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Science Forum Index » Optics Forum » beam "distortion" by parabolic mirror
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| chibitul |
 Posted: Tue Nov 11, 2003 8:04 pm |
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Hi, suppose I have an ideal gaussian beam focused by an ideal lens. Now
the beam expands, and I use a parabolic mirror to colimate it and also
deflect it 90 degree at the same time. because I use an "off axis"
system (the input beam is at 90 degree in respect to the axis of the
parabola), the outgoing beam will be colimated (in geometrical optics),
but the wavefront will have some distortion (stretched in one side and
squeezed in the other side). Therefore the beam is not gaussian anymore
(profile is not symmetric) and I am not sure what happens as the beam
propagates. Could someone point me to the right direction (book, web
site, etc). I need to look a little deeper into this aspect and I need a
good starting point. Thanks. |
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| Bas |
| Posted: Wed Nov 12, 2003 6:07 am |
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Guest
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My first guess would be to treat the beam as a product of a gaussian
in x and one in y. Have the beam radii evolve with the standard
formulas, but now with two different versions for x and y:
amplitude ~ exp(-(x^2/wx^2+y^2/wy^2)
intensity ~ amplitude^2 !!
w(z)=w0*sqrt(1+(labda*z/(pi*w0^2))^2)
with the w0 the minimum beam radius at z=0
Use this formula twice but with different values w0x and w0y to get
wx(z) and wy(z). If you are unlucky the location of the beam waist
might even happen at different values of z.
Check any book on gaussian optics to check if i am right.
You might get some more complex aberations except from the 'elliptical
distortion ', but i don't have any experience with that. You would
probably need some optical system design software for that.
Good luck,
Bas
chibitul <ch1b1tul@eudoramail.com> wrote in message news:<ch1b1tul-8C2E58.20041111112003@newsclstr01.news.prodigy.com>...
Quote: Hi, suppose I have an ideal gaussian beam focused by an ideal lens. Now
the beam expands, and I use a parabolic mirror to colimate it and also
deflect it 90 degree at the same time. because I use an "off axis"
system (the input beam is at 90 degree in respect to the axis of the
parabola), the outgoing beam will be colimated (in geometrical optics),
but the wavefront will have some distortion (stretched in one side and
squeezed in the other side). Therefore the beam is not gaussian anymore
(profile is not symmetric) and I am not sure what happens as the beam
propagates. Could someone point me to the right direction (book, web
site, etc). I need to look a little deeper into this aspect and I need a
good starting point. Thanks. |
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| Bob May |
| Posted: Wed Nov 12, 2003 2:10 pm |
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Guest
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To send a beam offaxis, you need to use the offaxis part of the parabola,
not the central part of the curve. The beam needs to be on axis to the
parabolic axis in order to get rid of the distortions otherwise you are
looking at the offaxis illumination of a parabola which produces a lot of
coma in the modified beam.
--
Bob May
Losing weight is easy! If you ever want to lose weight, eat and drink less.
Works evevery time it is tried! |
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| chibitul |
| Posted: Wed Nov 12, 2003 7:09 pm |
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Guest
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In article <1068664249.620629@news-1.nethere.net>,
"Bob May" <bobmay@nethere.com> wrote:
Quote: To send a beam offaxis, you need to use the offaxis part of the parabola,
not the central part of the curve. The beam needs to be on axis to the
parabolic axis in order to get rid of the distortions otherwise you are
looking at the offaxis illumination of a parabola which produces a lot of
coma in the modified beam.
This is pretty clear. Maybe it wasn't so clear in my post, but yes, I
use an off-axis part of the parabola. If you draw a picture (be careful)
you will see that the distance between rays changes, although the rays
will stay parallel after parabola.
Another way to think of it is this: you have an isotropic point source
in the focus of the parabola. The light will be colimated and will exit
along parallel to the axis of the parabola. But the intensity will
decrease with distance from the axis; the strongest ray will be on axis,
the ways further away from the axis will be "weaker" (intensity wise).
back to my initial question:
So you clearly have a flat wavefront after the system I explained in the
original post (lens-parabola), but the profile of the gaussian beam will
be stretched in one side and squeezed in the other side. How does it
propagate??? |
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| Phil Hobbs |
| Posted: Thu Nov 13, 2003 9:19 am |
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chibitul wrote:
Quote: In article <1068664249.620629@news-1.nethere.net>,
"Bob May" <bobmay@nethere.com> wrote:
To send a beam offaxis, you need to use the offaxis part of the parabola,
not the central part of the curve. The beam needs to be on axis to the
parabolic axis in order to get rid of the distortions otherwise you are
looking at the offaxis illumination of a parabola which produces a lot of
coma in the modified beam.
This is pretty clear. Maybe it wasn't so clear in my post, but yes, I
use an off-axis part of the parabola. If you draw a picture (be careful)
you will see that the distance between rays changes, although the rays
will stay parallel after parabola.
Another way to think of it is this: you have an isotropic point source
in the focus of the parabola. The light will be colimated and will exit
along parallel to the axis of the parabola. But the intensity will
decrease with distance from the axis; the strongest ray will be on axis,
the ways further away from the axis will be "weaker" (intensity wise).
back to my initial question:
So you clearly have a flat wavefront after the system I explained in the
original post (lens-parabola), but the profile of the gaussian beam will
be stretched in one side and squeezed in the other side. How does it
propagate???
Gaussians are separable, i.e. an elliptical Gaussian is the product of a
narrow Gaussian across the minor axis times a wide Gaussian across the
major axis. It propagates just as you'd expect--its NA is bigger in
the minor-axis direction. All the Gaussian beam formulae apply.
Cheers,
Phil Hobbs |
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| Phil Hobbs |
| Posted: Thu Nov 13, 2003 9:22 am |
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Guest
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chibitul wrote:
Quote: In article <1068664249.620629@news-1.nethere.net>,
"Bob May" <bobmay@nethere.com> wrote:
To send a beam offaxis, you need to use the offaxis part of the parabola,
not the central part of the curve. The beam needs to be on axis to the
parabolic axis in order to get rid of the distortions otherwise you are
looking at the offaxis illumination of a parabola which produces a lot of
coma in the modified beam.
This is pretty clear. Maybe it wasn't so clear in my post, but yes, I
use an off-axis part of the parabola. If you draw a picture (be careful)
you will see that the distance between rays changes, although the rays
will stay parallel after parabola.
Another way to think of it is this: you have an isotropic point source
in the focus of the parabola. The light will be colimated and will exit
along parallel to the axis of the parabola. But the intensity will
decrease with distance from the axis; the strongest ray will be on axis,
the ways further away from the axis will be "weaker" (intensity wise).
back to my initial question:
So you clearly have a flat wavefront after the system I explained in the
original post (lens-parabola), but the profile of the gaussian beam will
be stretched in one side and squeezed in the other side. How does it
propagate???
Oh, one other thing. Off-axis paraboloids of any significant NA are
astoundingly sensitive to misalignment--for an f/1 paraboloid (25 mm
diameter, 25 mm working distance) at 0.5 um, the spot diameter is
approximately equal to the off-axis distance--go one spot diameter off
axis, and the spot diameter doubles!
Cheers,
Phil Hobbs |
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| Bob May |
| Posted: Thu Nov 13, 2003 3:46 pm |
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Guest
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Assuming a perfect setup (see Phil's comments), you will have a circular
beam off of the parabola and you should have a smooth gaussian beam. If the
setup isn't perfect then the beam will have the distortions mentioned.
--
Bob May
Losing weight is easy! If you ever want to lose weight, eat and drink less.
Works evevery time it is tried! |
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| chibitul |
| Posted: Thu Nov 13, 2003 7:59 pm |
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Guest
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In article <1068756365.288631@news-1.nethere.net>,
"Bob May" <bobmay@nethere.com> wrote:
Quote: Assuming a perfect setup (see Phil's comments), you will have a circular
beam off of the parabola and you should have a smooth gaussian beam. If the
setup isn't perfect then the beam will have the distortions mentioned.
Please check this out. As you can see, I have 5 incoming rays, at equal
distance from each other. after parabola, the rays are no longer at the
same distance from each other. the beam seems streched in one side and
squeezed in the other side. How do I simulate this effect?
Thanks! |
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| chibitul |
| Posted: Thu Nov 13, 2003 8:00 pm |
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Guest
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In article <vr7mg2jv977q05@corp.supernews.com>,
Phil Hobbs <pcdhSpamMeSenseless@us.ibm.com> wrote:
Thanks, but I am not worried about misalignment. what i am worried about
is the squeezed-streching effect, as you can see if you look at this
picture:
http://www.pbase.com/image/23277352
The incoming rays are at the same distance fron each other, no longer
thue after parabola :(
Thanks!
Quote: Oh, one other thing. Off-axis paraboloids of any significant NA are
astoundingly sensitive to misalignment--for an f/1 paraboloid (25 mm
diameter, 25 mm working distance) at 0.5 um, the spot diameter is
approximately equal to the off-axis distance--go one spot diameter off
axis, and the spot diameter doubles!
Cheers,
Phil Hobbs
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| chibitul |
| Posted: Thu Nov 13, 2003 8:01 pm |
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Guest
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In article
<ch1b1tul-244E3F.19590313112003@newsclstr01.news.prodigy.com>,
chibitul <ch1b1tul@eudoramail.com> wrote:
Quote: In article <1068756365.288631@news-1.nethere.net>,
"Bob May" <bobmay@nethere.com> wrote:
Assuming a perfect setup (see Phil's comments), you will have a circular
beam off of the parabola and you should have a smooth gaussian beam. If the
setup isn't perfect then the beam will have the distortions mentioned.
Please check this out. As you can see, I have 5 incoming rays, at equal
Sorry, i forgot to include the link!
http://www.pbase.com/image/23277352
Quote: distance from each other. after parabola, the rays are no longer at the
same distance from each other. the beam seems streched in one side and
squeezed in the other side. How do I simulate this effect?
Thanks! |
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