Bath interferometry

Foucault testing gives a fairly quick assessment of how far the correction of a mirror has progressed, but in essence it is a subjective method. The judgment of when the shadows are equal on both sides of the Couder mask is subject to interpretation, hence the postions may suffer from observation bias.
Interfererometry is a much more objective method, and gives very repeatable results when the quality of the interferograms is good enough. A Bath interferometer is fairly easy to build and, being a common path instrument, it is also relatively insensitive to external influences like vibration. The excellent analysis software, DFTFringe made by Dale Eason, makes the path from interferogram to surface analysis very straightforward. Download the latest versione here.
Please refer to the Interferometry group for excellent help by a great users community. The website gives access to a mailing list, a wiki and lots of background information. It is highly recommended for starters to join this group.
Finally there is a document about Bath interferometry available for reading/download on my Articles page.

Below follow some considerations and design choices and also a way to determine the wavelength of your laser:

My Bath tester

At the time I built my first Bath interferometer I needed to test a couple of very fast mirrors. This immediately revealed a shortcoming of the simplest setup, the testbeam lightcone was not wide enough to cover the mirror. The divergence of this cone is determined by the focal length of the diverging lens and the width of the laserbeam. For this reason I removed the original lens from the laser, and replaced it with a film projector objective. An alternative could be a 10mm to 20mm eyepiece. The laser source is placed exactly in the focus of this objective, and hence the beamwidth is determined by the laser divergence and the objective focal length. Finally I inserted a diaphragm of about 5mm to limit the beam width in a controlled way.

My Bath is set up as in the schematic and photos below. The test head is mounted on a X-Y-Z translation platform, equipped with micrometer adjustments. Here the test setting is shown, albeit with a previous version of the tester.
It is important that the tester is heavy, mine weighs about 1kg, in order to minimize vibrations. Also it is desirable to have sufficient degree of freedom in camera positioning, especially when the mirror is very fast. This means that the camera objective must get very close to the splitter cube.


On the picture below you can see how I make the interferograms. The tester is behind the camera, the mirror is at some distance to the left. The camera LCD shows the mirror as it will be captured. When things are set up correctly, the brightly lit mirror can beseen inside a larger circle, which is the diverging reference beam. The mirror should be somewhere in the middle of this reference beam for best fringes. I zoom the camera fully in and set it to 400ISO, manual focus on the mirror, 2-sec timed exposure and a shutter speed of 1/15.


New and more compact Bath setup

The tester with the beam expander, as shown above, has proven a good concept. I decided to make a more integrated design, with a proper laser collimator and a larger diverging lens. The design is about 5cm across, including the expander. Since it is more compact and lower in weight the setup is less prone to vibrations too.


The laser is still the 5 for $5 from DealExtreme, the lenses are Surplus Shed parts: PA1035 for the collimator and PA1098 for the diverger. The beams are now a luxurious 6mm in diameter, through the 7.5mm by 10mm focal length biconvex diverger this delivers a better than F/2 ratio cone. It should be sufficient for the most daring mirrors...
The beamsplitter is now placed closer to the edge, so the camera lens can almost be pushed against it. I have re-measured a known mirror yielding identical results, so the tester works as it should.

Recently I have exchanged the laser with an Osram PLT5-510, approximately 515nm at 10mW. To enhance the contrast the laser die was oriented at a 45° angle. Below image gives the result on a 12" F/3 spherical mirror.

This gives a nice example of what to expect. It is taken with a Canon 450D DSLR, at 1600ISO and 1/250 sec. The large circle is caused by the vignetting of the camera objective (f is appr 55mm), anything else should be within, ideally centered and also centered on the sensor area. Some other circles are probably caused by internal reflections in the splitter cube or camera. This is also the case with the pair of bright spots, but these can be moved out of the igram by rotating the splitter a bit. Then a lot of diffraction spots can be seen (like drops in water), which are caused primarily by dirty optics.

These days I use an even faster exposure, of 1/1000. To be able to do this, I have to increase the laser power.


How to determine the laser wavelength

The laser that is used in the Bath interferometer is an el-cheapo deal extreme offer of 5 pcs for $5. This is really a bargain, but you can not be so sure about the laser wavelength. For this reason I have deviced a test to measure this wavelength. The test is based on a grating made of an old CD, with the aluminium removed, of which the period is referenced to a known wavelength from a fluorescent light bulb.
Care must be taken to use the CD tracks where they are vertical, i.e. along a horizontal line that would end in the center of the CD.


As a source I use a fluorescent light in a box with a frosted glass window and a small hole in the focus of a collimation lens. The lens projects this hole into a parallel beam, directed precisely over the hartline of the rail. The grating is placed in front of the lightsource, and when positioning the eye at the right spot you can see the white central beam and the first maximum of the different colors somewhat sideways as in the schematic below:

When you realize that constructive interference only happens when the path difference is an integral number of wavelengths, it is easy to deduce the relationship between grating period d, wavelength λ and angle α:
   sin(α) = λ/d

The angle α can be calculated from the setup as shown in the drawing:
   α = arctan(s/L)

In case of the yellow hydrogen line (546nm) the calculated value was approximately α=20° and consequently the grating period d=1596nm, which is about what you would expect based on the CD standard (1.6μm).


The above images show the angle measurements for the yellow/green (546nm) Hg line, where you can also see the other lines.
With this way of measuring the grating needs to have a slit to better define the viewing angle. Another way to do this is with the grating close to the lightsource, and the ruler measuring s on the side of the eye, in that case you don't need a slit on the grating.

In both cases, after the grating constant is determined (I will use the standard 1600nm and consider the 4nm a measurement error), a second measurement is done with the laser in place of the fluorescent light. The measured angle in this case α=24°, and hence the wavelength can be determined to be close to 651nm. I think the accuracy is probably in the order of a few nm.
Using the same method, I determined my new green Osram PLT5-510 laser to be 517nm.


A Current Source for laser diodes

With the idea to try a LUPI (Laser Unequal Path Interferometer) some day in the back of my mind, and the need to supply my red HL6501MG laser diode I decided to design a stable current source. Stability is required when the Laser output must be stable in terms of wavelength; current noise as well as thermal changes will cause mode jumps. Note that a Bath interferometer can get away with far simpler ways of current limiting, e.g. a simple resistor.

The circuit consists of two stages: a voltage regulator and an adjustable current source.
The first stage converts, stabilizes and cleans the supply voltage to a value that is required to run the second stage. It is a basic voltage regulator circuit, mine uses an LM317 (1.25V) device in combination with a 4.7V Zener that lifts up the reference. Current through the Zener should be about 5mA, to be set by R1 (1.25/R1). The 1k I used seems to be a tad high, but it works nevertheless. You can also use a dedicated regulator that outputs the required voltage directly, as long as you don't forget the input and output capacitors. The level I chose is 6V, because this positions the working voltage of most laser diodes (3V) nicely halfway.
The second stage is the actual adjustable current source, based on an OpAmp voltage comparator and a transistor that supplies the set current. The best option for an OpAmp is one that has a rail-to-rail output swing. Many OpAmps will work in practise though, as long as it runs on the 6V (either single rail or +/-3V spec) and can generate output fairly close to the upper rail (6V). The NE5534 I used goes up to 5.5, which is just above the 5.4V pinch-off of the transistor.
On the + input of the OpAmp a reference voltage is set by the potmeter and fixed resistor. In the schematic the reference will vary between full supply level (6V) and supply level minus 15% (5.2V). On the - input the emitter of the transistor is connected, which will be on a level of supply voltage minus the voltage drop over R3. This drop is equal to the current*R3, so in case the current is 20mA, the voltage drop is 0.44V.
The OpAmp will adjust the base voltage of the transistor in such a way that the + and - inputs are on approximately the same level, so in the 20mA example the voltage on the + input has to be set to appr 5.56V (6V - 0.44V).

Note: You have to tune the circuit with an Amp meter accross the output before connecting a laser diode. To keep the collector voltage of the transistor above the laser working voltage the current adjust range is best determined with R3. So, if current does not get high enough, lower the value of R3. If current gets too high, increase it a little. If you go for a higher supply voltage you may need to change R3 and R2 as well to get the range right. The indicated values give me a range of 0-80mA, which is just good enough to not blow up my new laser. Red laser pointer diodes need significantly less.
As input source I use a 9V wall wart. You could go to higher voltages, but then the LM317L may get hot at max current.


A PCB design has been made as well, measuring only 1.5" x 1.5"