That’s the speed of light in a vacuum. If you let light pass through some material, such as glass or water, it will move more slowly.
We can use the index of refraction (N) to describe the speed of light in a material. This is just the ratio of the speed of light (c) in a vacuum to the speed of light (V) in a material.
If you look at a material like glass, it has a refractive index of 1.52. I mean, it’s a big deal. This means that when light travels through glass, it travels only 0.667 times faster than in a vacuum, a figure of 1.97 x 108m/s.
What about some other materials? The refractive index (N) of the air in our atmosphere is 1.000273, which means that the speed of light is almost the same as in a vacuum. The water index is 1.33. The diamond has a refractive index of 2.417, which means that light travels through the diamond less than half as fast as it does in a vacuum.
But why does light travel slower in materials than it does in a vacuum? I’m going to tell you two very common but very wrong explanations.
The first is that when light enters something like glass, it is absorbed by the atoms in the glass and then reemitted in a short time, a delay that slows the light down. But it is easy to see that this is wrong. Although atoms do absorb light and then re-emit it, this process does not keep the light in its original direction. If this is true, then the light should scatter, and that doesn’t happen.
Another false interpretation is that light passes through glass, hits atoms and bounces off before finally passing through material. Such a bounce would make light go a longer way than it would in a vacuum, where there are no atoms to bounce off of. This seems to make sense-the wrong idea often does have some logical meaning. But in science, things are wrong because they don’t agree with the experimental data.
In this case, the beam of light entering the glass will also spread out as it passes through the material due to more“Collisions.”. It’s like a ball moving in an area with a bunch of nails. Each random collision moves the ball in a slightly different direction. Doing this with an infinite number of beams would mean that the light could eventually move in any number of directions. But in order to form an image, the beam must move through the material in a predictable way, rather than scattering randomly. If the light does scatter, you can only see the light in the sky, not the image.
Okay, so why does light travel slower through glass? The first thing to understand is that light is an electromagnetic wave. It’s like a wave in the ocean, but much colder. An electromagnetic wave has an oscillating electric field and an oscillating magnetic field, which is related to the electric and magnetic forces on the charge. As the Maxwell’s equations describes, an oscillating electric field generates a magnetic field, and an oscillating magnetic field generates an electric field. This interaction between fields is what allows light to travel through empty space. This doesn’t happen on other waves. Imagine a wave without water.
When an oscillating electric field from a light wave interacts with atoms in a material like glass, it causes interference in the atoms. This disturbance at the electronic level means that these atoms also produce electromagnetic waves. However, the electromagnetic waves coming from the atoms will be out of phase with the light entering the glass. When two waves are out of phase, they peak at slightly different times. The combination of the original electromagnetic wave and the electromagnetic wave from the stimulated atom will produce a new electromagnetic wave-the slower electromagnetic wave.
The speed of light using lidar
Now here’s an interesting experiment. What if you used the iPhone’s lidar to look at the combination of glass and water? If lidar determines distance by the time light travels, shouldn’t it give the wrong distance when passing through another material?
Let’s give it a try. I found this big container. The glass wall is about one centimeter thick. In the middle, I added some water to fill the 7.4 cm wide interior. When I lean it against the wall, it looks like this.
But when I scanned it with the lidar, what happened? Here are two different views of the same scene.
Of course, the wall is actually flat, but the lidar image shows a distinct indentation. This is because it takes longer for light to pass through glass and water, so it takes longer for light to travel. Sure, the iPhone may be smart, but it’s not that smart. It doesn’t know that light travels through different materials at different speeds. It just measures distance by the speed of light in the air, which, as we can see, is about the same as the speed of light in a vacuum.
Let’s make a quick estimate. How much should the wall be indented during the scan?
We’ll start with the time when light passes through glass/water and then comes back. Because the entire container-including both sides of the glass and the water inside-is 9.4 centimeters wide, the lidar assumes that it takes 62.7 nanoseconds for light to travel this distance in a vacuum. But the light must pass through a total of 4cm of glass (remember, each side of the container is 1cm, and the light has to pass through the whole thing twice because it bounces back) , which has a refractive index of 1.52. It passes through a total of 14.8 cm of water (again, because of reflection) , with a refractive index of 1.33. Therefore, this takes 85.9 nanoseconds of real time.
This means there is an additional travel time of 23.2 nanoseconds. During this time, light moves about 3 centimeters in a vacuum. This seems legal to me. Although I am not a real 3D modeling expert, I can imagine that the indentation on the wall is about 3 cm.
To tell the truth, I was a little surprised at the success of the experiment! But it does indicate two important things: one is the degree of vacuum in a vacuum. But it does show two important things. Lidar determines distance by measuring the time light travels, and light slows down as it passes through things like glass or water.
