Focusing UV light from a 275nm LED down to a small spot

[anvoice]

Hello, I'm trying to focus a 275nm (with proper safety precautions) LED that looks to be a few mm in length and width (the light-emitting portion) to a smaller dot size. The LED should probably be fairly close to the surface of the lens to collect more of the light. The dot size would hopefully be a few mm or smaller. I would prefer the dot to be 10mm or a bit more away from the lens, as it will be hard to position everything if focal point is too close. I do know that I need to use fused silica lenses, which brings up cost, and as this is a small project I was hoping not to inflate the budget. Hence my question, and a sanity check:

Would I be better served using a single fused silica ball lens, or 2 hemispherical lenses in this scenario? If I understand correctly in air, the focal point for a hemispherical lens will be Radius / (n - 1), whereas for a ball lens it is Radius / 2(n-1) where n is the refractive index (close to 1.5 for fused silica at 275nm). If so, that works out to about 10mm for a 10mm radius hemispherical lens (giving me about 5mm of distance from the lens surface), or 5mm for a spherical lens. If above is correct, I can't use spherical lenses as they will focus at the surface of the sphere. Then there is the fact that the light source isn't an ideal point, so the calculations wouldn't apply perfectly. A final factor to consider is that a 20mm diameter hemispherical fused silica lens costs four times that of a 10mm diameter, so if possible I was hoping to get away with a smaller lens. Would this work at all? Will I need to switch to larger radius of curvature lenses?

I am currently vigorously reading various sources to try to figure this out, but it would be nice to order the materials sooner rather than later. I was also hoping to buy the correct lenses on the first try, as they are both not cheap and take a while to arrive. Thanks in advance for any insight!

 

[tech99]

For the 10 mm hemisphere, the focal length seems to be 5/(1.5 -1) = 10 mm. It is 5mm thick, so we can find a suitable geometry I think as the fous is outside the lens. The formula for focal distances is 1/u + 1/v = 1/f, so if we place the lens 3mm from the diode junction, we have 1/3 - 1/10 = 1/v. So that v = 4.2 mm.

 

[anvoice]

For the 10 mm hemisphere, the focal length seems to be 5/(1.5 -1) = 10 mm. It is 5mm thick, so we can find a suitable geometry I think as the fous is outside the lens. The formula for focal distances is 1/u + 1/v = 1/f, so if we place the lens 3mm from the diode junction, we have 1/3 - 1/10 = 1/v. So that v = 4.2 mm.

Thanks! I'm guessing the 1/u + 1/v = 1/f formula applies to a pair plano convex lenses facing each other (not just one hemisphere), with v = 4.2mm being the distance from the flat portion of the second lens?

Also, I found some lenses with varying focal points (25-100mm) and a 12.7mm diameter for a reasonable price, and wonder if I can get away with using a 25mm focal length for the light source and then a 50mm for the image, to give me a bit of extra working distance to the sample (with 4.2mm will be trickier to position everything)?

 

[tech99]

The formula is just the simple one for a convex lens, so may be inaccurate for a thick lens. I think you need the shortest possible focal length to capture maximum light.

 

[anvoice]

The formula is just the simple one for a convex lens, so may be inaccurate for a thick lens. I think you need the shortest possible focal length to capture maximum light.

That applies if I use a biconvex lens, but also means I would have a short length to the spot image. Could that be remedied by using 2 plano convex lenses with varying focal lengths, one short to capture and collimate light, and one longer to project the image to a longer distance?

 

[Tom.G]

Could that be remedied by using 2 plano convex lenses with varying focal lengths, one short to capture and collimate light, and one longer to project the image to a longer distance?

Yes. The first lens acts as a collimator and the second lens you would choose for the desired working distance.

Something to watch out for is the beam spread from the LED. The data sheet should show that as either a graphical plot, or list it as an angle. The angle may be called FWHM (Full Width Half Maximum) or Half Angle.

For the lens closest to the LED to collect maximum light, the lens diameter should be big enough to capture most of the emitted beam.

Maximum light transmission is when the light strikes perpendicular to the lens surface, which of course is impossible with the more common lenses lens.

Two solutions to this is a long focal length lens placed a distance from the LED, or a concavo-convex lens. (for an image see:
http://www.icoachmath.com/physics/definition-of-convex-lens.html)

Note also that the light cone from an LED is often elliptical, not circular. Size your lens accordingly. If the beam is elliptical and you really need a small circular spot, you can either tilt the final lense, or you can try using one or two cylindrical lenses to reduce the astigmatism. For images see:
https://www.google.com/search?tbm=isch&&q=cylindrical+lenses

Another decent source for a collimator is a rifle scope, one of those things to mount on a rifle for good accuracy at a distance. They may not pass UV though. Even the cheap ones are pretty good. Shine the light source into the eyepiece and focus for a collimated beam out. You may have to remove the cross-hairs in it though, you can get diffraction effects from them.

Hope I didn't bury you with too much detail!

Cheers,
Tom

 

[anvoice]

Hope I didn't bury you with too much detail!

Wish I always had this much detail to work with! Thanks a bunch, this really helps.

In this case, a circular spot is not nearly as important as keeping costs down initially (what I have in mind doesn't need a circle, and if it doesn't work I'll have a collection of unusable optics). Concavo-convex doesn't seem to be easily available in fused silica either, and I feel if I use a small (otherwise it's not cheap) long focal length lens I'll lose too much light. My ideal solution is shaping up to be a couple of cheap 12.7mm lenses, one with a focal point of 25mm to collimate, one with a focal point of 50mm to focus. I would use a shorter focal length for the collimator and place the lens closer to capture more light, but I can't find a fused silica lens with a shorter focal point than 20mm (and that doubles its cost over the 25mm).

It'll be especially fun trying to visualize the spot, as UV-C is both invisible and hazardous. I wonder if an old smartphone camera matrix can capture UV-C (highly dubious, though IR works well).

 

[tech99]

Can you find a visible LED with similar characteristics for approximate adjustment purposes?

 

[Vanadium 50]

I do know that I need to use fused silica lenses

Yes you do. And not just any kind - you need UV specific fused silica or fused quartz.

I think @tech99 has a good idea. Make it work with a visible LED, and if you like it, then substitute the UV.

 

[Drakkith]

@anvoice why don't you contact someone over at Edmund Optics or another lens manufacturer and tell them what you need. Not only do they have a catalog of lenses readily available, they also have people experienced in exactly this area. Best case is you get professional help for free. Worst case is that you're no worse off than before asking.

 

[anvoice]

Can you find a visible LED with similar characteristics for approximate adjustment purposes?

Thanks for the suggestion, I'll look into it. It's probably a long shot, as I would need to match the diode geometry, cone angle, and account for the slight difference in refractive index.

I was actually hoping to use a full spectrum camera (which I don't have, so was looking at modifying an old smartphone if at all possible) to measure the spot, and calibrate with a known spot size red laser.

Make it work with a visible LED

Will look into that, assuming I can match LED specs to a satisfactory degree. I did get ultraviolet fused silica lenses.

why don't you contact someone over at Edmund Optics

There's a name I remember from my research days! I know they're probably the go to place for many researchers, but if I were to purchase their lenses I'd blow my budget. Excellent information source I think, so if I end up stuck I'll take your advice and contact them.