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Thread Subject:
polychromatic gaussian beam

Subject: polychromatic gaussian beam

From: sonia

Date: 29 Jan, 2011 20:06:03

Message: 1 of 11

hello,
does anyone have any matlab code for the intensity distribution of a polychromatic gaussian beam.


Thanks a lot to help me
Sonia

Subject: polychromatic gaussian beam

From: ImageAnalyst

Date: 29 Jan, 2011 21:09:55

Message: 2 of 11

On Jan 29, 3:06 pm, "sonia " <sonia_elwa...@yahoo.fr> wrote:
> hello,
> does anyone have any matlab code for the intensity distribution of a polychromatic gaussian beam.
>
> Thanks a lot to help me
> Sonia
--------------------------------------------------------------------------------------------------------
Sonia:

You didn't supply enough information. Do you already have the signal
in arrays in MATLAB? If not, use a detector of some sort and the
appropriate toolbox. What does polychromatic mean? Does that mean
you expect to have 2 or more 1D signals (row or column vectors), or 2D
images, each of a particular spectral component? Is your signal 1D or
2D?

Pretend you were sitting down with a consultant. Now imagine that
this consultant could solve your problem. What would he or she need
to know? What would you say? Do you think your problem could be
solved completely to your satisfaction with the limited information
you supplied us? I think not. Perhaps a question like how do you add
two numbers could be stated as briefly as you did, but do you really
think your problem is so incredibly trivial that it can be completely
described in as few words as you used?
ImageAnalyst

Subject: polychromatic gaussian beam

From: Bruno Luong

Date: 30 Jan, 2011 00:12:03

Message: 3 of 11

ImageAnalyst <imageanalyst@mailinator.com> wrote in message <32c05adb-9044-4226-84a7-cf723f000293@a5g2000vbs.googlegroups.com>...
> On Jan 29, 3:06 pm, "sonia " <sonia_elwa...@yahoo.fr> wrote:
> > hello,
> > does anyone have any matlab code for the intensity distribution of a polychromatic gaussian beam.
> >
> > Thanks a lot to help me
> > Sonia
> --------------------------------------------------------------------------------------------------------
> Sonia:
>
> You didn't supply enough information. Do you already have the signal
> in arrays in MATLAB?

Gaussian beam is an optical beam. It's a term to designates a particular analytical solution of a Maxwell's stationary equation, commonly used to describe a laser beam. It doesn't have to be in an array, because its analytic expression is known.

> If not, use a detector of some sort and the
> appropriate toolbox. What does polychromatic mean?

Multi wavelength. But here is where the lack of information, she needs to supply the spectral content of the beam.

> Does that mean
> you expect to have 2 or more 1D signals (row or column vectors), or 2D
> images, each of a particular spectral component? Is your signal 1D or
> 2D?

It's 3D, rotational symmetric.

Bruno

Subject: polychromatic gaussian beam

From: ImageAnalyst

Date: 30 Jan, 2011 00:54:22

Message: 4 of 11

On Jan 29, 7:12 pm, "Bruno Luong" <b.lu...@fogale.findmycountry>
wrote:
> It's 3D, rotational symmetric.
>
> Bruno
-------------------------------------
I figured all that. However I don't see how it can be assumed to be
3D unless you're doing a simulation, where you essentially have all
the intensities along the beam in 3D. If she has just a sensor
picture, like the beam hit some sensor such as a CCD, then you'd have
a 2D picture. This is most likely however it's possible she's
measuring across the pattern with a point or line sensor so that she
has only a 1D profile. A rotationally symmetric Gaussian would
describe the TEM00 mode (only) of a laser so maybe that's what she's
talking about. If so I wonder why she didn't find gausswin in the
help. The widths of the Gaussians for the different colors would
depend on the longitudinal and transverse chromatic aberrations of the
lens, and how far from the lens the signal is measured, focal length,
etc.
ImageAnalyst

Subject: polychromatic gaussian beam

From: Bruno Luong

Date: 30 Jan, 2011 07:39:04

Message: 5 of 11

ImageAnalyst <imageanalyst@mailinator.com> wrote in message <78687835-f708-42cf-98db-681988bec817@f36g2000yqe.googlegroups.com>...

> -------------------------------------
> I figured all that. However I don't see how it can be assumed to be
> 3D unless you're doing a simulation, where you essentially have all
> the intensities along the beam in 3D.

That's right. A Gaussian beam depends on 3 coordinates so it's 3d. What to argue about that? She did not mention she measure a Gaussian beam with a CCD (so no Image Analyst yet). If she measure by a CCD, then only the intensity of the beam on a plane of the CCD is calculated. This is a trivial part once the full Gaussian beam in 3D is described.

Bruno

Subject: polychromatic gaussian beam

From: sonia

Date: 30 Jan, 2011 09:26:03

Message: 6 of 11

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ii34io$9ac$1@fred.mathworks.com>...
> ImageAnalyst <imageanalyst@mailinator.com> wrote in message <78687835-f708-42cf-98db-681988bec817@f36g2000yqe.googlegroups.com>...
>
> > -------------------------------------
> > I figured all that. However I don't see how it can be assumed to be
> > 3D unless you're doing a simulation, where you essentially have all
> > the intensities along the beam in 3D.
>
> That's right. A Gaussian beam depends on 3 coordinates so it's 3d. What to argue about that? She did not mention she measure a Gaussian beam with a CCD (so no Image Analyst yet). If she measure by a CCD, then only the intensity of the beam on a plane of the CCD is calculated. This is a trivial part once the full Gaussian beam in 3D is described.
>
> Bruno

Thank you for all response,
by a polychromatic, I mea that it is a multiwavelenght beam.
So I would like to know haw to write a a Gausssian beam in 3D (x,y,lambda).

%%%here a sample of matlab code in 2D (x,y):

W0=5e-2;
for i=1:N
    for j=1:N
        gauss(i,j)=exp(-((((i)^2/(W0^2)))+((j-^2/(W0^2))));
    end
end
%%
I want to introduce another vector to determine;

P(sigma)*gauss(i,j).

with P(sigma)=P0*sqrt(B)*exp(-pi*B*(sigma-sigma0).*(sigma-sigma0));

%%%%

thanks

Subject: polychromatic gaussian beam

From: Bruno Luong

Date: 30 Jan, 2011 10:30:07

Message: 7 of 11

"sonia " <sonia_elwardi@yahoo.fr> wrote in message <ii3arb$m4d$1@fred.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ii34io$9ac$1@fred.mathworks.com>...
> > ImageAnalyst <imageanalyst@mailinator.com> wrote in message <78687835-f708-42cf-98db-681988bec817@f36g2000yqe.googlegroups.com>...
> >
> > > -------------------------------------
> > > I figured all that. However I don't see how it can be assumed to be
> > > 3D unless you're doing a simulation, where you essentially have all
> > > the intensities along the beam in 3D.
> >
> > That's right. A Gaussian beam depends on 3 coordinates so it's 3d. What to argue about that? She did not mention she measure a Gaussian beam with a CCD (so no Image Analyst yet). If she measure by a CCD, then only the intensity of the beam on a plane of the CCD is calculated. This is a trivial part once the full Gaussian beam in 3D is described.
> >
> > Bruno
>
> Thank you for all response,
> by a polychromatic, I mea that it is a multiwavelenght beam.
> So I would like to know haw to write a a Gausssian beam in 3D (x,y,lambda).
>
> %%%here a sample of matlab code in 2D (x,y):
>
> W0=5e-2;
> for i=1:N
> for j=1:N
> gauss(i,j)=exp(-((((i)^2/(W0^2)))+((j-^2/(W0^2))));
> end
> end
> %%
> I want to introduce another vector to determine;
>
> P(sigma)*gauss(i,j).
>
> with P(sigma)=P0*sqrt(B)*exp(-pi*B*(sigma-sigma0).*(sigma-sigma0));

Create a 3d grid (i,j,sigma) with NDGRID command, then write whatever formula you want.

Bruno

Subject: polychromatic gaussian beam

From: ImageAnalyst

Date: 30 Jan, 2011 15:03:35

Message: 8 of 11

It's clearer to me now. You're trying to construct a 2D multispectral
image, which is described by a 3D array, rather than a 3D volumetric
image where each dimension is a spatial dimension. To do that you
need to know the spectrum of your illumination. You need a function
of intensity (or energy or power or amplitude or whatever units you're
using) as a function of wavelength (lambda). Do you have that? If
so, just include a third loop where you're iterating over wavelength.
Then you will have your multispectral image.

Subject: polychromatic gaussian beam

From: Bruno Luong

Date: 30 Jan, 2011 16:03:03

Message: 9 of 11

ImageAnalyst <imageanalyst@mailinator.com> wrote in message <4f92a31d-60b7-4733-b781-f4d85ef22fe6@d11g2000yql.googlegroups.com>...
> You need a function
> of intensity (or energy or power or amplitude or whatever units you're
> using) as a function of wavelength (lambda). Do you have that?

As I understood, the P(:) function she gave is the intensity wavelength-dependent:

P(sigma)=P0*sqrt(B)*exp(-pi*B*(sigma-sigma0).*(sigma-sigma0))

Bruno

Subject: polychromatic gaussian beam

From: ImageAnalyst

Date: 30 Jan, 2011 16:59:26

Message: 10 of 11

On Jan 30, 11:03 am, "Bruno Luong" <b.lu...@fogale.findmycountry>
wrote:
> ImageAnalyst <imageanal...@mailinator.com> wrote in message <4f92a31d-60b7-4733-b781-f4d85ef22...@d11g2000yql.googlegroups.com>...
> > You need a function
> > of intensity (or energy or power or amplitude or whatever units you're
> > using) as a function of wavelength (lambda).  Do you have that?  
>
> As I understood, the P(:) function she gave is the intensity wavelength-dependent:
>
> P(sigma)=P0*sqrt(B)*exp(-pi*B*(sigma-sigma0).*(sigma-sigma0))
>
> Bruno

------------------------------------------------------
OK good. Then if she knows P0, B, and sigma0 (which is lambda at the
center wavelength) then she's all set. She just needs to convert
P(sigma) to an index in the loop over sigma, and do
gauss(i,j, wavelengthIndex) = exp......

Subject: polychromatic gaussian beam

From: sonia

Date: 9 Feb, 2011 13:48:02

Message: 11 of 11

ImageAnalyst <imageanalyst@mailinator.com> wrote in message <2dced7f1-c342-48b8-aba8-ef3c8a522f6d@w19g2000yqa.googlegroups.com>...
> On Jan 30, 11:03 am, "Bruno Luong" <b.lu...@fogale.findmycountry>
> wrote:
> > ImageAnalyst <imageanal...@mailinator.com> wrote in message <4f92a31d-60b7-4733-b781-f4d85ef22...@d11g2000yql.googlegroups.com>...
> > > You need a function
> > > of intensity (or energy or power or amplitude or whatever units you're
> > > using) as a function of wavelength (lambda).  Do you have that?  
> >
> > As I understood, the P(:) function she gave is the intensity wavelength-dependent:
> >
> > P(sigma)=P0*sqrt(B)*exp(-pi*B*(sigma-sigma0).*(sigma-sigma0))
> >
> > Bruno
>
> ------------------------------------------------------
> OK good. Then if she knows P0, B, and sigma0 (which is lambda at the
> center wavelength) then she's all set. She just needs to convert
> P(sigma) to an index in the loop over sigma, and do
> gauss(i,j, wavelengthIndex) = exp......


thank you for your help

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