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Old 12-03-2010, 10:38 AM #1
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Default Laser beam temperature formula?

Is there a formula to work out the estimate temperature of a beam if you take into account the power, wavelength, etc?
If not anyone know temperature estimates of say 100mw 500mw 1 watt 5 watt etc?

Thx
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Old 12-03-2010, 11:27 AM #2
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Default Re: Laser beam temperature formula?

I don't think the beam has any temperature per se.
Only when it hit's something and photons are absorbed instead of
being reflected or simply passing through, then things start to heat up.

So you would have to take into account WHAT you are warming up and it's color.

You also have to take into account the area of the dot you are focussing.

So I would go from this: power/area in mW/mm2, or W/m2 to keep it S.I.
hmmm a casio diode focussed to a 1cm2 dot would be 1000/100=10mW/mm2
or 1/0.0001=10.000W/m2

The unit Watt IIRC is defined as joule/s, so the amount of energy put out
for every instant of time.

Then you count the seconds of exposure, you can "divide away" the seconds as a unit
( ((j/s)*s)/m2 =j/m2 )

From joule/area I think you can get to temperature quite easily but I don't remember
quite how, would have to dig it up.

Passing the baton at this point...
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Old 12-03-2010, 06:18 PM #3
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Default Re: Laser beam temperature formula?

What's the temperature of an 8-ton car traveling at 70mph? A moving car has energy, and a barrage of photons has energy, but this energy is not heat energy. To convert it to heat, you would need some sort of system to do so, and since Systems have a range of efficiencies from 0% to 100%, there can be no prediction without knowing the system.

How long does 9 gallons of power weigh at a speed of 101300 pascals?
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Old 12-04-2010, 09:31 PM #4
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Default Re: Laser beam temperature formula?

Here you go.






Of course in real instances, the temp at the 'spot' will be lower: beam profile isn't perfectly circular, beam profile is messy and distributes power over a larger area, optics remove some power from the beam, etc.

Another note: the calculation assumes that the paper absorbs all of the incident light from the laser and then re-emits the absorbed energy as a black-body radiator would, which is why I used the Stefan-Boltzmann Law to approximate the temp. Keep this in mind when reviewing the calculation for the temp even if you disregarded thermal conductivity and optical element losses. In reality, it's likely an order of magnitude or so off.

Last edited by Limecat; 12-04-2010 at 11:31 PM. Reason: Further clarification
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Old 12-04-2010, 11:30 PM #5
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Default Re: Laser beam temperature formula?

14 assumptions later... that was quite the exercise in futility.
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Old 12-04-2010, 11:33 PM #6
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Default Re: Laser beam temperature formula?

Quote:
Originally Posted by Cyparagon View Post
14 assumptions later... that was quite the exercise in futility.
Futility, not so much. Even the optics equations used are approximations. Legitimate ones, as are mine.
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Old 12-05-2010, 02:51 PM #7
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Default Re: Laser beam temperature formula?

That's still not the temperature of the beam.
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Old 12-05-2010, 03:08 PM #8
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Default Re: Laser beam temperature formula?

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Originally Posted by Cyparagon View Post
That's still not the temperature of the beam.
The calculations do not imply that it is.
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Old 12-05-2010, 03:43 PM #9
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Default Re: Laser beam temperature formula?

but the question at hand is "what is the temp of the beam".


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Old 12-05-2010, 03:45 PM #10
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Default Re: Laser beam temperature formula?

Quote:
Originally Posted by chipdouglas View Post
but the question at hand is "what is the temp of the beam".


michael.
Of which I infer that he was actually asking about the temperature of the spot for any arbitrary spot size.
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Old 12-05-2010, 03:50 PM #11
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Default Re: Laser beam temperature formula?

What are you even asking blrock? The color temperature? The temperature of the space occupied by the beam? The temperature of a surface illuminated by the beam? All different things.

My guess is that any answer about "temperature" isn't even what you really want to know, rather you just want to know how fast a laser beam of certain characteristics can heat up the surface of something it intersects. The answer to that is: it depends a lot on the surface the beam actually hits just as much as the properties of the laser itself.
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