Micron-level accuracy over a meter?

[RJSakowski]

The "meter long" lead-screw, if used, would just be to move the stage over the full length at a steady pace via a stepper rather than by hand, out of fear of missing steps in the scale. But as you say a small lead screw could be used as long as it can be slid into position, hence my comments about maybe just using a micrometer for those last few mm.

By "backlash" (probably not the most appropriate term), I meant any potential movement in the mechanism between the microscope and the scale, like if a force is applied during use. Some is inevitable no matter how rigid (and I don't expect to be able to put in the time and expense to achieve lathe-like rigidity), and almost any would be in the micrometer range.

I can't calibrate the scale without some other scale that is also about a meter long. Ringing together a whole bunch of gauge blocks would probably accumulate small errors, but it's a thought. I don't know what other physical reference could be used. NIST probably has an actual, physical, meter-long meter in a vault, if only for historical reasons, but I doubt they will let me borrow it. ;-) Calibration of a scale is presumably done at the factory via optical means (e.g. laser interferometry), or at least one hopes, but with cheap scales, probably not?

If you wanted to move the read head at a steady pace, a length of threaded rod would be sufficient. Thread pitch accuracy wouldn't be an issue. The glass scales that I have used come with a calibration certificate but for best accuracy, they needed to be calibrated in situ and a scale factor used. I used a 6" bar to calibrate mine as it was the longest bar that I could measure with my micrometer set.

One thought regarding your calibration. If you made a suitable bar of arbitrary length, you could send it to a certified metrology laboratory. A simple calibration like that would be fairly inexpensive and then you would have a NIST traceable standard in hand. They should be able to calibrate to the same standard they use for gage blocks which should be to a microinch at worst.

 

[zondar]

True about the threaded rod, but proper lead-screws aren't that expensive anyway. The one I looked at, with a bronze nut, was about $30. Expenses at that level are fine even if only for a touch of classiness and smooth operation.

I think the problem with scales isn't 6 inches, over which they should be quite good, it's over the ~40 inches that I'd need. But I didn't know about a requirement for calibration in-situ. Did you find that it was actually off by a significant amount?

That's a great idea about finding a metrology lab! They will be fascinated once I say it's for gravity wave detection. ;-)

 

[RJSakowski]

True about the threaded rod, but proper lead-screws aren't that expensive anyway. The one I looked at, with a bronze nut, was about $30. Expenses at that level are fine even if only for a touch of classiness and smooth operation.

I think the problem with scales isn't 6 inches, over which they should be quite good, it's over the ~40 inches that I'd need. But I didn't know about a requirement for calibration in-situ. Did you find that it was actually off by a significant amount?

That's a great idea about finding a metrology lab! They will be fascinated once I say it's for gravity wave detection. ;-)

I have some numbers from when I calibrated in my notes and it appears the scales were off between 550 ppm and 1000ppm. I was surprised to find this much deviation. The calibration corrected that.

My method was to set up a straight edge on my table and sweep it to ensure it was parallel to the axis travel. A 1-2-3 block was set on one end as a stop and and a test indicator and the DRO zeroed on the face. A known length bare (6" parallel was then placed against the stop and the table moved to the opposite end. the table was adjusted until the test indicator zeroed again and the DRO reading noted. That reading was compared against the parallel length, as measured by micrometer, and the DRO scale was adjusted per the FRO manual.

Now that the cat is out of the bag, it would be great to see some details of what you are trying to do.

 

[JRaut]

You could buy a set of these large gage blocks to get your accurate overall distance. Then use the micrometer stage strategy others have brought up.

They’re not cheap, but I’m sure the $800 price tag is a (very) small fraction of what they cost new.

Pratt & Whitney 5" to 20" - Large Steel Gage Block Set in case - **READ** | eBay

Case is rough.

www.ebay.com

 

[Firebrick43]

why not just have a shop with a zeiss machine measure it for you?

 

[homebrewed]

Gravity is a particle.

Only if you look at it using methods that can detect particles. The wave function collapses to whatever method of observation is used. LIGO detects waves so it "sees" waves. The classic double-slit experiment that demonstrates interference patterns of electrons is a good example of this.

Diode lasers are an interesting way of showing this duality. The laser color is determined by quantum mechanics -- the energy due to the recombination of holes and electrons determines the photon energy -- but the light can then be used to generate an interference pattern, most easily explained using the light-as-wave argument.

 

[rwm]

I was kidding of course. We should not hijack this thread with the wave-particle duality discussion!
Are you really building a gravity wave detector? I assumed this was not possible on a small scale, hence LIGO.

 

[zondar]

I was kidding of course. We should not hijack this thread with the wave-particle duality discussion!
Are you really building a gravity wave detector? I assumed this was not possible on a small scale, hence LIGO.

No, of course I'm not trying to detect gravity waves. That's not possible without having a few billion dollars to invest in building such an instrument. But the guess was actually close!

I have an interest in historic scientific experiments, and thought I'd try to replicate a few as a hobby. So one idea was to construct a "Kater's pendulum", which was likely the first device used to calculate the force of gravity (lower case g) with enough accuracy to calculate local differences.

A Kater's pendulum is a reversible pendulum. It can be hung with the heavy side down, as would be normal, or hung with the heavy side up. Sharp, hard knife edges riding on a very hard plate are used to balance the pendulum to keep friction as low as possible.

The local gravity g can be calculated from a pendulum via T=2*Pi*sqrt(L/g), where T is the period of oscillation and L is the length of the pendulum. The problem, though, is that the period of a physical rigid-bodied pendulum (a "compound pendulum") isn't the same as that of an ideal pendulum, and that equation is only accurate in the ideal case.

The trick that Kater came up with has to do with the reversibility. The Kater's pendulum is hung one way, its period measured, then hung the other way, and its period measured. This is repeated over and over while adjusting a small weight along the pendulum's shaft until the two periods are identical. At that point, with a little math (look up on Wikipedia), it can be shown that the period should now match that of an ideal pendulum of length L to a very high degree.

This reduces the problem to finding L, the distance between the two knife-edge pivots, and of course measuring the period T. The usual things one does to help measure T reliably include having a long L and a heavy weight (on one end, the other end is as light as practical), with a relatively narrow angle of oscillation. The pendulum's pivot should also be firmly anchored to a very stable foundation and the pendulum shielded from disturbances.

Kater's pendulum was constructed from brass, and had about a meter's length L between pivots. He was able to measure the distance between pivots to about 2.5 microns using a microscope comparator. I wish I knew more details about how he did that! His result included corrections for temperature, etc., and provided a figure for g to 6 significant digits.

Instead of a copy of Kater's pendulum, I'd likely construct a refined version, a Repsold-Bessel pendulum. This is a fully symmetrical version, in which both ends are physically identical. So there's a heavy brass weight on one end, and an identically-shaped very light weight (in my case, probably a 3-D printed hollow plastic "weight" in the same shape) on the other. Everything else should be made the same. This does away with the need to fine-tune the position of the small weight to make the periods equal when reversed.

So here I am more than 100 years later. I have access to Invar instead of brass for the pendulum, I can measure the period T with nanosecond precision via electronic means instead of by comparing it to a pendulum clock as he did, and yet I can't achieve close to the same accuracy of the L measurement as he did! So frustrating!

 

[homebrewed]

In the Wikipedia entry for Kater's Pendulum it was mentioned that he used an optical comparator to determine the distance between the two knife edges. So the simplest explanation is that he had access to a reference length that was at least close to the length of his pendulum. Or chose its length to facilitate the measurement, slapped it into his optical comparator and wallah, as one of my co-workers used to say

 

[zondar]

Yes, exactly. In reading an original description of Kater's work, the distance between knife edges were compared via a microscope against three different physical scales. As expected, the resulting measurements varied, but were similar to their 5th or 6th significant digits. ("A man with two watches never knows what time it is.")

I will try to do an error budget analysis to see how good an estimate of g I could expect with what's available to me. But I'm not feeling very eager to spend $500 or more to construct my own traveling microscope for the sake of a single measurement, so I'd likely still have to find someone with a large and accurate DRO'd lathe / mill or go to a lab.

Project Gutenberg has a great E-book, "Development of Gravity Pendulums in the 19th Century" by Lenzen and Multhauf that goes into a century of developments in the field. Apparently, gravity pendulums were used up to the 1950's for geological studies, as only then were better instruments finally developed. The modern approach drops weights in a vacuum for a direct measurement of acceleration due to g, and then that's used as a reference for more portable machines, e.g. a weight on a spring or even micromachined devices.

Actually, I recently built a device that measured g via a micromachined accelerometer, but that had poor accuracy for this sort of precision work (it was for a totally different purpose).