Fundamental limit on timing resolution?

[Robert Atkinson 2Participant @robertatkinson2]

To be pedatic a schmitt trigger is a specfic discrete two transistor circuit with a single resistor for both emitters.  This common connection providing the feedback and thus hysteresis.
A comparator with feedback produces the same result with easier control over levels and the name was transferred…

Robert.

 

[S KParticipant @sk20060]

Moving on from Schmitt triggers, hopefully:

I have an IR emitter, a red laser, a 405 nm laser, and a suitable silicon detector.

What would a good vehicle be for testing various ideas? My own pendulum is probably not suitable for multiple reasons.

A stepper motor would be convenient, but I’d worry about the steps confounding the measurements. To get 1 step per 1 um, for example, e.g. by a belt drive, the ratio becomes a little ridiculous (something like 314:1 for a 2 cm long flag). A two-stage reduction would be about 17:1 each – still kind of high. And in either case, the rotational speed for the flag to move at 0.1 m/s would be too high for most steppers (about 2,400 RPM).

Linear translation, like via a lead-screw, would be a classic solution, but the same problems emerge: The screw would have to have an exceedingly fine pitch, and then the motor would have to rotate too fast. This would also likely be an expensive solution.

A combination of belt reduction and linear drive could work, but this becomes both expensive and more complicated.

Many or most DC motors would also show a form of cogging, at least at low speeds, but they could spin fast enough. Still ridiculous reduction is required, though.

What other options come to mind?

(Maybe I have to improve my pendulum and then use that.)

[S KParticipant @sk20060]

Ok, I’ll get sucked in again (sigh):

Because most Schmitt triggers have a rather wide hysteresis zone of a volt or so, as a “comparator,” they are limited to very low resolution – near digital – situations. They worked for John’s case because that’s exactly what he faced: rapid saturation to essentially digital levels.

Yes, I’m sure some old or obscure designs can have a narrower hysteresis zone or adjustible thresholds, etc., but modern Schmitt triggers will be non-adjustible 6-transistor CMOS circuits with poor part-to-part threshold matching, and are mostly used for cleaning up digital signals.

I hope we can at least agree that precision analog discrimination is best served by a “real” comparator.

[John HaineParticipant @johnhaine32865]

You might look at steppers driven in linear mode.  TI drv8834 and I think 8825 permit this.  Basically you apply sinusoids to the Vref inputs bypassing the internal sequencer. A way to get higher resolution microstepping.

And/or, use a differential screw.

There must be clever mechanisms for making small smooth movements.  My father used to work on electron microscopes where they had to move specimens by very small increments, used a number of differential screw type mechanisms.

[John HaineParticipant @johnhaine32865]

Somewhere – was it on this forum? – I posted about a surplus gadget I bought for the very nice DTI that was [art of it that used a very slightly eccentric roller to achieve very small movements.

Also, I did some measurements on opto interruptor precision a while back and published results in HSN.  I’ve put a copy of the article here:

https://www.model-engineer.co.uk/members/johnhaine32865/mediapress/opto-precision/

[BazyleParticipant @bazyle]

Whatever screw type small movement you devise could then simply be reduced by a lever giving a 10:1 or even 100:1 further reduction.

[Robert Atkinson 2Participant @robertatkinson2]

For a start I’d use a micrometer to get an idea of the static / low speed performance. You can try different slot and flag arragements light intensity etc.  An opto with analog output and seperate level detection circuit with a storage oscilloscope on the two signals will give useful information. Trigger on the output of the level detector.

An arrangement that saturates the photodetector will be slower than one that operates in the linear region.

For a moving target I’d use an excentric driving a “cross head” linear bearing. A DC motor with a decent rotating mass will give a smooth motion. See https://patentimages.storage.googleapis.com/39/05/df/d4f6bb88a090fd/EP1273347A3.pdf
For an application of this where sub micron repeatability over many hours of operation was required.

Robert.

[John HaineParticipant @johnhaine32865]

The saturation problem is only an issue if the flag interrupts the beam – on the “reveal” edge it’s probably better to get the fastest possible edge and use this for period timing.  Actually my sense is that the discussion is academic, for a pendulum clock in the Shortt / Fedchenko class nanosecond resolution is immaterial though I can’t immediately prove it.

[John Haine]

On John Haine Said:

The saturation problem is only an issue if the flag interrupts the beam – on the “reveal” edge it’s probably better to get the fastest possible edge and use this for period timing.  Actually my sense is that the discussion is academic, for a pendulum clock in the Shortt / Fedchenko class nanosecond resolution is immaterial though I can’t immediately prove it.

If using a flag that occudes the sensor for most of the sweep then use a full flag with a narrow slot at center of swing. If the speed of opto isn’t important why are we talking about diffraction limits?

Robert.

[Julie Ann]

On Julie Ann Said:

On SillyOldDuffer Said:

On Julie Ann Said:

…

There is no doubt that a Schmitt trigger is a comparator with hysteresis. Of course a Schmitt trigger as implemented in a logic IC, or an optocoupler, is not as well defined as a discrete circuit designed with a comparator IC, but they essentially do the same thing.

Julie

Do the same thing?  Not as I understand it.  Although both are based on comparators, the circuits are different……

SoD: As you earnestly commented recently in another thread, please read my post carefully before commenting.

Bit tart, Julie, are we on the same page? I read your post carefully and asked a legitimate question.

The topic is “Fundamental limit on timing resolution”, and we’ve got to the limitations of photo-sensors and associated electronics.  I’m asking in that context, it’s not an attack on you!

The context is measuring time, specifically:

does hysteresis improve or degrade the detection accuracy of a swinging pendulum?

No need to throw rocks at my examples.  In an attempt to explain my discomfort with the statement “they essentially do the same thing”, they highlight the difference between a plain comparator (no feedback), and a Schmitt Trigger with feedback. From where I’m sat there are circumstances calling for a plain comparator, and others that require one with simple feedback, or a Schmitt Trigger.

My question is a step beyond they “essentially do the same thing”.  I’m pursuing “in a real application, why choose one rather than the other?”

I’d much appreciate your professional assessment of comparator vs Schmitt Trigger for the purpose under discussion i.e.:

• Pendulum swinging inside a dark enclosure.  (Suggesting a low noise level)
• A flag on the bob interrupts an IR Beam aimed at a phototransistor
• When the beam is broken at BDC the bob’s speed is about 0.14m/s
• The phototransistor’s analogue output, a slope, is converted into sharp TTL for input to a microcontroller
• Repeatability is top priority, i.e the flag should always be detected at the exactly same point in space.
• Time accuracy and precision at detection should be as good as technology allows. (I’m trying for better than 30ns, which, in pendulum measuring world is “must do better”.)

Thanks in anticipation, I know you know your stuff!

Dave

[S KParticipant @sk20060]

I’d immediately agree that nanosecond timing is academic, but my concern is the opposite: might a possible timing accuracy limit be too large to be dismissed?

John measured the static resolution and found an S.D. of 0.15 micrometers using the Sharp opto.

Assuming the flag is 5 mm from the sensor (out of a 10 mm gap), what is the effect of the wavelength of light on position accuracy in a static test?

For 1 um light, the diffraction width at 5 mm would be about 70 um, which is large enough to be a concern. However, for the static case, you would presumably already be positioned at or near the 50% point (at the threshold). As I discussed earlier in the thread, around that point the diffraction width would cause a slope in the light intensity, which can combine with electronic noise to cause apparent position errors. If I assume that electronic noise plus the slope is responsible for all of the S.D.=0.15 um error, then I calculated that the signal to noise ratio would be about 667:1, which sounds reasonable as an upper limit.

From the above, it seems reasonable or at least plausible to conclude that the wavelength of light would indeed be partially responsible for the error that’s been found. If so, then changing from 1 um to 405nm light should reduce this 0.15 um error to 0.095 um. This would be a notable improvement, but either number would probably be judged to be good enough for most purposes.

All of the above is also confounded by the emitter and sensor’s size, shape and orientation, but that’s largely unknown.

How about the dynamic case? How would moving the flag at say 0.1 m/s change things? Note that any independent error from motion would combine with the static error in quadrature, so it can only get worse.

It’s almost certainly more complicated than this, but considering only latency and jitter: I had measured a 9 us latency in the Sharp’s output (in one direction). At 0.1 m/s this corresponds to a 0.9 um position offset, which is neither huge nor trivial, but it should be a constant in any event. I also measured 22 ns RMS jitter in the latency. This corresponds to 2.2 nm RMS of positional jitter, which is small enough to be discounted.

Thus, I think, there is only a very small difference between the static and dynamic scenarios. If correct, the wavelength of light combined with electronic noise remains the dominant source of error. This can be improved by using shorter wavelengths and/or lower noise electronics and/or smaller flag to sensor gap. However, its impact is modest in relation to most use cases for pendulums.

(The above may need to be redone with the opposite opto output direction, as I’m not sure I used the right one, but the jitter is too low to matter much anyway. Also, if I wanted to verify an improvement between 1 um and 400 nm light, or by lessening the distance between the flag and the sensor, etc., then a static test using a micrometer will likely do.)

 

[S K]

On S K Said:

…

I have an IR emitter, a red laser, a 405 nm laser, and a suitable silicon detector.

What would a good vehicle be for testing various ideas?…

Good question.  I experimented briefly with a notched disc spun by a small synchronous motor from an old electric clock powered by an variable frequency oscillator and power transistor.   Oscillator frequency and RPM can be both be measured accurately.  Never got as far as moving the sensor relative to the notch, fixed or spinning.  For detecting diffraction fringes, maybe a micrometer head, or some sort of pantograph?

 

(Maybe I have to improve my pendulum and then use that.)

Always good to improve the pendulum.

Electronic measuring is helpful too.  An oscilloscope will show the shape of the analogue signal as the bob sweeps past, and an Arduino Nano or picPET should time it “well enough” to detect issues.

Interesting challenge.

Dave

[Michael GilliganParticipant @michaelgilligan61133]

I’m not sufficiently well at the moment to participate in the discussion, or do any experimentation … but I am observing with great interest.

I will just mention, however that Blu-ray discs were invented specifically to overcome the limitations of red light on CD ordinaire

SK’s original concern is probably discussed in the literature.

MichaelG.

[S KParticipant @sk20060]

Unless an error is found in my math or logic in my previous post (quite possible), I think I’m satisfied that:

* Yes, the wavelength of light, in combination with electronic noise, sets fundamental limits on measurement accuracy. The math even seems ballpark-consistent with John’s measurement.

* Shorter wavelength light will improve resolution by the square root of the change in wavelength.

* Smaller flag to sensor gaps will also improve resolution by the square root of the change.

* Lower noise electronics will improve resolution linearly.

* Do not use a very narrow slit, which will decrease resolution over that of a single edge or a wider slit if too small. About 70 um slit width (or smaller) is the point at which it will start to harm resolution with a 5 mm flag-to-sensor gap and 1 um light.

* But finally, none of the above is urgently important for typical use in a pendulum. Even the Sharp opto is mostly good enough for general use.

[Michael GilliganParticipant @michaelgilligan61133]

Oops … I risk getting drawn-in … and I need to get to bed soon 🙁

Ponder this:

https://antrg.com/blog/2012/12/19/afm-bluray/

MichaelG.

[S KParticipant @sk20060]

The dynamic case is more complicated than I thought at first, since I had been assuming a point source of light and a point sensor.

The finite size of sensor and emitter turns out to be very important. This is because the flag causes a slope in the sensor’s output as the flag moves by. That slope, in combination with electronic noise, causes noise in the position measurement too.

To help with this, the sensor and emitter should both be as small as possible (the sensor in particular, since capacitance scales with the area). You want the column of light between the two to be as narrow as possible so that the time it takes to go from zero light to full light is as short as possible.

But very significant further improvement can be had by using slits in front of both the emitter and sensor. The slit’s widths should be as small as possible but not so small that it increases diffraction over that of the flag’s shadow on the sensor, so roughly equal or a little larger than the diffraction width – perhaps around 50-70 um, depending on the wavelength of light.

The slit’s length should also be smaller than the sensor, so that light is contained within the sensor’s area, and not extending over its edge. For a small sensor this makes positioning difficult.

The flag should still be as close to the sensor as practical.

Pinholes would work too in principle, and in particular would make it easier to limit the light to within the sensor’s area, but they would allow much less net light in, resulting in higher position noise due to lower signal/noise ratio. They also cause greater alignment difficulties than slits would.

Superior approaches?

I haven’t found an available sensor like this yet, but a split sensor (two photodetectors side by side with a very small gap between them) can be used to make differential measurements which will have certain advantages.

Another more complicated approach is to use a single flying slit (the flag itself has a slit) in combination with a Gaussian-profile light source such as from most columnated lasers. The slit of light impacting the sensor will then also follow a Gaussian profile as it sweeps across the laser’s profile and across the sensor. If you digitize the output with an ADC, you can then fit the data to a Gaussian and from this obtain a potentially far higher position resolution than any of the above. The speeds needed for a pendulum application should not be particularly challenging. Has anyone tried this?

 

[Michael GilliganParticipant @michaelgilligan61133]

As you are obviously getting serious about this … You might like to investigate Spatial Filtering. The concept is simple enough, but the hardware gets rather bulky.

https://www.newport.com/n/spatial-filters

MichaelG.

.

P.S.  _ I have [most of] one of these:

https://www.repairfaq.org/sam/brochures/SP331BESF/sp3311.html

which I hope to restore some-day

The spec. should give you a good idea of the practicalities.

[John HaineParticipant @johnhaine32865]

What are we actually trying to measure?  For a pendulum clock what matters for me is the time displayed, probably on an analogue clock face with a seconds hand.  A good target would be for the second hand to be pointing to the right seconds fiducial mark at the instant that the “pip” from a time signal (say GPS) is heard or an LED lights up or something similar. No free-running clock will keep this up for ever of course so occasionally a small correction might be needed.  What I don’t think we will be wanting to do is to use the pendulum as a  source for critical frequency control, for example locking a radio transmitter to it.

If that “specification” is reasonable, just how does the accuracy and repeatability of the sensing method contribute?  I don’t know the complete answer but I suspect that sensor noise can be largely neglected over long periods because real variations in the underlying pendulum rate will dominate, caused for example by uncompensated barometric and/or temperature changes, seismic vibration, and ultimately tides.

[S KParticipant @sk20060]

A lot of my musing is just intellectual curiosity. So making the best opto scheme I can is fun and interesting, even if it’s “too good” to matter.

However, I do have a longer-term goal in mind, for which I’d like to keep the S/N in per-period measurements as high as possible.

It’s somewhat common (here anyway) to discuss feeding air pressure, temperature, humidity, etc., into classical math calculations to try to compensate for their effects on a real pendulum. But what if you didn’t know the temperature coefficient of the rod, or how the (arbitrary) shape of the bob will behave in the air, or almost anything else about it?

An example possibility: For a continuously-running pendulum with an arbitrary period, a LSTM (long-short-term-memory) neural net with continuous incremental learning can operate on the last n periods of data to predict the next period. The recorded data would include the prior periods, plus measurements of temperature, air pressure, humidity, etc.

After making its next prediction, the neural net would be presented with the “correct” period , e.g. from a GPS disciplined oscillator, etc., and it would adjust its weights to refine its next prediction.

This neural net should learn the laws of physics, and to model the particularities of the given pendulum, without being “told” almost anything at all.

The above scheme does come close to crossing a controversial threshold that has been debated here before, in that you wonder who is doing the time-keeping, the pendulum or the corrections? But the corrections always come after the fact, and after training the corrections can be turned off if desired. If the latter is intended, then the NN probably would make less frequent updates during training, e.g. once per hour or day, in order to span longer time periods.

I have a quite different idea for run-down data, but it’s not well developed right now.

[S KParticipant @sk20060]

Just to add my thoughts on one possible run-down approach (again, not fully baked yet):

My weird goal is to obtain reasonably good time-keeping while having as little knowledge about the pendulum as possible. So, for example, I mentioned not knowing the temperature coefficient of the rod in the NN approach.

In the run-down approach, you can’t easily say what the period is, because it is continuously changing, it will be disturbed initially, it will slow to a low S/N regime, etc. This sounds more challenging and hence more fun than the continuous option.

So here’s one possibility among several that I’ve thought about: Record a full run-down, calculate the Allan variance and find the window size of the minima. Slide this window across the run-down data and compute the standard deviation within each window. Find the window with the minimum standard deviation, and use the mean of that as the period. If the window is very short, you might want to do a running average of the SD’s first rather than just rely on finding the minimum in isolation. If you want to actually keep time as opposed to just calculating a period, you simply use the same period during the entire next run-down.

There are probably better ways forward after the Allan variance is calculated, but this is simple and it should work. Will it be accurate? Probably not very, since for example it will not correct temperature-related errors, but it would be fun to see how well it does. Going further, this method could be followed by the NN scheme in order to do some of that compensation for temperature, etc.

[Julie AnnParticipant @julieann]

I suppose being accused of being tart is better than being accused of being a slut? 🙁

(For the avoidance of doubt the above is tongue in cheek.)

If we assume the pendulum is moving at 0.1m/s then it takes 10us to move 1 micron. If we want to resolve the  position to the equivalent of 30ns that is a positional accuracy of a few nanometres.

The measurement system needs to react faster than the time to be resolved. Otherwise one is relying on the measurement system delay being consistent to better than the accuracy required.

I wouldn’t use a ready made optocoupler with Schmitt trigger. It would be better to roll ones own detector using a PIN photodiode. Switching times around an nanosecond should be obtainable. To obtain a logic level use a fast comparator, like the AD8465, for instance. I would avoid hysteresis, or a few mV at most should noise be an issue.

Julie

[John HaineParticipant @johnhaine32865]

Over on the HSN Forum Tom Van Baak posted on the topic of what timing resolution is needed for high precision pendulum clock measurement.  You can see his post here.

He suggests that 1 us is enough, 0.1 us more than enough for short-term testing, and 1 ms / year for long term.  The best ever pendulum clock ever (the Littlemore) managed 50 ms over a year so the latter is 50x better, and Hall’s measurements were made to 1 us precision.

I think that variations on the order of nanoseconds from beat to beat will mainly arise from electronic and optical noise in the measurement system and will be “white”.  On longer timescales these variations average out – if you plotted the AVAR of the clock these would create a line going down at 1 decade of variation per decade of time and will usually be well below the variations of interest for timekeeping at time offsets of 10 s and above.

So whilst this discussion is interesting I think it’s academic from the p.o.v. of making an accurate clock. Even if Dave wanted to better the Littlemore clock 1 us is good enough (especially as its Achilles heel was probably ground vibration).

Once we can do short term measurements of the order of 1 us or a bit better more precision won’t help.  It would be different if making an atomic clock! Time is better spent on the actual clock in my view.

[S KParticipant @sk20060]

The statement that “0.1 us is (more than) good enough” sounds reasonable to me too. I have no doubt that the digital components can deliver that, but what of the rest?

John’s tests showed excellent position resolution that also seems at least, if not more than, sufficient, but they were static tests. They did not take into account the errors that will arise during dynamic running.

Taking the basic geometry of the Sharp as a starting point, 1 um light, a 1×1 mm emitter and sensor areas (a conservative guess), the flag swinging in the middle, a seconds pendulum with a swing amplitude of 0.1 m, and assuming 1000:1 signal to noise ratio (e.g. 5V signal, 5mV noise):

* The movement of the flag’s shadow dominates diffraction.

* The speed is 314 mm/s.

* The spatial gradient is 5V/mm.

* The signal’s slew rate is ~1,570 V/s.

* The estimated timing jitter is 3.18 us RMS.

* The estimated spatial jitter is 1 um RMS.

* By comparison, if measured with 100 ns resolution, then in that time, the pendulum would travel only 0.0314 um.

So the analog performance falls well below the performance implied by the digital logic. Is it still “more than good enough?”

Note that the above could be much worse if the S/N is worse (haha, is a Schmitt trigger good enough?).

Also, is it a coincidence that the ~3 us RMS timing jitter found here is about what I measured from an earlier pendulum using that opto? Maybe not.

Now, if I put 50 um slits in front of both the emitter and sensor, the situation changes dramatically:

* The slew rate becomes 31,400 V/s. (20x faster)

* The timing jitter becomes 159 ns RMS. (20x lower)

* The spatial jitter becomes 0.05 um RMS. (20x lower)

Now the dynamic performance of the analog and digital sections are much better matched, and tossing out “0.1 us resolution is more than good enough” makes more sense.

So, is there room for improvement after all?

 

 

 

 

[Robert Atkinson 2Participant @robertatkinson2]

For the best optical perfomance a mirror aligned with the axis of rotation deflecting a laser beam would give the best resolution as the movement of the spot is greatly amplified. This is how a galvanometer works. The mirror might have to be on a bracket to support it over the axis with most suspensions. A line generator (simple cylindrical lens) could be used to avoid issues with out of plane movement.

Robert.
(been suffering from a cold so a bit behind the curve on this one)

[John HaineParticipant @johnhaine32865]

Could someone explain what the increased resolution beyond say 1 us will do for us if we have it?

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