# Luminosity of lasers (math)



## FNinjaP90 (Mar 29, 2007)

A while ago I remember asking how many lumens lasers puts out. Someone told me that a laser can't be "assigned" a lumen rating. If any of you guys aren't familiar with lumens, it's what the rest of this forum will give an arm or leg to get more of in their flashlights. A small 2xCR123 light will give around 60 lumens, and a big spotlight will give around 1000 lumens.

According to wikipedia, ideal 555nm light will give 683lm/W. This is the highest _luminous efficacy_ possible for light, since the human eye is most sensitive to 555nm light. For example, incandescents give around 20lm/W, LEDs around 30lm/W, and HID's 100lm/W. Looking at the graph of photopic vision:






A 532nm laser has a luminosity function of .89, and the other, "dimmer" colors have their respective luminosity functions.

What does this mean?

For example, 100mW of pure 532nm light will have (683lm/W)(0.1W)(.89)=61 lumens. That's the same brightness of a Surefire E2e flashlight! And I thought that lasers were dim. 

A 200mW 635nm laser will only put out (683lm/W)(0.2W)(.24)=33 lumens, or appear half as bright as a green laser of half the power output. 473nm blue is even dimmer, and the near-IR 670nm red is very very dim.


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## 2xTrinity (Mar 29, 2007)

> For example, 100mW of pure 532nm light will have (683lm/W)(0.1W)(.89)=61 lumens. That's the same brightness of a Surefire E2e flashlight! And I thought that lasers were dim.


I have a 10mW 532, and in a ceiling bounce test I'll say it's almost as bright as some of my 10 lumen coin cell lights. Another good point worthy of note is that the green lasers will scatter more due to particles in the atmosphere -- so a 100mW 532 will have a much more visible beam than a 200mW 635, even though the lumen output is nearly the same. A blue laser should be even more apparent in terms of producing a visible beam -- it should also activate green fluorescent paint, and make for some interesting effects, 405nm violet should be even better. I know my 523nm can activate yellow and red fluorescent paints.

What doesn't make a lot of sense is how there was a thread earlier showing a 20mW 405nm laser diode from a BluRay player appearing almost as bright as a 5mW 532nm! I think that the camera must have been exaggerating the intensity compared to what the human eye would perceive.


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## allthatwhichis (Mar 29, 2007)

:huh2: :goodjob:


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## comozo (Mar 29, 2007)

2xTrinity said:


> I have a 10mW 532, and in a ceiling bounce test I'll say it's almost as bright as some of my 10 lumen coin cell lights. Another good point worthy of note is that the green lasers will scatter more due to particles in the atmosphere -- so a 100mW 532 will have a much more visible beam than a 200mW 635, even though the lumen output is nearly the same. A blue laser should be even more apparent in terms of producing a visible beam --


 The scatter is known a Rayleigh and is not do to particulates in the air but is entirely do too the molecules. Though blue wave lengths will scatter more human vision is less sensitive to blue so the blue light will appear less visible. Just look at the graph again.


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## pseudonomen137 (Mar 29, 2007)

Be careful about some of those generalizations. Lumens can figure total power of a specific wavelength, but candelas (lumens/steradian) take area into account too, which really changes things when you consider collimation.

Lumens are not a measure of brightness and you will want to be careful not to get the two confused (in fact, with lasers, the term 'brightness' takes on a completely different meaning scientifically). 2x lumens will not correspond to 2x visual brightness, and you have to be careful as to what you are considering to be "bright". Lumens will tell you the total visual brightness the beam can project, given a set area, but because of different spot sizes and such, it will not give you an accurate indication of how bright the dot is.

Honestly.. lumens just aren't a unit that is very compatible with lasers, though I guess this is useful to know nonetheless

("Hey, this kW CO2 laser is only 0 lumens... it can't be TOO dangerous" )


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## instinct (Mar 30, 2007)

allthatwhichis said:


> :huh2: :goodjob:



:lolsign: ditto


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## FNinjaP90 (Mar 30, 2007)

Looking at the equations I pulled up from Wikipedia,

The steradian(a unit of solid angle) is analgous to a jousting lance or laser beam(lower solid angle) compared to an ice cream cone or flashlight beam(higher solid angle).

Candela = 683(luminosity function)(W/sr)
Lumen=(Candela)(sr)

The steradians cancel out, and all you're left with is Lumen=683(luminosity function)(W). 

Am I right? Anyway, it's perfectly possible to calculate the laser beam's solid angle, assuming that the beam has an initial diameter of 0 and spreads out into space as a cone. The arclength of 1 steradian is 65.53deg. Figure 1mrad as the arclength(divergence) of the laser beam, convert that to degrees, divide it by 65.53deg, and square the figure to find the ratio of the laser beam solid angle to the solid angle of 1 steradian. 

Still, the solid angle(steradian) should cancel out in calculating lumens, which is logical since a laser with a large divergence illuminates an unlit room just as well as a laser with very small divergence. The same as how the Surefire turbohead has a tighter focus than a regular head, yet they both give the same lumen output with the same bulb. Candlepower(candela) increases as a beam is more tightly focused, but luminosity disregards focus and is only dependent on the total light output of the light source.



pseudonomen137 said:


> Be careful about some of those generalizations. Lumens can figure total power of a specific wavelength, but candelas (lumens/steradian) take area into account too, which really changes things when you consider collimation.
> 
> Lumens are not a measure of brightness and you will want to be careful not to get the two confused (in fact, with lasers, the term 'brightness' takes on a completely different meaning scientifically). 2x lumens will not correspond to 2x visual brightness, and you have to be careful as to what you are considering to be "bright". Lumens will tell you the total visual brightness the beam can project, given a set area, but because of different spot sizes and such, it will not give you an accurate indication of how bright the dot is.
> 
> ...



You're right, my original post should have replaced any instance of "brightness" with "apparent light output".

If we want to figure candela, then it seems that a 100mW 532nm laser with a divergence of 1mrad puts out 80 million candlepower.


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## 2xTrinity (Mar 30, 2007)

> Be careful about some of those generalizations. Lumens can figure total power of a specific wavelength, but candelas (lumens/steradian) take area into account too, which really changes things when you consider collimation.
> 
> Lumens are not a measure of brightness and you will want to be careful not to get the two confused (in fact, with lasers, the term 'brightness' takes on a completely different meaning scientifically). 2x lumens will not correspond to 2x visual brightness, and you have to be careful as to what you are considering to be "bright".


It's true that if you light up a same spot with double the lumens it won't appear twice as bright -- this is true even with omnidirectional lightbuls and flashlights as well -- switching from a 60W to a 100W light bulb in the same room won't necessarly look "doubly bright" even though the 100W puts out double the lumens, because the eye adjusts to the higher intensity, ofsetting some of the increase in apparent brightness. 

However, for the sake of finding out what power laser in <x> wavelength is needed to achieve a spot as bright as, say, a 5mW 650nm red laser, _all else equal_ (assuming same degree of divergence etc) the lumen figure is perfectly valid -- the "spot" produced by a 532nm green laser of ~1.3mW should look just as bright as the "spot" from a 650nm red.

Also, in comparing the lumen figure for my coin cell light, and my green laser, I pointed both beams up at a white ceiling and compare how well that the laser illuminates the whole surroundings -- the reflected light is essentially omnidirectional, so the lumens figure would apply there as well.

If anything I think the lumen is more useful than the candela figure, since the solid angle is so close to zero (extremely tight collimation) the candela quantity will be very large (this is why it's a bad idea to look directly into lasers...), but that means even slight differences in divergence for lasers will lead to huge differences in the candela figure, even though those differences won't be very apparent at all when pointing at things up closer, or creating a visible beam in fog -- in that context, the lumen figure is more relevant IMO.

Of course, if the purpose of the laser is to burn things, the only relevant figure is the wattage -- since that's a measure of how much heat energy you can pump into a target over a given time.


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## FNinjaP90 (Mar 30, 2007)

Let me try this analogy:

You need space for a certain number of employees in an office facility. You can either build a high-rise with many levels on a small piece of land, or you can build a single-story facility over a large piece of land. Both of these buildings house the same number of employees(lumens), but the high-rise puts more employees than the single-story in the same land area(candlepower). The single-story facility is analgous to a floodlight while the high-rise is analgous to a spotlight or a laser.


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## pseudonomen137 (Mar 30, 2007)

Yep, I see what you're saying 2xTrinity.



2xTrinity said:


> However, for the sake of finding out what power laser in <x> wavelength is needed to achieve a spot as bright as, say, a 5mW 650nm red laser, _all else equal_ (assuming same degree of divergence etc) the lumen figure is perfectly valid -- the "spot" produced by a 532nm green laser of ~1.3mW should look just as bright as the "spot" from a 650nm red.


 
I would be a bit wary about this though. The CIE photopic luminousity function is great for some tasks, but its really not at all accurate for a lot of laser work. If you compare powers of well balanced RGB projectors against the function, it won't seem right, but there are other factors (first and foremost being scotopic vision IMO) that throw it off.

Take, for instance, the OPs picture which shows 473nm only being ~1/8-1/9 of green. However in a projector, the green to blue ratio is normally going to be somewhere between 1/3-1 to get a decent balance.


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## Kiessling (Mar 30, 2007)

Sorry, but I can't resist and have to post something a little off-topic concerning the 30lm/W claim for LED:

LED has risen to more than 100lm/W and thus busted the small and medium HIDs and well as fluorescent for efficiency. The revolution is happening now. PowerLEDs are at 80+ lm/W right now, too. oo:

bernhard


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## 2xTrinity (Mar 30, 2007)

Kiessling said:


> I would be a bit wary about this though. The CIE photopic luminousity function is great for some tasks, but its really not at all accurate for a lot of laser work. If you compare powers of well balanced RGB projectors against the function, it won't seem right, but there are other factors (first and foremost being scotopic vision IMO) that throw it off.
> 
> Take, for instance, the OPs picture which shows 473nm only being ~1/8-1/9 of green. However in a projector, the green to blue ratio is normally going to be somewhere between 1/3-1 to get a decent balance.


You're right. 470nm blue are used to "drive" the white LEDs. I have a couple 5mm LEDs at that wavelength, and the 470nm are the brightest single-color LEDs I have, they're not that much dimmer than my brightest white 5mm LEDs. Based on how close they are to white LEDs drawing the same amount of power, then I agree 1/9th sensitivity cannot possibly be right in real-world conditions. Also, since we're talking about visible laser beams in a dark room or outside at night, certainly the scoptopic portion of the sprectrum is going to be relevant (which is more heavily weighted toward blue)


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## brighter (Mar 31, 2007)

FNinjaP90 said:


> For example, 100mW of pure 532nm light will have (683lm/W)(0.1W)(.89)=61 lumens. That's the same brightness of a Surefire E2e flashlight! And I thought that lasers were dim.


 
Are those maximum 683lm/W refering on 1W power of light or light powered by 1W from power supply? 

I'm confused here...

I have one red luxeon III (625nm) which is stated maximum 130lm and it's achieved from 4.5W draw from battery. What is the power of light then?


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## IMSabbel (Mar 31, 2007)

The 683 lm/W is of _course_ W in radiation power.
This means that the wall-plug (respectively battery) efficiency of lasers is still far lower than flashlights.

But if one were to get a breakthrough in green lasers (producing them solid state without frequency doubling), then this could be _really_ efficient. (just like nowadays GaAs infrared lasers are the best known way to convert electricity into photons. I have seen samples with >85% total effiency).


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## Kiessling (Mar 31, 2007)

683 lm/W (or so) is the absolute maximum lumen rating for 1W of light (green) ... meaning you get 683 lm out of a 1W souorce that is 100% efficient.
This is different for white light, there theh maximum is about 250-300lm IIRC.

And yes ... as I said ... LEDs made a big jump in efficiency to about 100+ lm/W recently. We're all excited about it, but maybe you laser guys in your elysium here haven't noticed yet ... 

bernhard


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