Precision pendulum techniques

[duncan webster 1Participant @duncanwebster1]

With my not serious hat still in place, is there any possibility of narrow slits acting like diffraction gratings and giving you a spread out spectrum?

[S KParticipant @sk20060]

Yes, the laser is PL204, sorry.

Yes, I see Duncan's mirror idea has a gain of 2X. That's something, but not a lot. With a gain that low, and hence the need for a long baseline, the beam divergence of a typical laser would start to be an issue.

Because noise is always present in any system (save at absolute zero temperature, which is not possible to achieve), nothing is ever "all the same shape."

A comparator does not "remove noise" in the sense that we want, because of the noise that precedes it (it also creates its own noise too…). Imagine two scenarios: In one, the photodiode produces an extremely rapid rise/fall time of say 1ns (which this photodiode is capable of under proper conditions). Any op-amp, comparator, Schmitt trigger, etc., sees maximum overdrive within 1ns and can respond as fast as it is able to. So the noise present in the PD's signal cannot influence the timing of the op-amp, etc., more than causing about 1ns of jitter. That's very good! (The op-amp, etc., will introduce its own noise too, but we worry about that later.)

In the measured scenario here, the rise and fall times are ~3ms (as I am currently seeing with a slit in front of it). That's 3,000,000 times slower (!), just because the pendulum is so slow. Now, as the voltage is very slowly crawling up, any superimposed noise on that signal (I'm seeing a lot) will also be amplified by the op-amp, comparator, etc., and will cause the output to trigger either earlier or later than the ideal switching point (threshold). Over that 3ms rise time, even a little noise will cause the output to trigger earlier or later potentially by many us – which is what we are seeing with the Sharp opto. It may even bounce many times as it crosses a noisy threshold (a latching comparator or Schmitt trigger might be needed).

So, the slower the slope of the input signal, the more that any noise on it will cause the trigger to jitter. We want as fast a rise/fall time as possible right at the PD, and also a fast comparator. But also, we somehow want a fast pendulum! The pendulum is literally a million times slower than my PD!

Diffraction due to a pinhole or slit causes the light to diverge, but does not significantly change its spectrum.

Edited By S K on 11/08/2023 15:38:16

Edited By S K on 11/08/2023 15:41:59

[Michael GilliganParticipant @michaelgilligan61133]

Posted by S K on 11/08/2023 15:35:02:

Yes, the laser is PL204, sorry.

Yes, I see Duncan's mirror idea has a gain of 2X. That's something, but not a lot. With a gain that low, and hence the need for a long baseline, the beam divergence of a typical laser would start to be an issue.

[…]

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I noticed, in the spec-sheet for your PL204 [which appears to have a decent collimation lens included] that the typical beam divergence is quoted as – 0.6 mrad

Does that double-negative mean that it actually converges, I wonder ?

Can you measure any change in spot-size ?

MichaelG.

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Ref: **LINK**

https://www.thorlabs.com/drawings/c79ae26fd0ed5f7f-F31E98B8-ACBD-DE2E-7D6A501A2CFF8C25/PL204-SpecSheet.pdf

[S KParticipant @sk20060]

At 15-20 feet (I didn't measure), the central spot was about the same (3 or so mm), so it was quite well columnated, at least over distances we might use. However, a number of thin, sharp, dimmer but still surprisingly-bright surrounding rings became apparent at that distance. Those were not seen close up, as there they were too close to the main spot to see. Perhaps they are dim enough that they could be ignored with an appropriate comparator threshold.

With a gain of only 2, the Gaussian main spot profile would still likely cause trouble with Duncan's scheme. Again, that's not an issue if the spot is stationary, but if it sweeps across the PD, a rising and then falling signal would be apparent.

Even that might be overcome if the amplification and threshold comparison was sufficiently noise-free, but I'm disturbed by the amount of noise I see on the scope, which is quite bad. An example is below. I'm not sure where it's from (Power fluctuations? Pickup from somewhere? Photon statistics?). I did add a simple RC filter on the power source of the PD bias as suggested by the spec sheet, but a robust output filter looks mandatory too.

Edited By S K on 12/08/2023 21:23:55

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 12/08/2023 21:19:38:

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Even that might be overcome if the amplification and threshold comparison was sufficiently noise-free, but I'm disturbed by the amount of noise I see on the scope, which is quite bad. An example is below. I'm not sure where it's from …

…

The noise is very high, seems constant and isn't related to the light input, so I suspect the DC circuit. Could the reverse bias voltage be too high causing the diode to break down like a Zener or Avalanche type? It's done deliberately to generate RF noise.

Or has the diode been accidentally forward biased?

Dave

[S KParticipant @sk20060]

It's not forward biased, and the reverse bias is only 5V out of a specified 25V max. I'd have used 10V or more, but the laser requires 5 and I only have one decent power supply. There's no difference between illuminated and not illuminated (as you point out), but I should disconnect the laser power completely to check that the laser isn't spitting too much noise back out onto the power supply.

It's about 35-40mV peak-to-peak, and about 6-7 mV RMS. I note that the scope is claiming 719 Hz, but that's probably spurious, as I don't see any oscillation when zoomed in (it just looks like noise).

It's probably just a "normal" amount of noise for a circuit with a ~5 MHz time constant (20 pF and 10k), and one with iffy grounding and excessively long wires (formed in a big loop!). I've seen worse. If I tightened things up, payed better attention to grounding, etc., it would drop some.

As well, there's no point in maintaining such high bandwidth if the illumination changes so slowly. I could drop it to somewhere around 1-10 kHz, which would also reduce noise considerably.

Edited By S K on 13/08/2023 00:21:51

[S KParticipant @sk20060]

I tried the "cylindrical mirror" idea, despite thinking that it wouldn't work well.

The cylinder was the Invar rod, which is semi-polished. The laser and photodetector were at right angles, with the photodetector about 6" from the rod. This yields a 45 degree angle of incidence of the light upon the rod when reflected to the diode. I could not include a slit since the amount of received light was much lower.

Here's a scope photo including 4-5 passes of the laser. I am still trying to interpret the details, but it's a poor result that is not promising. Maybe some related idea can still work, but this one will likely not.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by S K on 12/08/2023 21:19:38:

At 15-20 feet (I didn't measure), the central spot was about the same (3 or so mm), so it was quite well columnated, at least over distances we might use. However, a number of thin, sharp, dimmer but still surprisingly-bright surrounding rings became apparent at that distance. Those were not seen close up, as there they were too close to the main spot to see. Perhaps they are dim enough that they could be ignored with an appropriate comparator threshold.

[…]

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Thanks for checking

That sounds like a very satisfactory performance for a diode laser

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Next steps if you want to improve the beam are relatively complicated, bulky, and pricey

… probably best avoided , but for academic interest try investigating the terms ‘Top Hat’ and ‘Spatial Filter’

MichaelG.

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Potentially superfluous background info. https://en.wikipedia.org/wiki/Airy_disk

Edited By Michael Gilligan on 13/08/2023 05:56:42

[S KParticipant @sk20060]

Yes, an Airy disk.

Any more ideas about optical gain?

[S KParticipant @sk20060]

Another thought: Someone here had mentioned including an accelerometer, I assume in or on the bob. Accelerometers can be noisy too, and they require power at the bob, so the question is how to use one to full advantage, if it's practical long term at all.

One probably not-so-great way is to poll it and record when, say, velocity is at a maximum. But a possible improved method is to record it as rapidly as possible and then fit a function to the data of a whole swing, or perform an auto-correlation between swings. This sounds like it would reduce noise, e.g. by the square root of the number of polled data points.

Anyway, what is the experience people have had with accelerometers?

[Michael GilliganParticipant @michaelgilligan61133]

Posted by S K on 13/08/2023 06:54:41:

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Any more ideas about optical gain?

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Yes … but you dismissed them so pointedly that I have just been trying to keep them to myself until I am in a position to do some practical work.

As the date for that seems to be getting ever-further-away, I had better speak-up:

Demonstrably excellent as some of the optical sensing/triggering systems for clocks may be … I think we have reached the limit of their usefulness, and are now “barking up the wrong tree”

I was pleased to see your observation that the pendulum itself is moving too slowly to be measured

This is the very essence of the problem, and we need a different approach.

My disruptive idea comes with a nod of respect to Hipp

What we need to do is detect the physical point at which the pendulum reaches the peak of its swing

This is a direct spatial measurement, and requires no clever processing of speeds or times.

… At that point the velocity of the pendulum is zero.

Measuring it does not require light-beam gates, it just requires some appropriate optics.

There was a recent thread about a ‘travelling microscope’ … and that general principle is traditionally used for the accurate reading of instrument scales [a visit, real or virtual, to the Greenwich Observatory would be informative].

All we need, as I have previously suggested, is a camera with microscope optics … to detect to pixel resolution the physical position of that peak. The timekeeping follows naturally from that.

I have long believed that the fundamental requirement for good timekeeping is to keep the pendulum swing constant. … This is obviously not practical in the real world, but the more accurately we can measure it, the closer we will get to that ‘stretch target’.

[ steps off soapbox, to a roar of silence from the audience]

MichaelG.

[John HaineParticipant @johnhaine32865]

Hmm, I'm not entirely sure about this Michael. For one thing, the rate of change of position with deflection at the peak is by definition zero so you could find that there are several pixels to choose from. Also I think that means that the system is more vulnerable to noise effects.

And what are we trying to achieve? We want to know the time of a particular pendulum position for two reasons – to assess its timekeeping; and to decide when to impulse it. The peak of swing is exactly the wrong moment to impulse a pendulum by conventional means – i.e. delivering a small momentum to it (a/k/a "hitting" it). Rather, as all its energy is potential at this point, we need to gently but instantaneously take hold and lift it to the desired operating amplitude – a difficult thing to do. Or, knowing the period, we could wait a quarter period and impulse at the zero crossing, but then there is uncertainty in the position of the zero crossing as a result of the timing means (probably a microprocessor).

I suggested a lens above with no explanation, but essentially Michael's idea of using a microscope to image the shadow of a vane or slot on the opto sensor and detecting the edge. Since the effective width of the pulse will be larger according to the magnification it will pass much more quickly across the sensor aperture and the effect of threshold errors on timing will be less by the same factor. The same technique could be applied to another sensor at the extreme of swing to control the amplitude.

I certainly agree that constant amplitude can be a requirement, but I don't think it's fundamental. After all, Clock B deliberately allows the amplitude to vary with barometric pressure to achieve compensation. Doug Bateman's clock, which he described in a couple of articles in HJ, used a home-built opto interrupter to sense the extreme of swing and essentially inhibit impulsing and achieved better than 1 second of arc precision. He also has barometric compensation using an aneroid capsule.

[John HaineParticipant @johnhaine32865]

…

Anyway, what is the experience people have had with accelerometers?

A few years ago I had a student who built a sensor using a 9-axis (I think) sensor chip interfaced to an Arduino to monitor pendulum motion and upload measurements via Bluetooth. It worked very well except that battery life was limited. However he also looked into applying "wireless power" and showed both theoretically and practically that using standard coils and chips you could easily transfer enough power to run the processor system continuously. The concern I had was that the EM force between the coils would perturb the pendulum but this proved unfounded. You could position the pickup coil near the suspension where its movement (and hence coupling variation) would be small, with thin wires run down the rod to the sensor. I think the sampling rate he used was about 10Hz which should be fine for a 1m pendulum. I could dig out more details if this is of interest. Today one could use an Arduino Nano33BLE which comes complete with Bluetooth and a 9 DoF sensor.

I know of a clock in the US which is being monitored with Pocket Labs sensors though I'm not sure they are really up to the job. These are quite expensive but there are much cheaper devices available. Neither of these use wireless power so would need adaptation.

The real issue with using these simple accelerometers I think is that they don't have enough accuracy or resolution to really detect any significant deviation from sinusoidal motion.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 13/08/2023 10:40:51:

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Hmm, I'm not entirely sure about this Michael. […]

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That’s fine, John

I was asked for thoughts, and I have provided them

… it’s something I have been pondering in solitude for a long while now, and I am no nearer to being able to test the idea. The next-best-thing was to put it out there and challenge the zeitgeist.

Any and all reasoned objections will be welcomed.

MichaelG.

[John HaineParticipant @johnhaine32865]

Michael, any suggestions you have for the optical design and components to use for a "magnifying" sensor would be very helpful.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 13/08/2023 11:06:58:

Michael, any suggestions you have for the optical design and components to use for a "magnifying" sensor would be very helpful.

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If I survive the next several hours in the garden, I will jot down a few thoughts this evening.

Doing it really well might be a little complicated, but as a demonstration of concept the optical side can be done with a cheap USB webcam. … My stumbling-block has been not knowing how to grab the the data.

More anon

MichaelG.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Michael Gilligan on 13/08/2023 08:14:36:

Posted by S K on 13/08/2023 06:54:41:

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Any more ideas about optical gain?

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…

I was pleased to see your observation that the pendulum itself is moving too slowly to be measured

This is the very essence of the problem, and we need a different approach.

…

MichaelG.

Um, I'm not convinced of that at all. Many pendulum clocks have been built with light beam detectors, and others with permanent magnets inducing current in a coil, with similar rise time characteristics. Fedchenko used a permanent magnet / coil detector, and his clock worked quite well!

Most likely something is wrong with SK's experimental set-up. I think the noise level is far higher than it should be.

Having said that, my experimental pendulum is noisy, and uncertainty introduced by the beam detector as described by SK might explain it.

I'm going to measure how noisy the sensor in my cheapo Arduino module in hope I can do it quickly. (I don't have much spare time at the moment and the earlier question about whether of not my data has a normal distribution has dropped me into deep water. Q-Q plots, Shapiro-Wilk and Kolmogorov-Smirnov – yer wot? Also John has sent me a couple of papers to read, and am struggling with the maths. Years ago I attended a class called 'Maths for Scientists'; should have been called 'Last Hope for Boys Too Dim to Understand Calculus'.

If my Arduino module's sensor is as noisy as SK's I'll have to think again. If the sensor is quiet, he will!

Dave

[SillyOldDufferModerator @sillyoldduffer]

It appears the sensor in my cheap Arduino module works better than SK's.

The module uses this circuit:

The photo-transistor is decoupled by a 0.1μF capacitor, and so is the supply.

With an oscilloscope connected between ground and the top of the photo-transistor, waving my hand produced this output:

The phototransistor is 240mV above ground
Noise level is about 80mV
Signal level is 1580mV above ground

Testing wasn't straightforward. I did the experiment on my dining table next to a south facing window. Warm and cloudy here and the light level is very changeable today. Even with a curtain drawn, sunshine causes havoc. I think strong ambient IR from the sun floods the unshielded phototransistor from all sides and causes its sensitivity to vary wildly. IR and light sensors have to be shielded, with peculiar results if they're not.

Dave

Dave

[S KParticipant @sk20060]

When people say "just" in this sort of context, I'm fond of responding "nothing is 'just' anything!"

Cameras: These would be difficult to use for automated timing. You would want a very fast frame rate (much faster than the typical 30-60Hz), and a pretty powerful computer (something like an Nvidia Jetson) to do the calculations in real time. I did try this, and at 240 Hz frame rates I was getting about 0.5mm resolution. One could translate that position resolution into time resolution, and likely find that it's similar to a simple optical sensor's, i.e. one with a ~0.5mm aperture. Adding microscope optics will not necessarily help, because you would just be amplifying the motion blur. But throw a Ph.D. student at it and it can be done, and one way or another done better than a simple opto sensor. I'm not the one to try it right now, though.

Noise: The electronic noise at the photodiode as seen in my scope traces is not particularly pertinent. Why? Because that photodiode's intrinsic speed is about a million times faster than the speed of the shadow across the sensor. The next step would be to reduce the bandwidth and hence the noise until it's appropriate for the shadow's speed. A phototransistor is slower but has internal gain when compared to a photodiode. Given how slow the pendulum is, perhaps that's a better starting choice.

A question for Dave related to this: What is the RMS jitter in your period measurements? From one of your charts, I'm seeing ~1.1ms, but that seems way too large compared to the 3-5us John and I are getting with the Sharp optos.

Lenses: I mentioned that using a lens is fundamentally similar to using a smaller aperture. My idea was to use a plano-convex lens to focus the laser's beam to a point right at the flag. Thus, the flag would cut off a point rather than sweep across a beam. But I'm afraid that focusing a laser that way may be more difficult than it sounds. John's idea, I think, is to place a (plano-concave?) lens after the flag, which sounds easier. But either approach, unfortunately, reduces the light at the sensor just like an aperture does. I think I'd need some more convincing that a lens is any better than an aperture, given that an aperture is very easy to implement.

Inertial measurement units: I've used 9 DOF ones in a very fun project that I haven't posted anywhere. They are noisy. But I think the fitting or auto-correlation approach could work well. (This is also not a direction I'll be taking any time soon.)

Back to basics: My original concern was that the 3-5us jitter of the Sharp opto seemed like a lot. I've since learned that it's quite reasonable simply because of how slow the pendulum's motion is. Using a GHz photodiode (as mine is) just won't help and may even make matters worse. But a few things have become clear: use the smallest aperture you can, read at BDC (for convenience, I was actually reading at one extremity), and focus on reducing noise. Much beyond that, and it looks like life gets tougher.

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 13/08/2023 16:45:19:

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Noise: The electronic noise at the photodiode as seen in my scope traces is not particularly pertinent.

A question for Dave related to this: What is the RMS jitter in your period measurements? From one of your charts, I'm seeing ~1.1ms, but that seems way too large compared to the 3-5us John and I are getting with the Sharp optos.

Lenses: I mentioned that using a lens is fundamentally similar to using a smaller aperture. … John's idea, I think, is to place a (plano-concave?) lens after the flag, which sounds easier. But either approach, unfortunately, reduces the light at the sensor just like an aperture does. I think I'd need some more convincing that a lens is any better than an aperture, given that an aperture is very easy to implement.

…

Noise not pertinent? On the 11th: 'In the measured scenario here, the rise and fall times are ~3ms (as I am currently seeing with a slit in front of it). That's 3,000,000 times slower (!), just because the pendulum is so slow. Now, as the voltage is very slowly crawling up, any superimposed noise on that signal (I'm seeing a lot) will also be amplified by the op-amp, comparator, etc., and will cause the output to trigger either earlier or later than the ideal switching point (threshold). Over that 3ms rise time, even a little noise will cause the output to trigger earlier or later potentially by many us – which is what we are seeing with the Sharp opto. It may even bounce many times as it crosses a noisy threshold (a latching comparator or Schmitt trigger might be needed).'

Cause of Jitter in my measurements, I don't know – very much still under investigation.

• Previously suspected to be mechanical, but suspension and other improvements didn't reduce it.
• Might be the beam sensor – a hot topic as per this thread!
• A build error due to a CAD mistake. The plastic holder supporting the sensor and electromagnet is too short to allow it to be positioned to break the beam at BDC. Thus the bob is always impulsed late, a known cause of disturbance. (John posted a graph.)
• Possible design error: may be the plastic holder isn't strong enough to resist flexing when the electromagnet is pulsed. Glued at the moment instead of being bolted down, so even if strong enough could be moving slightly on the base when It's supposed to be rigid.

For simplicity I'm an aperture man too! A potential advantage of a lens is they gather more light, if needed. Don't think it is, there should be plenty of signal inside a clock case even from a weedy emitter struggling to poke energy through tightly spaced slits because the beam only has to travel about 300mm maximum. I think a 1mW laser would be detectable several hundred metres away.

Dave

[S KParticipant @sk20060]

The noise at present is not pertinent because the photodiode's bandwidth is absurdly larger than the required bandwidth, like by a factor of a million, and I'd reduce it dramatically before going much further. The circuit would still benefit from a fast comparator, though: Match the bandwidth of the sensor to the input light's rate of change, then use a fast comparator for timing.

So is your RMS jitter really ~1.1ms as I read it? Your suspension looks really solid, but I can't comment about the rest.

In the scenarios I've imagined, the use of lenses actually reduces the amount of light at the photodiode. With a strong source, that should be acceptable. Using a plano-convex lens before the flag and a bi-convex lens after the flag to refocus the diverging light back towards the diode could save most of the light, though that's starting to get a bit fussy.

One thing I may try soon is using the laser in conjunction with half of the Sharp opto (the receiving side), per discussions a while back. I don't know if it can handle the full blast of the laser, but I could include a very tight slit or pinhole (and a filter if needed). The combination may improve both the time resolution as well as immunity to stray light.

 

Edited By S K on 13/08/2023 18:49:11

[Michael GilliganParticipant @michaelgilligan61133]

As promised, John …

This is very simple stuff, but if I have glossed-over anything, just shout

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Here is the board from a little webcam:

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I removed the lens assembly [ you can see its footprint] to reveal the sensor chip:

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The small brick-red rectangle is the active area.

I have never managed to identify the actual chip, but it appears to be a 1/9” sensor with 640×480 active pixels on a 2.5 micron pitch.

All of which is largely irrelevant, except that it means the focal length of the lens is small, and therefore it can be focussed over a wide range with only short adjustments.

The camera is UVC [Universal Video Class], which means that it will run ‘driverless’ on most any modern computer.

Conveniently, that includes the Raspberry Pi, on which it works nicely with the GUVC application.

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Now … [assuming that we have the complete camera before us] first remove the decorative ‘trim ring’ and confirm that the lens screws freely in and out.

Plug it into your computer of choice, with whatever viewing software you have, and adjust the focus so that a -1/4” wide target just over-fills the frame-width … at which point, each of the 640 pixels is representing 10 microns.

[sorry about the mixed units, it just works out tidily that way].

You now have a microscopic view of an adequately wide field, with approximately 10 micron resolution … this could, of course, be meticulously calibrated, but I see no need in the present application.

… I can leave you to calculate how good that would be in milliradians at your chosen radius.

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Your mission, should you decide to accept it, is to find a way to grab the data, and then apply whatever logic to trigger an impulse at the chosen point whenever the swing has decayed by whatever amount you choose.

Matthias Hipp will be honoured, I will be grateful, and this guy should be impressed:

**LINK** : http://www.rogerj.co.uk/clock.htm

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by S K on 13/08/2023 16:45:19:

When people say "just" in this sort of context, I'm fond of responding "nothing is 'just' anything!"

Cameras: These would be difficult to use for automated timing. […]

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Sorry … I have only just read this, I was busy writing what I promised for John.

You appear to have completely missed the point of my suggestion.

MichaelG.

[S KParticipant @sk20060]

OK, a bit more detailed explanation may help.

So do you intend to project a shadow directly onto the sensor? If so, I don't see a great difference, actually. You will still have to read out entire frames and process them. Sluggish frame rates, motion blur, rolling shutter issues, etc., will all still be an issue.

Edit: No, I guess you still want to use a lens. OK, I give up. What are you intending that I apparently have totally missed?

By the way, that's a rather odd looking sensor. There are four very large regions surrounding the supposed active area in a configuration that I've never seen before. I am not sure what that's about.

Edit #2: Maybe the central region is the entire chip and the periphery is just for interconnect. It's hard to tell, but that would make more sense.

Edited By S K on 13/08/2023 19:37:56

[Michael GilliganParticipant @michaelgilligan61133]

Please just simply read the notes that I made for John

Yes the lens would be in place

No there is no likely problem with blur

All it attempts to do is detect the peak travel of the pendulum … at which instant the pendulum would be stationary.

With a notional ten micron resolution, I think it should be useful.

Over and out

MichaelG.

[Author]

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