Hypercentric optics: A camera lens that can see behind objects

Today in Applied Sciences I will show you an unusual

camera

lens

that can actually see around

objects

. I know it's a provocative title, but you also know how much I hate clickbait. This is just real physics, so let me show you the setup. The

camera

lens

is a huge thing here with the Fernell lens on the front and we're going to look at these two dominoes and if we go around to the other side, this lens is so big that the way it works is the camera. inside this way, so I'm going to mount the camera here and then we'll show how to look around that Domino, okay, here we are at the lens in its normal setting and I'm just going to adjust it. the

optics

and see what happens absolutely strange, the Domino that is behind actually looks bigger than the Domino that is in front, we just push this back to its normal position and you can see that it is clearly behind the front Domino, so no I'm moving the lens. or anything, I'm just adjusting the

optics

, it's a really strange effect, let me show you a different setup.

In this setup I have pins arranged at different distances from the camera lens and the green one is smaller because it is further away because that is normal, right? This lens doesn't perceive the world the same way your eyes or normal camera lenses do, so now they all appear to be the same height if we step back, the green one is smaller again, so basically this lens has the ability to have different perspectives of the world. world there is no world perspective or even negative perspective, but you will be surprised how simple it is to build one of these, so let me show you how it is built, so this whole time I have been adjusting the camera perspective as much as I can.

What I've been doing is pushing this piece back and forth and it slides forward into the tube here it's just a particle board with the camera there normal camera lens on the camera is a wide angle and at the end of this tube there is a fernell lens and that's it, so basically just moving a camera back and forth closer to the fernell lens gives you this incredible amount of control over perspective, let's see why this works, it doesn't have to be a lens fernell, of course, it's just having a really large diameter is useful and for now it's easier to get lenses with large diameters, so conceptually let's see how this could work, like imagine you're an insect sitting on the lens looking this way to the Dom from this point of view.

You see the whole back Domino just fine, but if you were an insect sitting in the middle of the lens looking this way you wouldn't be able to see it because the Domino in front blocks it, so at least conceptually we can imagine all the light rays hitting it. The front of this lens has the ability to build all kinds of different images. We could have a point of view from here if we knew how to select the light rays there or we could have a point of view from very far away. near the center and how we select, how we make an image from all these different options, it turns out that it's the aperture that does it, so we have this infinite number of possible images that we could create with a lens and put an aperture on the system is actually the way we select all the possibilities that you know in an image and you know, as you know from photography, if you have a smaller aperture, the image is sharper because you have rejected some of those other possibilities.

The blur in Part B comes from the fact that you have all these rays of light coming in and if you just mix them all together you get blur, but if we select with the right size aperture we get all kinds of control over what happens in the image. be and if you say well, you know it could hold a lens like this, this does not have an aperture, in this case the aperture is the lens itself, the diameter of the hole located in the plane of the lens and, as we will see, See the location of the aperture relative to the plane of this lens and its focal plane is really critical to getting this perspective control, so let me draw some ray diagrams so you can see this so that it turns out your eyeballs and almost all cameras normal.

Lenses have this routine where the aperture is placed very close to the lens, critically, it's within a focal length of the lens, so if this is the glass lens here, we place the aperture here and it forms this system known as endocentric optics and that's the trick. is that this red line is a distant object of the same height as the black line and the more distant rays will focus on a smaller point or shorter object in the image plane here, so this is very normal , but things further away are smaller. It's the most obvious thing in the world, but there's no law of physics that says it has to be that way, so if we change things up a bit and put the aperture at the focal point of the lens, the system behaves very differently in this case.

In this case, the aperture limits what can pass through this entire optical system, so although each of these

objects

still emits rays in all different directions, each of these is a point emitter, the aperture and The focal length of the lens are set in such a way. that only a select beam of these rays passes through and if you place the aperture right at the focal point of the lens, it is very specific to select these rays so that they only come from parallel rays entering the lens, so if you have two objects that are the same height, different lens distances, both project light in all directions, our system selects up to the point where it only looks at the rays that come in parallel, so they actually have the same height in the plane from image.

I can see another side effect of this is that you can't see from the side outside of this, the field of view is actually zero degrees because the lens only accepts light that comes parallel to the optical axis here, so it's interesting its field of view in this case is as big as the lenses, that's their maximum, which is why the front elements of these telecentric lenses are so big, some of them are ridiculously big. If you want an image of a large object with a telecentric lens, it must be quite large. that's why we have this Fornell lens here and then if we go one step further and move the aperture behind the focal point of the lens, then the system continues and then the distant objects actually pass through and have a larger image. the focal plane, so in a way this is a way of seeing around objects because if you follow the red strokes, it actually goes over this shorter black object in front so you can visualize around things and if you had a really large diameter lens you can see completely around objects, so where is the aperture in my setup?

We've got the camera here sliding around like this here's the giant Fornell lens in front, where's the aperture? It's actually in the lens here, we can reuse it, so even though this lens has its own aperture, it still works downwards, select all the rays that come through this giant Fornell lens in the front, so it still works to create this telecentric,

hypercentric

or end-centric system by simply positioning the camera in relation to the front of the lens here, then you might be wondering why we have a lens here, for example, why don't we just remove the lens from the camera and we use it directly?

That's how I started this whole experiment and I had a lot of problems, the problem is that the aperture has to be very very close to the focal plane, so yes this hole gets stuck and it becomes very difficult to build a system that produces good images, but I'll show you what. My first attempt was and I had problems when I started this project. I thought I had a very good source for these. It was $5 on eBay and it's a really huge, heavy, very high quality lens straight out of a projection TV. It has a couple of fatal flaws, although they ended up ruining this, but even aside from the fatal flaws, I'm going to show you how I thought I was going to do this.

I 3D printed this converter bracket and even got an aperture from an old broken lens, so I thought I placed the aperture right on the focal plane of the lens and did this so it would come together like this, it actually continues there, it's very tight and then I put on a plastic cap that goes on the camera so when this is all put together it looks pretty good I thought it looked good almost works actually it's not that good it's not as good at demonstrating this as Fernell's setup and why is that this aperture has to be very close to the film plane that's there so you can see, I even turned it down because I was really like, you know, precisely placing it as close as possible there and then I found out that the images just aren't so good when the aperture is so close to the image plane that you end up with all kinds of problems because the light rays shoot very obliquely towards the film plane sensor and that causes the problems.

Another big problem is that this lens was probably made for a red lens. Green-blue projection TV, in other words this one only had one shooting color, I know this because it says the critical x-ray part doesn't work without this lens in place, so it definitely came from a CRT projection TV and those are usually red, green, blue. So this lens is not chromatically corrected, in other words it has huge chromatic aberration in EM. It just doesn't look that good even if the Fernnell lens can outperform it, which is pretty interesting if you want to replicate it, here's the setup that worked.

For me you want a 200 millimeter Fornell lens if it is the largest diameter you can get and there is a middle ground if you get a Fernnell lens that has too short a focal length that is a problem because then the aperture has to be very close and then your camera lens can't really absorb all the light to make an image and if you get it without a lens with too long a focal length, you will come back here and the system will have too much magnification, so if you put an object here It is too expanded to create a pleasant experience.

It's best to have the least amount of magnification, so 200 millimeters here and then the camera lens should be as wide angle as possible for these Micro Four Thirds cameras that I'm using. a 12 millimeter wide angle lens and this is good because when it is placed here at the telecentric point, the acceptance angle of the camera lens aligns quite well with the light coming in from the outside, so it works well, you may have noticed something. more about these lenses, that's strange, is it possible to make a telecentric lens that focuses at infinity? No, actually, it's not possible, in fact it gets harder and harder as you get closer to infinity, hence all the examples I've shown.

Things are usually happening pretty close in front of the lens and if you search the web you will always find that telecentric lenses have specific ranges that they work in, so they typically work at less than a meter working distance for these. lenses, even the largest ones. and the reason for this is that optically it becomes increasingly difficult to make a telecentric system focus at a far distance. It would be nice if we could do that because then you could take this lens and point it at the moon and inspect. You know, the little rocks here because they have a constant magnification, regardless of the distance, they have the same magnification, so it would be nice to be able to use that feature, but it turns out that optically it's not that possible, you can't get one for free. lunch, basically, some quick construction details on this.

I used my favorite shaper to cut these parts out of particle board and the reason I use this is because I wanted it to be relatively thick and cheap and I didn't really want to cut a 3/8 inch piece of acrylic on my laser cutter, so that cheap wood is the best way to do it and then the tube itself is a concrete shape, so if you visit your local Home Depot or any store where they sell these cardboard tubes in different diameters. pour concrete forms, but the funny thing is that they only sell three different sizes: 8, 10, and 12 inches in my store, but there are actually about 20 or 30 sizes on the shelf and it's funny that they actually stack them to ship more . efficiently, so the same 12 inch pipe could be, you know, eleven eleven point five twelve twelve point five and they're all together so if you go to the store you can find two of the diameter you want if you know what you're searching and then the construction is quite simple.

I simply glued all the pieces together, sprayed them with black paint, screwed the lens to the front, and added this little piece of black electrical tape to keep light from leaking to the edge of the lens. These four nail lenses are very sensitive to internal light reflections, so just a little black tape to avoid those light reflections. Another easy way to experiment with telecentric lenses is to use macro extension tubes for your camera so you'll know how they work. put your lens there and then connect it to thecamera body and normally what it's used for is to focus very close to what the lens can normally focus, but what you can do is put a piece of black material here with an aperture sticking out. and then put it on your camera and make sure the aperture plane is exactly the distance of the Flan behind this lens, so now you have an aperture at the focal plane of the lens, now you have a telecentric lens, so if you put this thing on your camera you will have a telecentric city, but the front diameter of your lens will always be the limiting factor, so for this 50 millimeter lens you will only get a field of view this large, so if we are looking at small objects it works , you just know that's the limitation, be sure and check out the links in the description if you're interested, I actually found quite a few good sources on how to play with this and understand optics a little better.

I should also point out that there are uses for these things, it's not just a curiosity if you're interested. When doing metrology or production line inspection, both telecentric and

hypercentric

lenses are useful because if you have a conveyor belt and you want to inspect all the products here, it's good to have a lens that can look well around the corners, so if you're looking down at it with computer vision and objects pass by, you can see the sides of objects at the same time without moving the lens, that's useful and also if you're doing measurements, having a lens for it has constant magnification is great because you can measure the distance between the holes at the top of an object and the bottom of an object and know that they are exactly the same because optically you don't know how to make them small because they are far away Anyway I hope you found it interesting and see you next time, goodbye.