Collimating mirrors

rzeheb · Post by **rzeheb** » Fri Jul 17, 2009 6:10 pm

O.K., here's a nubie question: Must the collimating mirror be parabolic or will spherical work? If both work, what are the pros/cons?

BobH · Post by **BobH** » Sat Jul 18, 2009 2:00 am

A spherical mirror is best when you want to go from a diverging beam to a converging beam. Use a parabolic mirror when you want to go from a diverging beam to a collimated beam. Both are made to be used on axis. If you must tilt it to use it, tilt it as little as necessary to avoid aberrations in your holograms.

rzeheb · Post by **rzeheb** » Sun Jul 19, 2009 11:35 am

Thanks Bob. Exactly what I needed to learn.

Colin Kaminski · Post by **Colin Kaminski** » Thu Aug 06, 2009 3:53 pm

BobH wrote:A spherical mirror is best when you want to go from a diverging beam to a converging beam. Use a parabolic mirror when you want to go from a diverging beam to a collimated beam. Both are made to be used on axis. If you must tilt it to use it, tilt it as little as necessary to avoid aberrations in your holograms.

Because we have to use these off axis I was under the impression the the spherical aberration was less than the coma aberration and you would use a spherical for both applications. Why would one choose a parabolic for a collimating beam?

BobH · Post by **BobH** » Fri Aug 07, 2009 1:26 am

Colin Kaminski wrote:Because we have to use these off axis I was under the impression the the spherical aberration was less than the coma aberration and you would use a spherical for both applications. Why would one choose a parabolic for a collimating beam?

For the same reason a parabolic is used for a telescope!

Colin Kaminski · Post by **Colin Kaminski** » Fri Aug 07, 2009 5:51 pm

But, since I am using the mirror 10 degress off axis is not coma the cominating factor? I only have access to parabolic mirrors but I was always thinking a spherical would be better.

BobH · Post by **BobH** » Sat Aug 08, 2009 12:24 am

I'm pretty sure you'll get coma using a spherical mirror off its axis too, but you'll have spherical aberration as well. If you use a parabolic mirror off axis to make an H-1, then use the same mirror at the same angle to reconstruct the real image for making an H-2, you'll cancel out the coma and astigmatism. I don't think that's true for the spherical aberration.

Kaveh · Post by **Kaveh** » Sat Aug 08, 2009 8:47 am

BobH wrote:...If you use a parabolic mirror off axis to make an H-1, then use the same mirror at the same angle to reconstruct the real image for making an H-2, you'll cancel out the coma and astigmatism. ...

Bob, I am not sure about that. I think you will just add more in the second stage...

BobH · Post by **BobH** » Sat Aug 08, 2009 2:38 pm

Here's a sketch to explain:

If you make the hologram (H) with the recording reference beam shown in red, you'll have coma and astigmatism in the image. If you reconstruct that hologram with the beam path shown in blue, you'll have exactly the opposite aberrations. That's why, if two matched mirrors are used, you get an unaberrated focal point after going through the whole system.

The sketch shown is functionally the same as if one were to pitch the hologram over and reconstruct it with the recording path. That's why the coma and astigmatism in the image recorded by the hologram are corrected in the reconstruction process, if the geometry of the reference beam is maintained.

Kaveh · Post by **Kaveh** » Sat Aug 08, 2009 4:13 pm

Bob, I am not convinced. I think the aberrations will add, rather than cancel. Hard to explain, but let me try...

If there are no aberrations at all in the first collimated beam, then all rays will be parallel after reflection from the mirror. But we know there will be aberrations, so not all rays will be parallel. Suppose there is astigmatism, which easier for me to visualize. This means rays in one plane will be parallel while those in the perpendicular plane will not.

For the sake of argument, let us suppose that there is a slight divergence in the collimated beam, as we look at the beam the way you have drawn it. In the perpendicular plane they will be parallel.

For reconstruction, we need the opposite, i.e. converging in the first plane, but parallel again in the plane perpendicular to that. But in your diagram, the first set are again diverging, so we will not get a perfect reconstruction.

What you want is a complete time-reversed beam in the reconstruction, but you are not getting that in this case.

Hope I make sense. If not I will produce a diagram.