F110B Präsentation Dave Rowe

Bath Interferometer

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Bath Interferometer by Julien Vandermarlière




[edit] Introduction

The Bath interferometer was invented by Karl-Ludwig Bath more than thirty years ago and is derived from the Gates interferometer described in Malacara's book (Physical Optics & Light Measurement, Vol 26, Meth. of Exp. Phys.). The Bath interferometer differs from the Gates configuration by the addition of a small lens.

Bath interferometers are quite easy to build. It is a common path interferometer that uses a small lens as a reference surface generator. Since both the test and reference beams share a path through the air between the optics and the interferometer, some of the deleterious effects of bad seeing in this optical path can be avoided. W.H. Steel (Optica Acta, 1970, n°10, 721-724) noticed that in the common path interferometer "....both beams go through the system under test and vibration changes the two optical paths by the same amount."

[edit] Principle of Operation

For an introduction to interferometry and the Bath interferometer see Interferometry and Fringe Analysis

Image:BathRightAngle.png This diagram shows the right-angle version of the Bath interferometer. A collimated light source is divided by the beamsplitter into the (blue) reference beam and the (red) test beam. The reference beam hits the mirror under test, reflects from this surface and passes through the lens. It comes to a focus at F3. The test beam is expanded into a spherical wave by the lens, which has a focus at F1. The expanding beam illuminates the mirror being tested and comes back to focus at F2. The two expanding beams pass back through the beamsplitter and interfere at the detector. In practice, a complete optical system, not just a mirror as in the example above, can be tested by the Bath.
Image:DR_BathOriginal.png This drawing shows the original Bath configuration, with performance equivalent to the right-angle configuration. In this diagram the beams are drawn with zero width for clarity. However, in practice the beam configuration is nearly identical to the first figure. In this figure the lens is drawn in the upper beam. In the previous figure it was drawn in the lower beam. In the operation of the interferometer it makes no difference which beam the lens is placed in.

[edit] Measurement Astigmatism

Because the focal locations F1 and F2 are separated laterally by the beam-to-beam distance, measurement astigmatism is inherent in the interferometer. For most measurement situations the astigmatism is small enough to be tolerated without correction. For those situations where the astigmatism is large enough to be bothersome, it can be calculated and removed from the wavefront error analysis.

The measurement-induced aberration is determined by calculating the difference in path length between the longest and shortest distances through the optical system for rays that originate at F1 and terminate at F2. For the case where a mirror is being tested at its center of curvature, the path-length difference, OPD, attributed to astigmatism is given by



D is the diameter of the mirror under test
d is the beam-to-beam separation
R is the radius of curvature of the mirror
OPD is the path difference between the longest and shortest paths to the mirror that originate at F1 and terminate at F2

The following table gives the measurement-induced astigmatism for various beam-to-beam separations, when measuring a mirror at its center of curvature:

Wavefront Optical Path Difference in Waves at 550 nm for a Selection of Mirror Diameters and Focal Ratios
 150 mm f/6200 mm f/5300 mm f/4
6 mm beam separation 0.016 wave 0.020 wave 0.027 wave
8 mm beam separation 0.028 wave 0.036 wave 0.047 wave
10 mm beam separation 0.044 wave 0.057 wave 0.074 wave

See Aberrations in the Bath Interferometer for the mathematical analysis.

[edit] Examples

[edit] Bath FAQ

What parts do I need to build a Bath interferometer?
  • Optics
-- A small 50-50 cube beamsplitter, in the range of 10 to 15 mm for the right-angle Bath interferometer, and 20 to 25 mm for the Bath interferometer having the original beam-splitting configuration. Two right angle prisms can also be contacted together with an oil to form the beamsplitter, although this type of beamsplitting cube will not have equal intensities. For very small interferometers, a 5 mm cube might work well. In any case, one should carefully layout the interferometer before building it.
-- A light source. Since the Bath is a common path interferometer, almost any collimated light source will work. The easiest to use is probably a red laser pointer. Green pointers are more expensive, but provide a brighter image. That usually is a disadvantage because geen laser pointers can not be made to run in non-lasing mode, which can be useful to reduce background artifacts generated from coherence effects within the laser. For laser powers above 1 mW eye protection is recommended. See the section on laser safety. Non-coherent sources also work in the Bath because it is a common path interferometer. So, a simple LED, or a laser operated below lasing threshold also work well. If numerical nulling of a conic is desired, then the light source should have a well-defined, stable, and accurately known wavelength.
-- A small biconvex lens, about 10mm fl and 10mm diameter. The desire is to have the beams no further apart than about 7mm. The 10mm x 10mm fl lens will work well for 99% of all the mirrors you would test. However you can optimize as stated next. The focal length of the lens can be matched to both the optical system under test and the beam diameter from the light source. A shorter focal length (in effect a larger illuminating beam diameter) produces a more widely divergent test beam. Too large a divergent beam can be a disadvantage as well. That will create less contrasty or dimmer igrams but they usually are still usable. You can experiment on your own to optimize if you desire.
-- A small front surface mirror with aperture sufficient to fully reflect the divergent test beam. A small right angle prism works equally well and can be easier to mount since it has a wide base.
  • Mechanical
X,Y,Z stage. The stage can be made by hand if desired. The purpose of the stage is to position the interferometer to achieve the desired fringe pattern. The key features are fine and smooth control. These are not essential but are merely a convenience. The range of movement can be 1/2 inch or greater.
What are the sources of error that are specific to the Bath Interferometer?
The Bath interferometer suffers from astigmatism (but very small for most mirrors see table in above section), as it is inherently an off-axis interferometer configuration. The astigmatism can be removed from the wavefront analysis using techniques available in the OpenFringe or other analyses programs.
As a general rule beam separation should be kept less than 8 mm, as larger distances introduce more astigmatism as described in the introduction. An option is to grind down one side of the lens to allow closer placement of the two beams.
How critical are the components?
Most component surface figure is not critical because of the common path design. You can use cheaper components because of it.
  • Lens - The lens can be plano-convex as well. Odd clumps in the projected beam may indicate a bad glass melt. You can test the lens by taking measurements with the lens one way and then reverse it to see if it changes the results.
  • Beamsplitter - A beamsplitter does not have to be 50/50 for using Port A of the original Bath configuration.  :
    Bath Original config Port A
    Bath Original config Port A
    However the right angle version must use a 50/50 beam splitter for highest contrast fringes.
 Right_Angle Configuration
Right_Angle Configuration
Given a choice of beamsplitter sizes what is best?
Generally smaller is best. Smaller is best for testing fast optics less than f/4. A 15m cubes is typical. However, there is a tradeoff. Smaller cubes can vignette the rapidly expanding beam from the lens or mirror. Larger splitters prevent the camera from getting close to the focus of the interferometer lens and may cause vignetting by the camera lens.
Where can I get the parts?
Surplus Shed and Edmund Optics are good sources.
www.ukaoptics.com For Webcam modifications.
Do cheap beamsplitters from suppliers such as Surplus Shed work?
Yes, however they work best with the right angle version and a laser poiner. When using a laser pointer you must rotate the laser to achieve equal beam intensities because the cube acts as a polarizing filter and changes the intensities of the polarized laser beams exiting the splitter. This is worse with the original Bath configuration but happens with the right angle version as well. This may be true for any beamsplitter and not just those from Surplus Shed.

When red laser pointer are operated below the laser mode voltage, the light is not polarized.

Are gas lasers better than laser diode pointers?
They can be but usually have a smaller beam diameter so they have to be expanded more than a laser diode beam. They are larger and can pose a problem if stage positioners are used due to weight.
My laser pointer has a rectangular beam. Will it work?
Yes, however you must make sure that the lens will expand the narrow part of the beam to cover your mirror.
What is critical about part placement?
No part placement is critical. Beam separation distance needs to be watched.
  • Lens to beamsplitter distance is not critical. The range is between 1/4 inch to 3/4 inch. The tradeoff is that the closer the lens is to the splitter the less likely it is that part of the expanding beam will fall outside the splitter.
  • Right angle mirror placement - For the right angle mirror configuration the mirror should be placed close to the front of the cube to minimize beam separation. That also means that the laser beam should enter close to the front as well.
What adjustment do I need on the optics?
Apart from the stage to move the whole interferometer, no adjustments are needed for the optics. It is helpful to be able to move the lens and laser left/right/up/down in relation to each other. For the right angle configuration, once the beams are made parallel and close together the cube and mirror can be glued down. Double sided adhesive tape can also be used. First make sure the two bright reflections are not in the fringe pattern. (See two bright spots below)
I get two bright spots in the middle of my fringe pattern. Can I remove them?
All Bath interferometers exhibit them, due to internal reflections from the laser. These spots can be eliminated from the fringe pattern by rotating the cube a few degrees.
How do you align the optics?
  • Initial setup for right angle version--
  1. Start without the lens and get beams parallel and as close together as possible. Hold a piece of white dull paper in front to see the beams as they exit.
  2. Insert lens into beam and visually adjust it or laser so that outgoing beam is in center of the lens. Hold a white card about 1 foot in front of the interferometer. There will be a large diffuse beam and a bright laser beam. The bright laser beam should be about the same distance from the center of the diffuse beam as the beam separation coming out of the interferometer. If it is not then adjust the lens or laser position until it is. Move the card further away from the interferometer and again make sure the beam centers remain constant. The beam from the lens will continue to expand while the other beam should remain close to its center.
  3. Find the return beam from the test mirror at the front of the interferometer by placing a white card at the front of the interferometer so that it does not block the output beams. Adjust the system so that the return beams fall on the card not into the lens of the interferometer.

Move the interferometer toward or away from the mirror under test until the focused beam from the mirror under test is 1/8 inch or larger in diameter. Inspect it for even illumination. If illumination is not even or round then try adjusting tiny lens or laser to make it so.

  • Getting fringes
move the z control until the expanding return beam is about 1/16 of an inch in diameter on the front of the interferometer.
Move the X,Y stage controls (left, right) to position the unexpanded return beam off of the card and into the center of the lens. The expanding return beam will enter where the reference beam came out of the interferometer.
Use a white paper or card screen or a ground glass at the exit port to see a projected image. You should see two bright regions that may overlap. One region will be much larger than the other. Adjust the X,Y stage controls until two bright diffuse circular regions overlap. Ignore the two very bright dots. You may now see fringes or you may not. Next play with the controls until you see fringes. You may need to let it settle a second after you make an adjustment. Usually it is easier to see fringes by beginning with the interferometer outside of focus and slowly bringing it closer to focus. What you need to look for is a black dot that has a ring around it that fades in and out (or seems to pulsate)--this is the first fringe seen. Slowly move the interferometer toward the mirror. This "bull's eye" pattern will expand to cover more of the mirror as you get to focus. As you bring it closer to focus the fringes will drift outside of the view and you will need to use the X/Y/Z controls to bring them back. You will notice that depending on which (X/Y/Z) axis is very gently turned, the bullseye will expand to more linear fringes (which is what you want).
If you are using a laser diode below the lasing threshold then you can look into the output. It is much easier to see the fringes that way than through any camera. When not using a laser diode and not below lasing threshold be cautious here--it is strongly advised to view the fringes on a computer monitor or the output of a digital device, camera, etc. Camera positioning does play a factor in viewing the two return beams so that they seem to overlap and produce fringes. The digital device can use its own positioning stage at times in some setups to correctly view the overlapping beams. Tilt in the image, caused by misaligned camera position, can produce an elliptical mirror shape instead of the ideal circular one; that will influence the results in subsequent software analysis. The highest return intensity results for the 50/50 beamsplitter: The intensity will be half the maximum intensity of the laser * the reflection coefficient of the mirror.
My interferograms do not look as smooth as I want. What can I do?
  • If you are using a diode laser you can reduce the voltage until the diode stops lasing and is just a red diode.
  • Clean all of the optical components. Dust in the system causes diffraction rings.
  • Some laser pointers have a very cheap plastic lens with bubbles or residue on the surface that make them less than ideal. They are still usable but make the fringes bumpy. Some laser pointers allow the lens to be removed. If you can--without harming the lens housing--inspect the surface of both sides of the plano-convex lens with a 25mm or so eyepiece and see if there is any film or residue on the surfaces remaining from the casting process that has trapped dust particles, hair, etc. Use a soft tissue (the plastic is soft) and gently wipe the surface to remove veins,spots, or cloth dust marks. This can improve the beam quality. After you are able to get fringes you can look for a better laser pointer. Higher priced pointers can also have surface defects or residue on the lens surface so check them, too.
I can not see all of the fringes because the intensity falls off at the side.
You may need to adjust the lens so that the illumination is even on the mirror under test.
The images below show the results of uneven illumination.

Another source is vibration of the mirror on the stand.

How can I tell when laser diode is not in lase mode?
Reduce the voltage until the laser beam stops being rectangular and looks more circular.
What are ways to image the interferograms and turn them into digital pictures for analysis?
The ideal camera would let you preview the fringe pattern with good resolution and in real time. This is not a requirement but a real convenience when adjusting the interferometer controls.
  • Web cam - Webcams typically have too short of a focal length lens but work well if the lens is replaced by a longer focal length. It is possible to remove the webcam lens and place the body in back of a 35mm SLR camera lens (35mm or 24mm wide angle lens). One needs to make a holder for both the webcam body and the 35mm lenses to hold them in position. They usually have real time high resolution preview when attached to the computer. Older web cams might have lower resolution and the images will not be as sharp/clear as newer webcams or digital cameras.
  • Digital Camera - Can work well but usually does not have a high resolution real time preview. Sometime the zoom lens on a digital camera will vignette the image. Two digital SLR cameras that are known to work well are the Cannon Digital Rebel and the Nikon D40. Other digital SLR cameras will probably work as well. Their advantage over point and shoot cameras is their wide lens opening and ability to use manual control. Manual control of focus and exposure is probably a must for any digital camera that will be used. A fast shutter is sometimes also needed to stop vibration-induced blur. 1/200 of a second works well with most laser pointers sources.
  • Video Camera - Many Video cameras are not ideal because their zoom lens vignettes the beam, but they have been known to work.
My web camera lens is too wide angle and makes the interferogram too small to analyze. How do I make the image big enough?
One way is to replace the lens with a longer focal length lens like the 12mm and 25mm FL shown here from Edmund.. Most web cams can be taken apart and the lens removed to reveal a M12 X .5mm threaded lens holder. Some of the 25mm lenses may have too long of back focus and will not focus using the lens holder in the web cam. You will have to make some sort of adapter. Another cheap way, is to put a 25mm lens used on an old 8-16mm camera. It use a "C" mount. There are many on eBay.
Make a magnifying relay telescope and place it between the interferometer and the web cam to magnify the image. Low power finder scopes can be tried. Ideal would be to aquire a 50mm achromat coupled with 24 to 55mm eyepieces.
My zoom camera lens vignettes the fringe image. What can I do?
  • Get as close to the beamsplitter as you can. Almost touching it is best. If that does not work then see below.
  • Make a reducing relay telescope and place it between the beamsplitter and the camera.
  • Try a different lens.
What is a collimating telescope?
The collimating telescope and "Kepler" telescope described by Dave Rowe and Wolfgang Rohr in their Bath interferometer pictures can be made from two positive lenses. One lens is up to about .5 to .9 the focal length of the other. It reduces the expanding beam so that it can be captured by a camera with a small diameter lens. The shorter focal length lens is placed close to the interferometer output.
What is a beam expanding telescope?
A beam expanding telescope increases the diameter of an input beam. This may be useful in a Bath interferometer to increase the beam width so that a higher numerical aperture (lower f/ratio) optical system can be tested.
It consists of a small negative lens, which diverges the input beam, followed by a positive lens, with re-collimates the divergent beam. The diameter of the positive lens must be slightly larger than the desired diameter of the expanded beam. The virtual focal point of the negative lens must coincide with the real focal point of the positive lens to achieve collimation.
Here is an example of a 16X Galilean beam expander with very good optical performance that can be built from off-the-shelf cemented doublet lenses from Edmund Optical, Inc., website Edmund Optics. The small laser beam to be expanded enters from the left, and emerges about 16 times larger in diameter. The airspace between the two lenses has been optimized to give good collimation for the different laser wavelengths listed. The lenses must be oriented as shown in the drawing, and very well centered to each other.
Image:Galilean Beam Expander 600 x 300.gif
Galilean Beam Expander using Edmund Optics lenses.

Another way to expand the beam of diodes is to use two idential prisms in what is termed an "anamorphic pair"--two identical prisms mounted at an incident angle.

What is the wavelength of a red laser diode pointer?
There are three different wavelengths 635, 650, and 670nm. 650nm is the most common. Some pointers will have a label with a range that includes more than one of these wavelengths. A small sample of 5 measured in Dec 2006 were 650nm except for a very old one that was 670nm.

Laser tubes HeNe run at 632.6nm

[edit] External Links

Tutorial on the Bath interferometer and interferogram analysis software by Michael Scherman
Bath Interferometer (in German)
Original publication by Karl-Ludwig Bath in the german astronomical magazine "Sterne und Weltraum"
reference: Sterne und Weltraum, 1973/6, p.177-180:
German, high res 1988KB, German, low res 1285KB
English, high res 1047KB, English, low res 408KB
Comparison of Real Foucault Images of a Telescope Mirror and Simulated Foucault from Interferometric Data
Introduction to Interferometric Optical Testing (Modern Optical Testing)
Interferometry and Fringe Analysis
James Lerch ATM Pages
Bath Interferometer Usage Dialog
Quantifying Surface Features visible in a Foucault image
Bath Interferometer, Surface Analysis, and the inventer
Optical Testing
Charles Rydel site about Bath Interferometer

Fringe Analysis Software :

Atmos fringe

Interferometric simulator :