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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