f/0.38 camera lens made with oil immersion microscope objective

today on applied science I'd like to talk to you about low F number camera lenses that's right if you're like me you've always been intrigued by camera lenses that do really well in low light and so the F number of a lens is the ratio of the entrance pupil when you look down the end of the lens take that diameter of the clear aperture and divide by the focal length of the lens and this ratio will tell you how bright the image is that the lens produces so most modern good fast lenses a fast lens meaning low F number is could be about f1. 4 that's a very common fast lens the fastest lens ever made in a commercial production or used anywhere commercially is the uh f0. 7 lens used by Stanley cubric for the movie Barry Lindon and this movie was famously lit with candle light with no external artificial lighting so that's pretty fast um and you might have heard that there's a lens F 0. 33 produced by Zeiss but this is actually a joke lens it does not function it was made just for the hype because there's lots of low F number lens enthusiasts out there but this is actually a working F 0. 38 lens so let me show you how I built this I've got an Ethernet based single board camera from IDs here and the reason I used that one is because one I found a killer deal on them on eBay and then also I needed a camera with manual controls um you can through the software control the exposure and the gain of the sensor which is important for comparing images to other cameras so I've got this mounted in a 3D printed frame and this is carbon pla to try to make it as rigid as possible and then I've got a fine pitch uh slide adjuster here and a kinematic mount with a microscope objective in it and the kinematic Mount allows the axis of the microscope objective to be aligned to the camera axis the objective is pretty unusual it's a 40x so medium magnification U microscope objective but it is designed for oil immersion so it has a numerical aperture of 1. 3 this is the type of microscope objective that you put a little drop of oil under and the oil optically couples the microscope objective to your slide but in this case we're going to use this coupling oil to couple it to the camera sensor now the challenge is this camera sensor has a protective glass cover and beneath the cover there's a very thin slice of either air or vacuum between the glass and the sensor itself and it's actually this little bit of air that causes um the coupling oil to not be able to do its job so we have to remove that piece of glass very carefully without damaging the sensor so that the oil can actually touch the image sensor itself and provide this Optical coupling path to the microscope objective now I went through quite a few of these cameras um this is a very low yield process removing this piece of glass without destroying the camera I think I probably went through a total of eight I think and maybe two of them work I tried various different methods maybe gluing something to the top of the glass and then yanking upwards and this kind of sort of worked but um it would leave the glass you not in one piece and then you'd end up having to pick the pieces out anyway so the method that I found that worked the best was a little bit of heat to soften the epoxy that's holding the glass down and then to just push at it little by little uh the thing we have to be careful about is inside that bead of epoxy that goes around the perimeter there's Bond wires and so if you lean on the epoxy or cut it away all those Bond wires are gone and there's no chance it's going to work I had a total of three IDs board cameras and then also was able to buy more of the image sensors themselves from Digi key I went through so many I knew I was going to just be replacing image sensors and luckily I got pretty good practice at um T removing and reflowing the image sensor itself so that was actually very easy compared to this glass removal procedure once I got a camera sensor with the glass remove and still working I put everything together and added an infrared filter to the front just because these sensors are so sensitive to infrared light they make the image look weird and then added a Makita battery pack as a nice convenient portable power source so let's take a look at some test footage we've got the f. 38 lens on the left that we just put together and my normal camera rig uh micro 4/3 camera with an f1. 4 lens on the right so in theory the F 0. 38 lens should be four stops faster and we're looking at my workbench here with a candle uh it's kind of a nice little token to Barry Lyon there but at least it's a candle so you kind of know how bright it should be and yeah indeed the lens is quite a bit brighter there's no doubt about it and especially when we look in shadowed areas uh you can really see those extra stops making a difference the one thing that might be surprising is that the depth of field is huge in fact it's massive like I even did some close-ups without me refocusing this F 0. 38 lens um you can focus as close as a foot even and that's

as sharp as the stuff off in the distance in the shop so this is a little bit of a surprise I was kind of expecting you know super narrow depth of field with that you know dreamy kind of cinematic look and you know blown out candle flames and all that kind of thing but um the reason that it's not that is because the focal length is just so short so this microscope objective has a focal length of about 4 mm and as it turns out the depth of field is very dependent on not just the F number but also the focal length of the lens so dependent on the focal length that even having a super low F number is not enough to make up for this very short focal length so even though this implementation doesn't deliver amazing cinematic performance I did learn quite a few interesting things about uh low F number lens systems and I think you will be surprised by some of this stuff too so let's talk about how I even got started with all this in a previous video I used a large Fel lens to focus an image down onto a plant leaf and then developed the plant leaf with iodine so I needed a lens that produced a very bright image it had to be a low F number and I said that I had this Fel lens which was f0. 5 and someone in the comments said no that's not possible the theoretical minimum F number in air is 0. 5 so there's no way that cheap piece of plastic is getting anywhere near f0. 5 okay well we can measure it I mean you can see that no matter where I shine into this lens it is in fact being focused down and we can measure the lens focal length and I said the definition of f number is the clear diameter the entrance pupil divided by the focal length all these things are very easy to measure it's f0. 5 isn't it and in fact if you go to reputable manufacturers websites like Edmund Optics they sell Fel lenses that are getting close to f0. 5 so the deal is that to have a meaningful F number the lens system must be free of spherical and coma aberration so at first I found this to be a very unsatisfying requirement I mean it's sort of like saying all metals are steel except for the ones that aren't I mean okay but here's how to think about it if you have a lens that has a lot of spherical aberration like this Fel lens does then that means that some of the light rays going into the front of the lens are not being focused down to the right place they're not contributing meaningfully to the image contrast and so you could have a terrible lens I mean imagine like just a warped piece of glass it's hardly a lens you could sort of declare that the focal length is something I mean there's kind of an image here it's really hard to see what's going on I mean it's sort of there but there's so many aberration in this lens it is hard to see that there's even an image there so you know you could argue well it's the focal length is somewhere around here and the lens could be arbitrarily wide it could just be a broken piece of glass or something so I kind of get it so there is a hard requirement that in order to give a lens system an F number it does have to be corrected of spherical and coma aberration so the next question is in that F 0. 38 lens that we've been working on it sure seemed like there was an awful lot of aberration in there at least some spherical and coma aberration does that mean that it's not really F 0. 38 because of this requirement yeah I think the answer is actually yes to some extent unfortunately there's no hard line between has aberration and doesn't have any aberration and so if your lens system is not quite perfectly corrected then that indeed means that the F number is not as meaningful but as usual with complicated systems there isn't really like one number that describes it and to really fully explain how an optical system works you basically just have to draw array diagram the next question is why can't we just keep adding more lens elements to like crush more light down like we've got a funnel and we can just shove more and more light down to the next funnel and eventually to the focal plane uh the answer is you can and it does work the only problem is it also makes the focal length longer so it does accept more light into that huge front first element um but since the focal length is also longer it doesn't actually make the F number any lower and as it turns out the real limiting factor in what your minimum F number can be is the distance and the interplay between the final element and the focal plane itself so imagine in the limmit if we really wanted to get all the light from this lens down to the focal plane we could bring them really close together so that the focal length is super short and there's essentially no distance between the focal plane and the lens and if we were to draw a point on this focal plane and then draw the Rays coming down from this final lens element to the focal plane we could get these so close together that it's basically 180° so that the focal plane is getting light shined on it from every angle

available and in that case the half angle would be 90 and sin 90 is 1 so that's why a numerical aperture one is the limit in air because you literally can't get any more light shining onto the focal plane from your lens you're basically attacking it from all angles now we can see with this real world lens that is um f0. 5 because we measured it just ignore the aberration thing for a minute we can see that this lens is nowhere near numerical aperture one right I mean it has a focal length of about here you can see the image forming on the card and even though we measured the focal length and the diameter of this lens and got f0. 5 I know that's not quite right but it is in theory f0. 5 we can measure the angle that this is making and it's nowhere near uh numerical aperture one so that also raises the question how are these two things related F number and numerical aperture if you look around on the internet you'll just see that it's 1/ 2 * the F number is numerical aperture as if it was just you know a law I also found this to be very unsatisfying so I found a website with a pretty convincing geometric proof for how these two things are related numeric aperture and F number and we've got a lens here that's D in diameter and focal length F and if we take the arct tangent of d/2 over F and then take the sign of that we have numerical aperture n here is just the refractive index of the medium and it's one for air and so this website is saying that the precise value is actually sine of R tan but for small angles tangent and sign are about the same so you can just say sine of arc sign which you know cancels out and approximately numerical aperture is equal to 1 over two * the F number so at first I thought oh great this solves the problem I was having with these weird F number fernel lenses an F number of 0. 5 for this Fel lens doesn't equate at all to numerical aperture one it's not even close maybe this is the reason for it is that the exact uh definition is different from the approximation which is what everyone uses so I plotted it out and then had another problem so here we see the blue line is the precise value from that website s of arc tangent and we're relating numerical aperture on the Y AIS and F number on the x-axis the red line is the so-called approximation so sign a of arc sign or really just one over two * the F number and I could tell something weird was going on because all these colored dots are real world measurements that I took from actual microscope objectives and wouldn't you know it they all seem to fall on the so-called approximation line and they have nothing I mean none of them are falling on the so-called exact line so I did more digging around and could not really find any support of this idea that um sign of the art tangent is really the precise value everyone seems to say that 1 over 2 * the F number is numerical aperture and that in fact is exact so let me show you what I think is going on here so it's true that there's no math or geometry errors going on in here if this diagram is correct then the formula is correct but we know the formula doesn't really represent what we've measured in the real world and if you search around on the internet no one else is really saying this either everyone seems to suggest that 1 over 2f is the numerical aperture it's not sign of arc tangent so what else could be going on here after a ton more searching I found out that if you have a lens system that is corrected of spherical and coma aberration it's called a plantic and that plane in the middle the principal plane is actually curved and this explains why that the true formula is actually sin arc S not sin Arc tan because that principal plane is curved and instead of opposite over adjacent it's adjacent over hypotenuse and so then all everything works out so I was kind of surprised to learn this and I think it's correct but um clearly there could be a lot of discussion in the comments if I'm wrong about all this but this would explain uh why at very low F numbers um the relationship holds it's one over two times the F number is numerical aperture and it also explains why um the Fel lenses that seem to have low F numbers but not amazingly great numerical apertures are also allowed to exist in the world it's because with huge amounts of spherical and coma aberration um the plane is flat and it's not curved and you end up with it doesn't follow this relationship it could be something else the addition of this coupling oil is actually simpler to understand I think than all this other stuff the whole purpose of that oil is just to match the index of refraction of that

final lens element and allow a light Ray to come in at a very steep angle whereas if there was air between the lens and the camera sensor uh the light Ray would have to be refracted there and it would not be coming in at such a high angle so it's really the purpose of all this is just to get as much light crammed into the sensor as possible and that oil just allows that final element to couple in a little bit better so anyway I knew we got kind of heavy on the math there at the end but this kind of stuff puzzled me for a very long time and I asked Optics experts and searched around on the web and read Optics books and really was not able to put all this together for quite a while um it's interesting how seemingly simple questions are difficult to answer um if you don't have enough background information um but anyway I hope you found that interesting and uh you know for future topics I definitely want to build a large oil coupled lens of course a lot of you are thinking well if this little prototype worked great why can't we build like a large you know a lens for a micro 4/3 camera with this same Optical coupling and get you know a super uh shallow depth of field with the Highlight Gathering ability so that's on my list of things to look into and I think it's going to happen at some point okay I hope you found that interesting see you next time bye