Yesterday was a bit of a disaster to the point where I ended up not being able to sleep all night. So rather than sit there and let things get on top of me, I started work on my optics research. It's something I wanted to do since before I was even at uni, infact I remember discussing the possibility of designing optics way back in my interviews. Last night, with Google at my disposal, and the whole night ahead of me, I started searching and learning some of the things that I've always wanted to know.
Okay, so I'm going to go ahead and skip the obvious things. Anyone familiar with DSLRs will know that lenses are made of glass, are damn expensive, and come in all sorts of focal lengths and apertures. The primary purpose of a lens is to focus a wide area of light down to a point on the focal plane (aka the sensor or the film). Light enters the lens, and hit a number or 'elements', defracting and dispersing through each one in different ways in order to correct 'abberations'. With me? I hope so because that was the obvious stuff.
My aim is to start prototyping lenses. To start with I will make simple lenses (single elements) and get to grips with the math behind optical science. Then I will start progressing into compound lens design before moving into the big old world of multi lens designs, like the lenses we use every day on our SLRs. The focal length plays a big factor in knowing how big and how far away the lens needs to be from the focal plane. I love 50mm lenses, I never go out with my camera without one, so to start with I am going to try and prototype a simple single lens with a focal length of 50mm.
Having decided that, I then needed to find an aperture. The aperture is the opening through with light can be transmitted. As I am designing the actual lens and not a diaphragm, I am effectively deciding how much light can be transmitted 'wide open'. Buying materials is going to be expensive, so I decided to make the aperture the same as whatever diameter material I could get hold of economically.
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| Biconvex lens focusing to the image plane |
This brings us into the technical bit. To make glass optics I would need optical grade glass with as close to zero stress as possible within it's structure, and I would have to grind and polish it. This is not easy, and doesn't really suit the tools I have at my disposal. I have always been interested however in the viability of plastic DSLR lenses as a cheap alternative to glass. So I decided to look into optical plastic. The plastic I settled for isn't the most ideal atall, but it is very easily attainable for a very low price. It's name is Polymethylmethacrylate (PMMA), also known as clear acrylic. While it may seem a bit jokey trying to make a lens using PMMA, it does have extensive use in eye wear optics. There are many ways of measuring optical performances of solids. One of them is the Refractive Index, which measures the solids ability to transmit light. Air comes in at 1.002 while PMMA comes in at 1.49, followed by variants of glass at 1.50. This shows that the material has promise.
One of the down sides of PMMA however compared to glass is it's relatively disappointing Abbe number. This measures how the light splits as it passes through a solid body. The acrylic measures at ~52 while the most professional grade ultra low dispersion glass used sparingly through professional grade lenses (such as Canons L lenses) comes in at 80+, a huge difference. This helps me build up an expectation of how my lens will perform. While I expect the lens to focus correctly, I also expect there to be a large amount of chromatic abberations (areas where the wavelenghts of light have caused colour fringing as they pass through the optics at different speeds).
Anyway back to what I was saying, I can buy 300mm lengths of 40mm diameter cast PMMA rod for £20, so that should be good enough to get me started. Given that I intend to turn the optic in a lathe, I anticipate using the entire diameter of the rod, therefore giving me an open apeture of 40mm. Simple maths tells us that 40/50=1.25 for a simple singular lens element. Therefore the lens I am designing will be 50mm f1:1.25.
Having sorted all that, the last thing to do was calculate the surface curvature radius of the lens so I could start modelling it. Now in optical design there is a standard that says if your lens is thin enough, treat it like it's zero thickness, otherwise things get messy. So given that my maths is more than a little shaky I decided to go with the 'Thin lens element design' standards, allowing me to use the 'Lens makers equation' to figure out the radii. I'm not sure if the equation can be rearranged to give you the radius given the focal length and material RI's, because when I worked it out manually it failed miserably In the end I used a premade online calculator and plugged in radi until I got to the focal length I want. I kept the two radii the same, (but inverse, one will be positive and one will be negative because I'm designing a biconvex lens), and by massive coincidence, to get a focal length of around 50.6mm the radii had to be offset each side by exactly 50mm from the central plane of the element. For a second I thought it was a joke, but after changing the RI to the measurements for glass, it spat out totally different numbers, confirming that it was actually correct and that it was actually just a coincidence that I had to offset by the same length as my focal distance.
So anyway, long story short, here is the design for my first lens. It is a 50mm simple lens, that must be fixed at eactly 50mm from the focal plane (so just ahead of the mount as Canon EOS bodies have 44mm between the sensor and the mount). It has an apeture of 1:1.25 and a diameter of 40mm. It doesn't feature any SA (spherical aberration) or CA correction, but one step at a time right?
