Thanks for the link Michael, interesting reading.

On 17 February 2024 at 09:38 Robert Atkinson 2 Said:

An example of a current system is the Renishaw XL80 https://www.renishaw.com/en/xl-80-laser-system–8268

Somehow the forum has destroyed the  link you supply. There should be a double minus sign between ‘m’ and ‘8268’.

I looked at that page and while it was clear on its linear resolution, it was a little wooly on angular measurement.

Further digging led me to this page:

https://www.renishaw.com/en/xr20-rotary-axis-calibrator–15763 (again a double dash between ‘r’ and ‘15763’)

That claims +/- 1 arc second accuracy. I may be misunderstanding the Moore literature but that appears to claim +/- 1/10 arc second accuracy, which to me is an order of magnitude improvement.

I would note that Renishaw feel the need to provide a five page document on ‘error budget’ (bottom of page) explaining how they arrive at that number. Things were so much simpler in 1965.

Likely very few of us require accuracy to + – one minute never mind down to 10ths of a second, but it’s still an interesting problem for how that degree of accuracy can be verified with some level of certainty.

While it’s about checking a very good dividing head with a high end surveyors theodolite and not a rotary table. Both are in reality no different as far as checking there rotational accuracy. https://www.youtube.com/watch?v=3NcIu0EF6lQ

His idea is in my opinion quite clever and valid, but I’ve used high magnification 36x rifle scopes over long enough distances to have some idea that there’s a built in flaw. The unavoidable and varying temperature induced mirage over the distances shown in the video would be well in excess of the 1 second accuracy of the theodolite itself. In other words the target can easily shift optically up, down, left, right or even combinations. What happens is the targets zero point will shift optically to a position where it physically isn’t located despite what your eyes are telling you. That optical mirage can also be present even at night just due to the various temperature gradients as it’s not consistent over distances like that shown in the video due to ground temperature change. Even more so with any roads or water between the theodolite and the target. Wind can also affect those optical effects since it helps to also shift that mirages direction. One thing that does help his measurement checks is the elevation drop between where he was checking from and the target location as that should reduce those effects. Obviously it would be much more time consuming, but doing those exact same readings over a period of at least 10 days and then averaging your results should be much more accurate.

Yes, very interesting video. It is a technique I have considered. I have a “total station” type theodolite which has electronic rather than scales and also has a laser distance measurement built in. Mine is a odd make, Stonex,  model STS5R. This has 1 arc second resolution and 5 arc second absolute accuracy so good enough for checking any practical rotary table or indexer. It uses resolvers (multiphase transformers with relative movement between windings. These have infinite resolution unlike optical encoders. The distance measurement is 1mm resoution and 2 ppm + 2mm accuracy from 1m to about 3km so 2mm at short range and 5mm at 3000m. Lots of interesting measurements you can make.

Going back to the original subject, I happened to be looking for information on another instrument and saw what appears to be a Moore 1440 indexer being used to check a polygon with a modern automatic collimator on page 3 of this document.
https://www.taylor-hobson.com/-/media/ametektaylorhobson/files/product-downloads/autocollimators/autocollimators-en.pdf?la=en&revision=0777311d-fe86-40fc-8a33-c1cf93ff44c2

Robert.

The UKAS document says:

“Index and rotary tables

Various techniques are used for the calibration of rotary devices, and uncertainties can be as low as ± 0.3 seconds of arc.”

Interestingly that is 3 times tha accurcy claimed by Moore in the original document, but see comment on NPL below who can acheive an order of magitude better..

The 0.3 for indexer plus the ± 0.2 seconds of arc for the autocollimator give the 0.5 total for the Polygon.

Obviously Taylor Hobson are going to use collimator techniques because that is what they make.

That said NPL stil use comparison with another index table using mirror and auto collimator but their tables are ± 0.02 to 0.05 seconds of arc and ± 0.01 seconds of arc for the autocollimator

https://www.npl.co.uk/products-services/dimensional/angle-standards-instruments

Their primary standards for angle are Sine Bar based. For example the Small Angle Generator used for autocollimator calibration
http://resource.npl.co.uk/docs/science_technology/dimensional/moy-scmi/moy-scmi-95-print.pdf

The critical slip gauge thickness, mirror flatness etc are now all measured by laser interferometry.

It should be noted that the 0.5 second accuracy of the autocollimator is almost irrelevant in the measurements, since that is the error over the ±5 minutes range of the equipment. In the calibration of the polygon, the range of measurements will be seconds of arc, not minutes.

I’m satisfied that when lapping my surface table the repeatability of the autocollimator and the baseline of the mirror gave me a resolution of 2µ inch. Controlling the temperature profile of the shed was far more difficult than measuring the flatness of the surface table.

On 18 February 2024 at 22:23 Mark Rand Said:

It should be noted that the 0.5 second accuracy of the autocollimator is almost irrelevant in the measurements, since that is the error over the ±5 minutes range of the equipment. In the calibration of the polygon, the range of measurements will be seconds of arc, not minutes.

I’m satisfied that when lapping my surface table the repeatability of the autocollimator and the baseline of the mirror gave me a resolution of 2µ inch. Controlling the temperature profile of the shed was far more difficult than measuring the flatness of the surface table.

Hi Mark,

Not quite 5 minutes, according to Taylor Hobson. On the document I linked to eariler the accuracy line in the specification table has a * note “* Normally over a centre portion of the range for visual this is the central 60 seconds”
And you have to add the mirror errors to that…
Yes, you can get very precise relative measurements but absolute is another matter.

Robert.