Download RE: [interferometry] Re: LUPI - Shack variation Ric: The original

RE: [interferometry] Re: LUPI - Shack variation
Ric:
The original paper states the focus of the lens lies just outside
the face of the cube with spacers added for the pinhoe.
Yes, my explanation was a bit over simplified.
> I can give you part numbers for an off the shelf lens and cube from
Melles
> Griot if you are planning to build a Shack cube.
Yes that would be interesting and appreciated,thanks,
Here are the Melles Griot part numbers:
Plano convex lens: 01 LPX 137
Beam splitter cube: 03 BSC 011 or 03 BSD 014 depending on which AR coating you choose.
FYI, you have to polish the AR coating off the plano side of the lens and the surface of the cube that you
will cement the lens to. If you don’t do this you will get strong interference fringes at the lens/cube
interface. Speaking from experience…
James
---------------------------------------------> Because the pinhole and focus of the reference surface lie on the face of the cube, the beam splitter
cube does not add spherical aberration to the diverging/converging beams. And,& since the test beam
exiting (and then re-entering) the cube is a spherical wavefront, all rays leave the cube perpendicular to
the air/glass interface at the spherical reference surface (lens), therefore there is no refraction at the
air/glass boundary and hence no spherical aberration added.
I have the original paper somewhere, and from memory a small space ( 3mm or so ) between the prism
faces and source/focus is of no consequence, and less prone for the instrument to be rendered useless
by a single piece of dust. It must be remembered too that the Fizeau interferometer is not an optical
system operating in the way that a telescope is. Some spherical aberration in the system , behind the
reference surface, is allowable because the shape of the fringes is already determined by the
interferometer cavity. The Twymann - LUPI configuration doesn't have that luxury as the optical quality of
most of the optical elements will have a direct impact on the measurement.
Consideration of a Shack cube was made, when I built my interferometer 10 yrs ago, but decided on
the Ceravolo variant ( which could almost be described as an `air-spaced' Shack) , simply because of the
ease of changing reference surfaces with different AR coatings for single and double pass testing
situations.
~Mark
-------------------------------------------We have several shack cubes. Each has a different coating on the reference surface to match a specific
test arrangement, e.g. coated vs. uncoated.. As you may know, fringe contrast is a challenge in the
Shack. It’s tough to find a coating to match a specific test arrangement. Ideally you want 1:1 intensity
between the test and reference beams. This is tough to achieve with the Shack. Lack of coherence in our
HeNe laser compounds this problem. I just set up our Shack cube for uncoated mirrors for use with our
new continuous wave stabilized laser. In fact the glue is drying as we speak. I’ll have my first shot at
testing some finished 15” and 18” mirrors with the new laser tomorrow. Hopes of high (or at least higher)
contrast are high as this laser has a much longer coherence length than the typical HeNe laser. It also
puts out 4x the power so I’m hoping there is enough brightness to image the pupil of the mirror under test
onto a fine ground microscope slide for re-imaging by the CCD camera.
James
-------------------------------------------Re: LUPI is up and operational
> Could you elaborate on your comments below? I am currently using A Shack
> (Fizeau) interferometer and projecting fringes directly onto a CCD chip with
> no intervening optics.
Without "re-imaging" the pupil on the CCD there are a few interesting issues
that crop up.
These issues are important to me because at EUV wavelengths (where I work),
there really
are no re-imaging optics that one can use. So I'm always projecting the pupil
onto the
CCD without intervening lenses.
The first issue is diffraction. Since you're "out of focus," all of the features
get blurred out.
But it's not blurred in the "smeared" sense of the word. It's actually that your
nice sharp
pupil is convolved with an out of focus pattern that leads to ripples. Ripples
form because
of short range interference. It's similar to the ripple patterns you see in a
Foucault test
when the knife edge is out of focus. Edge diffraction is a good example of this.
So you
might have to throw away some data near the edges, and that's not ideal.
A second issue is one I haven't seen discussed widely. If there's no additional
re-imaging
lens, then (depending on your NA or f/#) you're projecting a spherically
diverging beam
onto a planar detector. There is a coordinate distortion that occurrs as you
transform from
angle space (natural to the spherical wave) to the linear space on the CCD. The
distortion
takes a perfectly regular, unifotm tilt fringe pattern and makes the fringes
appear more
widely spaced near the edges. Off the top of my head, it's the ArcTangent that
you need to
correct for.
The correction can be applied at different points in the analysis. Since I write
my own code
for Zernike polynomial fitting, I actually "distort" the radius value in my
analysis. Then
there's no second step, the Zernike fitting takes place in the coordinates of
the spherically
diverging wave.
One more note on diffraction. A Lawrence Livermore physicist named Don Phillion
whom I
collaborate with, makes the extra step of mathematically removing the effects of
diffraction using a numerical propagation routine. Since the interferometer
measures the
amplitude and phase of the wave at every point in the CCD, he can (in principle)
calculate
the amplitude and phase of the wave at any other place in his system. He uses a
Fresnel
transform, I believe. It's like a Fourier transform but you keep the quadratic
terms. If you
look into it, you'll quickly find that it takes a LOT of CPU horsepower to
perform those
calculations.
Ken
--------------------------------RE: [interferometry] Shack / Fizeau Contrast Problems
Kurt:
Yes, I did buy the laser from Mr. Gizmos. It was pulled from some sort of graphic printing machine…
James
James Mulherin
President/Master Optician
Optical Mechanics, Inc.
jcmulherin@...
www.ProSpecMirrors.com
Tel: (319) 351-3960
Fax: (319) 351-3943
From: sentto-12361731-125-1081230420-jcmulherin=opticalmechanics.com@...
[mailto:sentto-12361731-125-1081230420-jcmulherin=opticalmechanics.com@...] On Behalf Of Kurt
Mihalco
Sent: Monday, April 05, 2004 10:17 PM
To: [email protected]
Subject: RE: [interferometry] Shack / Fizeau Contrast Problems
James,
Sounds like you’re gonna beat me to the punch! I’m still machining and assembling my interferometer.
I’ve done a lot of messing around with the Uniphase uGreen lasers, so feel free to contact me direct with
any questions. I’ll be glad to help if I can.
Regards,
Kurt Mihalco
mihalco@...
P.S. Did you get yours from Mr. Gizmos? I’ve seen him list pretty them regularly.
-----Original Message----From: James Mulherin [mailto:jcmulherin@...]
Sent: Monday, April 05, 2004 3:52 PM
To: [email protected]
Subject: RE: [interferometry] Shack / Fizeau Contrast Problems
Kurt:
Thanks a bunch for the tip. I just bought a Uniphase SLM uGreen single mode CW laser on E-bay for
$400. This includes the laser and controller. Now all I need is a 5V-10A power supply…
Looking forward to higher fringe contrast,
James
James Mulherin
President/Master Optician
Optical Mechanics, Inc.
jcmulherin@...
www.ProSpecMirrors.com
Tel: (319) 351-3960
Fax: (319) 351-3943
From: sentto-12361731-79-1080843354-jcmulherin=opticalmechanics.com@...
[mailto:sentto-12361731-79-1080843354-jcmulherin=opticalmechanics.com@...] On Behalf Of Kurt
Mihalco
Sent: Thursday, April 01, 2004 10:49 AM
To: [email protected]
Subject: RE: [interferometry] Shack / Fizeau Contrast Problems
Hi Jeff,
I think you hit the nail on the head regarding fringe contrast problems due to the coherence length of
multimode lasers. In the Ceravolo interferometer I’m currently in the process of building, I’m using a
surplus Uniphase green DPSS laser that operates with a Single Longitudinal Mode (>20M coherence
length), and *should* take care of the fringe contrast issues. I’ll report back results (probably a few
months off). These lasers come up pretty regularly on EBay for $200-$400 (usually pulls from surplus
equipment). Do a search on “Uniphase laser”, and look for 46XX, 47XX models, or those named
uGreen, SLM, and/or DPSS. New ones from JDSU are around $5K. Do your homework before buying
one, as the power controller / laser heads are adjusted for each other, and some sold are not necessarily
matched sets. See Sam’s laser FAQ for a whole bunch of info on these lasers. Links are:
http://repairfaq.org/sam/laserssl.htm#ssljuug
and
http://repairfaq.org/sam/laserstr.htm#strjuugt
Regards,
Kurt
Jeff wrote…
<<snip>>
The cause of this problem is multiple longitudinal modes running
simultaneously within the laser cavity. The longer the laser tube,
the more modes you will have. These modes cause a complete loss of
laser coherence every half cavity length, coming back into sync at
integer multiples of the cavity length.
So, when testing your friend's new primary in your Ceravolo rig,
you may or may not get fringes depending on whether the path length
difference between the reference and test beams is nearly an integral
number of laser tube-lengths or not.
<<snip>>
----------------------------------------------Even more Shack / Fizeau Contrast Problems
--- In [email protected], "James Mulherin"
<jcmulherin@o...> wrote:
> Jeff:
>
> Which do you think is the bigger factor with regards to fringe
contrast?
>
> a) Matching the test and reference beam intensity
>
> b) Coherence of the test and reference beam
>
> Another factor is matching the polarization angle of the test and
reference
> beams. Do you think this is as big a factor as a and b above?
>
James:
Think of the problem this way... To get really high contrast
fringes, you need really good cancellation of the test and
refence beams where you expect a black fringe. This means that
the two intensities much match, the direction of linear
polarization of the two beams must match, and the phase difference
must be exactly 180 degrees. Easy right?
If your test beam is too bright (such as when testing an aluminized
mirror with an uncoated fizeau reference) then you can mathematically
break the test beam into two components... one that matches the
intensity of the reference and causes a perfect black fringe, and
a "left over" component that shines through and kills the contrast.
Likewise, if the direction of polarization is slightly off, you can
decompose the offending beam into a component that strictly matches
the polarization of the other beam, giving perfect contrast, and an
orthogonal polarization component that shines through and kills the
contrast.
For longitudinal modes, you can think of the beam decomposed into
each individual mode. Each mode creats its own interferogram. And
each interferogram is phase shifted as compared to all of the other
interferograms. Superpose them all together and you get a mess.
In my humble opinion, I don't think that the polarization angle
issue is a big one for most AI's (amateur interferometrists). You
can experiment with crossed polaroids in the test leg to see this
effect and the effect of beam intensity mismatch.
The best way to demonstrate the cavity length effect is to mock
up a Twyman Green with parallel beams and with the reference
element on a sliding rail and see it for yourself. Its pretty
convincing when you see it in person.
Regards... Jeff
--------------------------------------Shack / Fizeau Contrast Problems
--- In [email protected], "James Mulherin"
<jcmulherin@o...> wrote:
> I am designing an interferometer that will polarization rotation
> techniques to improve fringe contrast. Any insights you can share
> in this area would be of great interest to me. As you probably
> know, getting good fringe contrast from a Shack cube is a
> challenge.
>
> James
Hi James:
I have some experience with Shack interferometers, and I am not
particularly fond of the topology. It suffers from the same issues
as the Ceravolo (and all Fizeau) topologies built by amateurs,
namely unreliable fringe contrast.
Since the shortcomings of the Ceravolo and Shack layouts are not
often discussed, and perhaps not well understood, I'll spend a few
words here explaining the issue...
If you construct a standard Twyman green (dual arm) interferometer
and place the reference mirror on a linear slide, you will notice
that as you slide the mirror along the optical axis (changing the
reference arm path length) that the fringe contrast gets better,
then worse (almost fading out completely), then gets better again
as you slide. The period of this contrast fade-in fade-out cycle
always matches (exactly) the length of the laser cavity.
The cause of this problem is multiple longitudinal modes running
simultaneously within the laser cavity. The longer the laser tube,
the more modes you will have. These modes cause a complete loss of
laser coherence every half cavity length, coming back into sync at
integer multiples of the cavity length.
So, when testing your friend's new primary in your Ceravolo rig,
you may or may not get fringes depending on whether the path length
difference between the reference and test beams is nearly an integral
number of laser tube-lengths or not.
In any topology with a parallel reference beam and reference flat,
the path length can be adjusted via a sliding rail until maximum
fringe contrast is obtained. But with a spherical reference surface,
it must be placed at its radius of curvature from the diverger...
there is no adjustment of the reference path available. Likewise you
cannot adjust the position of the optic under test. Thus, you are
stuck with the possibility that your interferometer will not test
everything presented to it because the path length difference is
not an integral number of laser tube lengths.
I have witnessed for myself, several perplexed ATM's who after
successfully testing their own mirrors, cannot understand why their
friend's mirror does not produce fringes in the same test rig only
minutes later. The answer of course is in that 1/2 cavity length.
One solution for the Ceravolo machine is an assortment of references
with different focal lengths. Another solution for those with lots
of $$$$$ is to use a fancy stabilized single mode laser like Zygo.
Common path interferometers on the other hand, never have this issue
because by definition the reference and test legs are exactly equal.
Thus fringe contrast never suffers from this particular disease.
Hope this helps... Jeff