Energy Density and Perceived Beam Brightness

[Kyle]

I'm unsure of whether or not this issue was complicated enough for the "Advanced Technical Discussion" forum, so I've placed it here.

With all of the hype over the 445nm diodes and the quest to find the right optics to tame their multimode outputs, I've been thinking a bit about the correlation between energy density and apparent beam brightness.

For example, drlava has said to expect about a 3.5mm by 1.5mm beam from a single 445nm diode using the lensing system he has devised. To obtain a squarer beam, I've considered splitting the beam in half using a mirror and sending one half through a half waveplate and combining the split beam via a polarizing beam splitter cube. Negating the slight amount of divergence that would occur within the system, I assume one could obtain about a 1.75mm by 1.5mm beam by using this method.

Assuming a 20% loss through the lensing and combining optics, running the diode at 1W would yield 800mW in a 1.75mm by 1.5mm beam, which represents 800mW of energy in an area of about 2.625 square millimeters. I calculate this beam to have an energy density of approximately 304.762mW per square millimeter.

Now, drlava says that in a knife-edged dual diode setup, one could expect a 3.5mm square beam. Assuming a 10% loss through the optics, this would yield 1800mW in an area of about 12.25 square millimeters. If my calculations are correct, this beam would have an energy density less than half that of the setup above, at approximately 146.939mW per square millimeter.

From personal experience, it seems that smaller beams appear brighter than larger beams at similar output powers, presumably because the energy density is lower in the larger beam. From what I've read it takes about four times the output power to be perceived by the eye as twice as bright. As 1800mW is only 2.25 times the power of 800mW, I assume that the 1800mW beam will look about 56.25% brighter than an 800mW beam. However, this seems to assume that both beams are of the same size. Considering the differing beam dimensions in the two setups described above, I calculate that the larger 1800mW beam will appear only about 27.12% brighter than the smaller 800mW beam as the energy density in the larger beam is slightly less than half that of the smaller beam.

I do realize my calculations include a lot of assumptions rather than scientifically acquired data and that I've completely ignored the use of significant figures; I'm just trying to get a reasonable idea of how much brighter a dual diode setup would be over a single diode setup.

Does anyone agree, disagree, or have personal experience with this issue? Is it reasonable to assume that a larger, more powerful beam from a drlava dual diode kit will only appear a bit over one quarter brighter than a single diode kit that has additional optics to compress the beam, or am I just crazy for contemplating the issue?

In short: I'm thinking that a dual diode setup with a larger beam will only appear marginally brighter than a less powerful, single diode setup using a waveplate and PBS cube to compress the beam even further, as the energy density will be higher in the smaller beam.

All comments, corrections, et cetera are appreciated.

- Kyle

[kitatit]

Hi Kyle,

Great questions and well put.

I don't know the answers to these questions either. I wondered
exactly the same thing. I'm wondering how a 3.2w 642nm Kvant with a
4x5mm beam 1.6mrad will balance with a 2watt 3mm diameter beam with 2 mrad and a duel or quad Dr Lava corrected blue.

I second Kyles questions.

Any insights would be greatly appreciated.


Thanks to all you blue pioneers out there forging a new
future for us all to follow.

Kit

[Kyle]

Thanks Kit; I second your gratitude towards those doing all the research with the 445nm diodes!

I might be able to answer a few of your questions. Assuming that the specifications you listed are exact, a 4mm by 5mm beam with 1.6mRad divergence will measure 20mm by 21mm at 10 meters from the aperture, assuming that both axes diverge at 1.6mRad. A 3mm diameter beam with 2.0mRad divergence will be 23mm in diameter at the same distance. Assuming that a drlava dual or quad kit has a 3.5mm by 3.5mm initial beam with 1.0mRad divergence on both axes, it will have a 13.5mm by 13.5mm beam at 10 meters.

I've attached a very rough sketch showing the approximate overlap at 10 meters.

Here are two great divergence calculators:

Divergence Calculator
Diameter at a Distance Calculator

I'm also wondering if the 1.6mRad divergence figure Kvant lists is the diagonal divergence of the beam or simply the divergence of one axis.

In actuality, drlava's kits, with under 1.0mRad divergence on both axes has a diagonal divergence of less than the square root of 2 (Pythagorean theorem) or about 1.4mRad. This is helpful depending on wether or not you want to know whether the square/rectangular beam will fit within a circular beam, such as the beams of many green DPSS lasers.

If you already have at least one of the lasers you're thinking of, it'd be helpful to calculate the true divergence using the first calculator I linked to.

As far as color balance goes, according to Chroma you'll need 3.12W of 640nm and 1.6W of 445nm to balance 2.0W of 532nm green. Negating losses through your dichros, I'd say that theoretically you're pretty well set for a decent D65 (approximately 6500 kelvin color temperature) white balance using a drlava dual kit driving each diode at around 1W each.

As far as brightness relative to your 2.0 watts of green, I would almost say with certainty that you'll have to scale your green's output power down if you want your red and blue beams to be equally as bright as your green beam. Although I haven't built a projector myself yet I'm pretty sure you can do this within most laser show software applications.

Anyway, I hoped this helped a bit.

- Kyle

[mccarrot]

For example, drlava has said to expect about a 3.5mm by 1.5mm beam from a single 445nm diode using the lensing system he has devised. To obtain a squarer beam, I've considered splitting the beam in half using a mirror and sending one half through a half waveplate and combining the split beam via a polarizing beam splitter cube. Negating the slight amount of divergence that would occur within the system, I assume one could obtain about a 1.75mm by 1.5mm beam by using this method.

This will not work, the 1,5mm beam is the fast axis with the biggest divergence and will be the long line after it diverge. so cutting the 3,5mm slow axis in half will only make the the line twice as thin.

For example: without correction optics I here have a 3,5mm (slow) x 1mm (fast) beam with 0,2mrad (slow) x 2,6mrad (fast) this give me a beam of 8mm (slow) x 100mm (fast) after 30 meters.

Cutting the slow axis (the 3,5mm beam in half) wil end up in a 4mm x 100mm beam after 100 meters. so it will be even more a line.

I hope you can follow me.

what we do is we increase the beam diameter of the fast axis (the 1mm beam) so the divergence will be bigger.

you can use prism pairs to increase the beam width (high losses) or cylindrical lenses.

[Kyle]

This will not work, the 1,5mm beam is the fast axis with the biggest divergence and will be the long line after it diverge. so cutting the 3,5mm slow axis in half will only make the the line twice as thin.

For example: without correction optics I here have a 3,5mm (slow) x 1mm (fast) beam with 0,2mrad (slow) x 2,6mrad (fast) this give me a beam of 8mm (slow) x 100mm (fast) after 30 meters.

Cutting the slow axis (the 3,5mm beam in half) wil end up in a 4mm x 100mm beam after 100 meters. so it will be even more a line.

I hope you can follow me.

what we do is we increase the beam diameter of the fast axis (the 1mm beam) so the divergence will be bigger.

you can use prism pairs to increase the beam width (high losses) or cylindrical lenses.

Ah, okay! Thank you, mccarrot! That makes perfect sense. For some reason I was thinking that the wider axis was the fast axis... doh!

But by increasing the beam diameter of the fast axis you reduce its divergence, no?

Before drlava announced his setup I was contemplating using a single lens and an anamorphic prism pair, but worried about the initial beam size I would achieve using that method. IIRC, I read that an ~8mm focal length lens produced an 8mm by 2mm initial beam with about 1.6mRad divergence on the fast axis. I guess if you used a prism pair to magnify the fast axis by about four times you could get an 8mm square beam with about 0.4mRad divergence on the fast axis. Send that large beam through a 2.5x minifying telescope and you could achieve a 3.2mm square beam with about 1.0mRad divergence, but this essentially creates a larger beam with much higher losses than drlava's cylindrical lens setup.

Still, the question of the correlation between energy density and beam brightness remains.

Thanks again, mccarrot.

- Kyle

[mccarrot]

here you can find a table which shows brightness vs beam diameter

http://www.arctoslaser.de/en/arctos_arguments.htm

[mccarrot]

AI read that an ~8mm focal length lens produced an 8mm by 2mm initial beam with about 1.6mRad divergence on the fast axis. I guess if you used a prism pair to magnify the fast axis by about four times you could get an 8mm square beam with about 0.4mRad divergence on the fast axis. Send that large beam through a 2.5x minifying telescope and you could achieve a 3.2mm square beam with about 1.0mRad divergence, but this essentially creates a larger beam with much higher losses than drlava's cylindrical lens setup.

Why not use a f4.0 lens with aprox 4x1 mm beam, use a cylindrical 4x telescope to increase the 1mm beam to 4mm and end up with a 4x4mm beam with <1mRad


(please note above numbers are not 100% accurate)

[Kyle]

mccarrot,

Thanks for the link! According to the Artcos chart, when the output power is tripled and the beam size is increased by two-thirds, the "brightness" only increases by a little over seven percent. If that is an accurate figure, it doesn't seem wise to upgrade to the more powerful unit simply for extra brightness.

Also, I did not know that a 4mm focal length lens could achieve <1mRad divergence, I thought that they produced beams with >2mRad divergence.

At least with your setup you wouldn't have as much loss, however the beam is 25% larger.

Thanks again.

- Kyle

[mccarrot]

mccarrot,
Also, I did not know that a 4mm focal length lens could achieve <1mRad divergence, I thought that they produced beams with >2mRad divergence.

a 4mm focal lenght will give you a 1mm beam with divergence of 2-3mRad, but after a set of cylindirical lenses you get 1mRad with a 4mm beam.

[ElektroFreak]

I would think that by equalizing and expanding the beam from a multimode diode you would actually hurt the beams perceived brightness since the energy density at any point in the beam will not be as high as it would be if the beam were allowed to remain a flat line profile. I've been thinking about the ideas being tossed around here regarding complex optics for these, but as I've said before the 1.6 mrad by .18 mrad that I'm getting right now with only an Aixiz glass lens assembly seems pretty damn good. Couple that with the increased energy density of the flat beam profile and I think that the perceived brightness should be quite nice. I don't think I'll need much better than that myself based on what I've seen in the way of beam shows and graphics. Of course lower energy density is better if you're audience scanning, but I never scan any spectators myself.