This is a completely different line of thinking that does not involve an interferometer, but if you want to accuratley measure the absolute position of a CNC machine you could use an absolute magnetic encoder AS5047 chip. https://ams.com/as5047p They are under $10 and will give you 16,384 positions (14 bit) per revolution. Attach a pulley and a belt to the CNC head and you have a very accurate tape measure that could be used as a DRO and for servo position control.

http://massmind.ecomorder.com/techref/ecomprice.asp?p=416078

I would like to know 'how' to make a DIY inexpensive z-axis stage for my Nikon MM-11 (frankinscope) with epi illumination and Wyko Interferometer objectives and have the encoder read out the position for vertical scanning Interferometery.  I have everything I need except the stage (and knowledge).   I'm not a physics guy,  just an inquisitive uneducated DIY'er in  interferometry.  

Hi all, i would like to try interferometry by self mixing technique according to this paper here:

https://www.researchgate.net/publication/261243145_Progress_on_Self-mixing_Sensors_for_In-situ_Displacement_Measurement

I personally prefer the self mixing technique as it would allow low part count and self alignment and it can be fabricated on a single compact PCB. By your experience, may there be any performance differences, by inspection of this setup and the Mikkelson interferometry method.

Thank you.

Awright, I typo'ed the title, which means the link is typo'ed as well. Mea culpa, I'm not going to change it.

It would be interesting to see if the recorded error measurements on a CNC machine, using internferometry, were repeatable becuase if this was the case the noise profile of each axis could be recorded and then used to correct deviations for each XYZ point within the machine's range of movement.

I just now had a conversation with a friend, and we came up with a way to do absolute positioning using laser interferometry. You wouldn't be able to measure travel as it happens, but if you were willing to stop and let the vibrations settle down our proposed system would tell you the absolute position to within a wavelength.

I've been looking into the linear CCD chips used in scanners (got a couple off of eBay). They've got good resolution (5000 px/in), and are easy to interface to an Arduino. Could measure fringe position to a very fine resolution, and send the results over a serial port.

If only I wasn't in the hackaday prize contest, I'd run off and try some things out. Have to put this off a couple of months.

You just need to count the pulses and pulse timing, the position is a statistical entity anyway, wavelets may give you the full range from ideal position (the perfect machine) to the very dynamic true position. Why do it in hardware when you can do it with maths?

I agree that counting pulses is the way to go, but any vibration will scatter the interference fringes and you won't be able to count them as they file past.

The upshot is that you can't count them while moving (too much vibration), and when you stop you know where you are within a fringe, but don't know how many have passed by.

Yes you need some form of differential measurement to stabilise the system enough. The logic used in noise cancelling headphones may be of use. Remember you need to measure in three dimensions anyway so the system should be able to pull itself toward a local 0,0,0 to eliminate the noise, that would then leave you with the true X,Y,Z pulse count, the ideal position mesurement.

Instead of counting pulses, use a matched filter. Use an ADC channel to get brightness and do correlation with a pre-recorded fringe and find where you are in the fringe to a very small fraction, noise allowing. You should be able to count while moving; that is how a Fourier Transform spectrometer works. Robert Forward at Hughes Research used gas lasers in the late 1960's and measured sub-angstrom (I guess that means sub sub nanometers) displacements. He dithered the mirror position with a piezo driver to get a reference frequency. In those days they used lock-in amplifiers. Today you would do it in DSP software. This was for a space based gravity wave detector. I have the Hughes papers somewhere.

Two detectors give you phase and direction. You have to know which side of the null (equal path length) you are on.

So, given what we can do today with 8mm steel rod and upcycled optics and sensors from scanners, I would think count as you move and as fine positioning as you care to try for is doable. Question is, do you really need in interferometer? How far apart are the pixels in the linear array from a scanner?

Yes, this is called screw mapping. It is done when the machine is built, the screw has been changed or sent out for rebuild or if the control's memory gets wiped (Many machines, even recent, have battery backed SRAM). In the control there is a set of parameters and you enter the deviation at whatever interval it specifies. It uses this chart internally to adjust the position on the fly.

A simple algorithm like a Hidden Markov Model may suffice for learning to differentiate between in-motion signal and the noise in the system Peter Walsh described.
More hardware could be needed still, to either avoid a more complicated algorithm or reduce settling time. E.g. If we have an instrument grade laser, and a bunch of fiber optics and CCDs (no rolling shutter), we may be able to put multiple beams on each moving part and decompose signal and noise from their aggregate. This could be as simple as https://en.wikipedia.org/wiki/Joint_(audio_engineering)

The way Heidenhain's encoders work is by using a micro-engraved ruler which the laser reads, the exact same way as optical disk drives work except they use rulers with position data encoded on them instead of disks. This arrangement will however make the system sensitive to e.g. localized heating radiated from the end-mill.
Acoustic waves of several megahertz can travel through materials such as steel and high frequencies never cease to be a problem because of harmonics and resonance. Fluid bearings act as a low-pass filter.

The combination of instrument laser beams spanning the whole measured distance along with fluid bearings actuated without solid surface-to-surface contacts anywhere is the best system I know of for reducing the random variables of vibration and heat expansion. Compared to an optical bench, the surface here is like a convoluted stack of air hockey tables where the pucks are kept in place by raising and lowering the tables. The tables of course have complicated geometries, like screws. Alternatively more expensive linear electric motors with conventional fluid bearings can be used, but the requirement of no solid surface-to-surface contact has to be maintained...
I believe that the fluid film reduces the tolerance requirements needed to machine these components. That should make them cheaper to produce.

There are milling machines with scales built in, it is usually an option from the factory. Heat from the cutter is inconsequential, it is heat from the screws, motors, and spindles that you have to deal with (I used to be a tech working on CNC machines.) Higher end machines have oil cooled screws. Well, not really cooled, the temperature is regulated to match the temperature of the rest of the machine. 

Making a cnc machine with hydrodynamic bearings would be a mess and a pain and you would not gain anything. I am not aware of any thing other than specialized machines that use them. Modern linear guides are very accurate, have a long life and are much easier to design a machine around.  A modern machine with or without scales is more than capable enough to machine any part for an interferometer. There is nothing terribly precise in one, it is the laser that matters and all the cnc machines in the world won't make a difference there. 

Do you mean hydrostatic, or actually hydrodynamic?

I built a "weather station" for my HP-5528A system, and am very pleased with the results.  I will be sending my laser out for calibration in the near future, and then will be trying to compare measurements against a ceramic gage-block set.  I'm having a couple minor issues though...

***anyone know where to get connectors for the HP receivers.  The connector looks like a BNC shell with four pins inside (two male and two female).

***has anyone used a wavelength compensator?  how does the accuracy compare to using a weather station?

***does anyone here have an understanding of deadpath error?  if so can you ELI5 to me?

Oh, I know those connectors and see them time to time. What do you need?

I have some arbitrary goal; terraform Venus because there is more carbon, oxygen, and sunlight there than on Mars. - I'll want to dim the sun a little bit, so I need to build a sunscreen band around the planet. To do this I put an atmospheric heater like HAARP in low Venutian orbit and attempt to get some CO2 into this orbit, and I use the carbon to build the sunscreen out of that. 

This would obviously require an extraordinary effort to accomplish. Somewhere in this effort I am sure to require linear encoding at single nanometer precision, e.g. to measure thermal expansion of a million moving parts at once. So, I'll need a lot of interferometric linear encoders of high quality and low manufacturing cost. The more & better I can measure, the more likely the mission is to succeed. 

Since We have already proven that low cost & high quality interferometers can be mass-produced with optical disk drives, so this part of our vast engineering effort should at this stage be one of the least challenging tasks. Because of my goal, I am _strongly_ motivated to research how one might turn this off-the-shelf tech into something space-worthy, while also making progress on turning space exploration into something commercially viable.

This complex should sink into the reader's mind for a few... It is intended to turn a question of 'why' into a question of 'how'.

The low cost and weight of the CD-ROM interferometer is central to this issue. The device needs to either be isolated from harmful vibrations or backed by state-of-the-art & application dependent digital signal processing. Both of these tasks seem daunting for a lone hacker. - Is this the reason we are gathered here?

To be useful for metrology purposes the lasers need to be stabilized. That does not happen cheaply and especially not with DVD diodes. 

You're right... I have more confidence talking about industrial lasers than instrument lasers. For this though, should not one laser and many optical fibers suffice?

Yes, you can use fibers.

QUICK EXPLANATION OF INTERFEROMETRY

The interference pattern forms vertical alternating light/dark stripes. (It’s more complicated, but this is a good beginning explanation.)

The stripes are the interference between the waves from each path coming together. Where the crests match up you get a bright band. Where the crest matches a trough, you get a dark band. Since there is a slight angle difference across the viewing area of your target screen, you get slight differences in path length which results in the light and dark bands.

As one path gets longer or shorter, the stripes move left or right. You count the stripes as they pass by, and each stripe distance is one
half of a wavelength difference in length. (Because moving the mirror 1/2 wavelength adds 1 full wavelength of total travel.)

You can get wildly accurate measurements using this system. For example, put two light sensors on either side of a band, and hook them
up to a galvanometer that adjusts the mirrors. Set negative feedback so that the galvanometer adjusts based on the difference in measured light.

In other words, the band is kept centered between the two sensors. If one sensor measures more light than the other, the galvanometer moves the fringe to become more centered. The feedback voltage is then the signal to be recorded.

[I haven’t done this, but] I suspect you can detect differences of 1/512th of a wavelength positioning without much trouble. Depending on
the wavelength of your laser, that’s in the angstrom range. At that resolution, you can easily measure the gravitational attraction of the moon, most earthquakes, and all the trucks that drive by your house.

Simpler method is to use a ccd or cmos camera to read the fringes.

Interferometers are pretty neat, one place I worked we had a HP one for calibrating ball screws on the machines. The guys that calibrated the CMMs also brought in HP interferometers. The cal company that did our surface plates had a cool little one that just plugged in to USB on his laptop. I cant imagine how much that cost. 

Oh sure... *now* it's simpler. In the 70's and 80's it was a bit harder to get CCD or CMOS cameras :-)

Today I'd use a linear CCD scanner chip. 5000 pixels over an inch and can be read by an Arduino with the results sent to the serial port.

Hmmm... just now gave me an idea for my next project.