Source + types of lenses

OK - I’ve been working on the gears. The imaged around on the gear is 5cm (see below).

I did that because there are many lenses at 50mm in diameter.

So @rbowman can you suggest the lenses (and distances from the gear)?

I guess the important thing is what we want the field of view to be - 50mm is actually pretty big for the mask, because the size of the mask needs to be the size of the image formed by the lens, which is generally smaller than the lens. A reasonable compromise might be to form an image that’s around 20-25mm diagonal, which would be possible with standard SLR type lenses, or even to go smaller, say 8-12mm diagonal, which you could do with standard camera lenses designed for 2/3" sensors (much cheaper than the SLR type lenses, and easier to work with as they don’t need lots of electrical connections).

The lens that collects light passing through the mask and focuses it onto the sensor needs to be picked such that it will de-magnify the mask onto the input aperture of the sensor. If it’s a large-area photodiode, that’s ok; if it’s a spectrometer entrance slit then things get trickier. In either case, a small mask is helpful at this point. The diameter of that lens is set by the “f number” (aperture size) of the imaging lens; you need to ensure it collects as much of the light as possible. If we use a single lens between the mask and the sensor, the standard lens equation applies - i.e. if the distance between the mask and the lens is a, and the lens-to-sensor distance is b, 1/a+1/b=1/f. The diameter of the lens d is related to the mask-to-lens distance a, the image size w, and the f number of the lens n, by d = w + 2a/n. The de-magnification factor is a/b. To put some numbers in there, if we image a 12mm mask with an f=10mm lens, de-magnifying by a factor of 10, that gives b=1.1f=11mm, a=10b=110mm, and assuming our camera lens was a fairly standard f/3 aperture, we would ideally want a diameter d=12+2110/3=84. A 50mm lens will lose a fair bit of light, but is a sensible compromise, I think. Bear in mind this shrinks the mask to (approximately) 1.2mm, which will still be rather larger than a spectrometer slit. I think most single pixel cameras ignore this calculation to some extent, and just live with lower efficiency.

I’m also still not sure that spinning a mask about its centre will work, both because the suspended gear will wobble around (leading to blur) and because it will lead to degeneracy between masks (because they’re not totally independent). I’d strongly favour an annular mask, where we just use an off-axis section of the mask.

In terms of other designs, I will build and test whatever designs are available - so if you have another design and you can provide specs, I will laser cut or 3D print it and test it. Once we have a good test setup, switching in different mask designs won’t be too hard. The basic firmware and setup is the same. I’m also concerned about wobble, but still want to test it.

A few thoughts:

  1. I agree about slit size causing issues - not just because it’s small, but also light coming from an angle will be lower intensity than light coming straight on. Since this is all combined to the single value, deconvoluting light from large angles as lower intensity and light from straight on as higher intensity will be hard. I’d suggest adding a diffusor right in front of the slit - this will cause all light from all indecent angles to produce the same detector response, and it makes an easier ‘target’ to hit by the concentrator.

  2. Our concern is retaining only intensity information from all light sources, and concentrating light - we don’t need to worry about retaining the actual image… so do we need a two lens setup? Couldn’t we do this -->

The problem with making the mask gear too small is it becomes hard to make. If we can keep it large(ish), then the whole thing can be laser cut. If it’s too small, we can’t ensure reasonably comparable gears using a laser cutter. This is a preference not a requirement, but it certainly would make testing easier!


Hi Greg,
you’re right, the second lens isn’t needed for imaging - which means a lower quality lens (e.g. a plastic aspheric or fresnel lens) will do. However, a lens is still helpful for concentrating light, which is ultimately what we need to do. It turns out that concentrating light is surprisingly hard, because there’s a quantity (“specific brightness” or power per unit area, per unit solid angle, per unit wavelength) that is basically impossible to increase. In practice, what that means is that in order to concentrate light from a given area into a smaller area, you need to start with light that’s roughly collimated, and end up with light that’s focusing more tightly. Hence, a lens is a good way to concentrate the light coming through the mask into the sensor.

Sensitivity to the angle of the light entering the spectrometer would certainly result in the image being brighter in the centre than at the edges. However, that should be easy enough to calibrate out. Adding a diffuser might help, but it will do so by wasting a lot of light (essentially bringing the whole image down to the brightness level of the dimmest bits). Does that make sense?

OK - well i think we need a pretty flexible setup for testing - there are a lot of options here and testing will get this all answered quickly!

I’m getting everyone’s kits ready to send out, since it’s taken so long to get the specs I may be able to laser cut some things and buy a few different kinds of lenses to include in the kits.

If we know we’re going to be messing around, what’s a good range of lenses or things I could include in the kits to ship? Think broadly, because all the cost is in getting it there, not usually in the items :slight_smile:

Throw me some links, I’ll order them ASAP and include them. If we’re on it enough, I can also laser cut some example gears. I have a nice laser cutter here.


I’m not sure the suppliers I usually use fall into that category - a “simple” achromatic lens from e.g. ThorLabs is typically £50-100. For the “collection” lens (gathering light after the mask) a plastic asphere might be good - e.g. 31 AP 29 from Comar. For the “imaging” bit it really depends how much light we need to collect (that’s basically directly proportional to cost). A simple M12 security camera type lens would do if you have a bright enough source (just search aliexpress, amazon, etc.) and didn’t mind having a really small mask. Something designed for a mirrorless camera could be a better option - that one I linked to ought to work quite nicely.