Definition beam diameter -> confusion?
Zuben El Genubi
diameters. Please, any comments are helpful and welcome.
- For a TEM00 Gaussian beam the beam radius w is defined as 1/e decay of
the electrical field E and 1/e^2 decay of the intensity I, respectively.
Accepted.
- For arbitrarily shaped laser beams the definition of radii and
diameters is based on the calculation of the first and second moments of
the measured intensity distribution I(x,y). Beam radius W is then twice
the standard deviation sigma of the intensity distribution. For TEM00
this W is exactly the beam radius w. ISO 11146 uses this definition for
measuremnt of M^2, as far as I know. Accepted.
- In practice, I experience beam measurements (strongly non-Gaussian)
where this radius W defined with second moments overestimates clearly
the subjective witdh of the beam as displayed in the profile screen.
Someone has similar observations?
- I found definitions in material processing for a beam radius w86,
which is the radius of a circular aperture transmitting 86% of the total
beam power. For TEM00 this again is exactly the radius w. Makes sense.
For arbitrarily shaped beams, this w86 can significantly be different
(smaller?) from the second moment radius W. Am I correct? For practical
aplications, w86 seems to be more appropriate concerning impact on
targets etc., although not theoretically best.
- Now I found that: For safety considerations in Europe, DIN EN
60825/IEC60825 is relevant. There the beam diameter d63 is used. Defined
as a cicular aperture with a diameter such, that 63% of total power is
transmitted. O.K., you can define that, but whats the reason ?? For
TEM00 beams it equals the point of 1/e (!) decay of the intensity (!!).
Such a nonsense to define a standard against all common practice in
science and technology?
Or am I completely confused?
Regards
Rainer Engelbrecht
Laser Engineer
University of Erlangen-Nürnberg, Germany
Repeating Decimal
zubenelgen...@gmx.de wrote on 1/17/03 6:03 AM:
> Here are some thougths and questions about definitions of laser beam
> diameters. Please, any comments are helpful and welcome.
>
> - For a TEM00 Gaussian beam the beam radius w is defined as 1/e decay of
> the electrical field E and 1/e^2 decay of the intensity I, respectively.
> Accepted.
>
> - For arbitrarily shaped laser beams the definition of radii and
> diameters is based on the calculation of the first and second moments of
> the measured intensity distribution I(x,y). Beam radius W is then twice
> the standard deviation sigma of the intensity distribution. For TEM00
> this W is exactly the beam radius w. ISO 11146 uses this definition for
> measuremnt of M^2, as far as I know. Accepted.
<snip>
Definitions are inventions--not fact! Good definitions, aside from getting
setting a standard are good because they are useful.
Bill
Christoph Bollig
> Here are some thougths and questions about definitions of laser beam
> diameters. Please, any comments are helpful and welcome.
>
> - For a TEM00 Gaussian beam the beam radius w is defined as 1/e decay of
> the electrical field E and 1/e^2 decay of the intensity I, respectively.
> Accepted.
>
> - For arbitrarily shaped laser beams the definition of radii and
> diameters is based on the calculation of the first and second moments of
> the measured intensity distribution I(x,y). Beam radius W is then twice
> the standard deviation sigma of the intensity distribution. For TEM00
> this W is exactly the beam radius w. ISO 11146 uses this definition for
> measuremnt of M^2, as far as I know. Accepted.
The reason they use this definition is the fact that the M2 laws are
exactly correct for any beam shape, no matter how screwed up or
complicated, only if you use this definition (at least as far as I
understand it).
Out of all the definitions here, it is also the only one which takes
the whole structure of the beam into account. For example, you could
think of a beam where the main part of the power (let's say the 86%
you mention below) is within a 10mm diameter (i.e. 5mm radius) circle.
If it is a Gaussian beam, 99% of the power is within a 15mm diameter.
(There is this relatively well-known rule that in order to get 99%
transmission, an aperture should have a diameter of at least three
times the radius of a Gaussian beam. Who on earth originally
formulated this rule using diameter and radius in one sentence???) If
you take a 20mm diameter circle, the Gaussian beam will transmit far
more then 99%.
However, you could think of a beam, which has strong ripples far away
from the centre. Some diode lasers seem to have such beams, or if you
have a laser which has most of the power in the TEM00 mode, but a
small amount in some much higher order modes, for whatever reason. You
could then still measure 10mm diameter using the 86% rule, but it
might have a significant amount of power lets say between the 15mm and
the 20mm circle. Only the second-moment will take these into account.
The same applies to the beam inside that circle. If you have a
top-head beam for example and a Gaussian beam, they might have the
same radius using the 86% rule, but only the second-moment takes the
full distribution into account.
> - In practice, I experience beam measurements (strongly non-Gaussian)
> where this radius W defined with second moments overestimates clearly
> the subjective witdh of the beam as displayed in the profile screen.
> Someone has similar observations?
There might be three reasons:
1.) The beam has strong "wings" i.e. it has some power quite far away
from the centre. That is normally not visible on the profile, but
influences your second-moment measurement.
2.) You have a noise problem.
3.) You have a problem with small amounts of light far away from the
centre, like from reflections of the focussing lens.
In all cases, this is a result of the fact that the second-moment
integral is an integral over the intensity multiplied with the square
of the distance to the centre of the beam (lets call it r2 , i.e.
r-square). BTW, the "centre point" has to be calculated using the
first-moment integral mentioned above.
The problem is that you also multiply your noise with r2, so that it
becomes more significant the further you go away from the centre.
Therefore, you have to define some point at which you cut off your
measurement. We have just build our own M2-Measurement setup. We
analyse the noise far away from the centre and use three times the
noise as cut-off criterium. That seems to work quite well.
I know that commercial systems also use similar criteria. The problem
is obviously that you might cut off part of your beam, if it does have
low-intensity wings.
The ISO 11146 will certainly give guides on how to handle the cut-off
problem. BTW, if someone has a copy, I would be very interested.
> - I found definitions in material processing for a beam radius w86,
> which is the radius of a circular aperture transmitting 86% of the total
> beam power. For TEM00 this again is exactly the radius w. Makes sense.
> For arbitrarily shaped beams, this w86 can significantly be different
> (smaller?) from the second moment radius W. Am I correct?
Yes, see above.
> For practical
> aplications, w86 seems to be more appropriate concerning impact on
> targets etc., although not theoretically best.
I guess for the impact on a target, you don't care whether the rest of
the power is close to the beam or far away. There might be other
applications where you do care.
> - Now I found that: For safety considerations in Europe, DIN EN
> 60825/IEC60825 is relevant. There the beam diameter d63 is used. Defined
> as a cicular aperture with a diameter such, that 63% of total power is
> transmitted. O.K., you can define that, but whats the reason ?? For
> TEM00 beams it equals the point of 1/e (!) decay of the intensity (!!).
> Such a nonsense to define a standard against all common practice in
> science and technology?
>
> Or am I completely confused?
I am not aware of this, but I am not too surprised. I have once
experienced how norms are drawn up, and it all depends on the people
involved (as usual).
I hope this helps,
Christoph
Leonard Migliore
Bollig <laser...@gmx.net> wrote:
> Hi Rainer,
>
> > Here are some thougths and questions about definitions of laser beam
> > diameters. Please, any comments are helpful and welcome.
> >
> > - For a TEM00 Gaussian beam the beam radius w is defined as 1/e decay of
> > the electrical field E and 1/e^2 decay of the intensity I, respectively.
> > Accepted.
> >
> > - For arbitrarily shaped laser beams the definition of radii and
> > diameters is based on the calculation of the first and second moments of
> > the measured intensity distribution I(x,y). Beam radius W is then twice
> > the standard deviation sigma of the intensity distribution. For TEM00
> > this W is exactly the beam radius w. ISO 11146 uses this definition for
> > measuremnt of M^2, as far as I know. Accepted.
>
> The reason they use this definition is the fact that the M2 laws are
> exactly correct for any beam shape, no matter how screwed up or
> complicated, only if you use this definition (at least as far as I
> understand it).
It was my understanding that M^2 works fine with any definition of beam
diameter for beams from stable resonators (help me, Prof. Siegman!).
The distribution of power in the beam stays the same as it propagates.
You would, though, get different M^2 values for the same beam if you
changed your definition for the diameter.
I ran into this in Bauerle's *Laser Processing and Chemistry*. Confused
the hell out of me.