Member postings for S K

A few updates and thoughts, including about the impact of diffraction and camera resolution:

I measured my slit to be 160 um wide. Project the laser through it, and it becomes painfully clear how serious a problem diffraction can be. Of course, a single edge, e.g. a flag, experiences diffraction too. This means that a hard edge will not yield a hard cut-off of the light. Instead, there will be a soft reduction in light that depends on the distance between the flag and sensor and the speed of the flag. The bottom line is that whatever flag or slit, etc., is used, it should be positioned as close to the sensor as practical. Even a centimeter is a lot!

Also because of diffraction, the use of a lens to magnify the motion of a flag will not work as well as hoped unless the distance between the flag and sensor is similarly short.

About the camera idea: For best resolution, I'd suggest directly projecting a shadow onto the bare sensor (no lens). You will not likely find a lens that will deliver the sort of resolution you are seeking. All of them, even a "telephoto," would actually be a wide angle (relatively speaking) compared to the raw pixel resolution. For example, if a field of view of say 100 mm is projected onto a sensor 10mm wide, then each pixel views a region 10 times larger than the size of the pixel itself, e.g. instead of 10um, you only get 100um resolution. For a camera to deliver "pixel resolution," it would have to observe a total field of view no bigger than the camera chip itself.

Again due to diffraction, in the direct projection scheme, the sensor should be as close to the flag as possible.

Where can one find information about the Bateman clock? I've searched and came up pretty empty. Thanks.

Edited By S K on 14/08/2023 14:54:24

We can try to measure better, impulse better, etc., but in the end, the pendulums are in control. 😄

I still wonder about the philosophy of a "free pendulum clock."

Does electromechanical impulsing and Hipp toggles have equal status with electromagnetic and optical means?

Is physical compensation, e.g. for temperature, more "pure" than entirely-detached measurement and computational compensation?

At what point does a pendulum become too "entangled" with outside electronics to still be a pendulum?

Edited By S K on 14/08/2023 01:00:12

Is that what he meant, really? There was talk about how the bob is motionless at its extremity, and claimed or implied that he could capture that motionless bob (how was my question).

If you use a continuous longer exposure, you could look for the extremity of a blur (but not a frozen flag). Flashes will risk missing the extremity and/or if close enough will appear as a blur too.

Anyway, I've already done this, as I said, looking precisely for the extremity because I wanted to do a Q finding. I did it with 240 Hz frames instead of longer ones, but that's not important. With all my pixel-peeping holding the camera inches from the pendulum, I was still only confident of ~0.5mm resolution of the extremity of the pendulum's motion. Can better be achieved? Probably some, but dreams of <=10 microns won't be easy.

Edited By S K on 13/08/2023 22:26:24

If you want to be understood, you will have to do better. Until then, I'm just going to presume that your idea, whatever it is, will most definitely suffer from the sorts of flaws that I've described.

Over and out.

Edited By S K on 13/08/2023 20:15:58

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

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

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.

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?

Yes, an Airy disk.

Any more ideas about optical gain?

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.

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

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

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

Another thought about Duncan's mirror idea: Unfortunately, if the baseline from the mirror to the sensor is the same as the pendulum's length, then it is no better than just flagging the end of the rod as normal. You would need a baseline much longer than the pendulum for it to make any sense. So I don't think it's very practical.

Yeah, no, let's not! Thank you!

Some more thought about the cylinder idea: The beam is not uniform across its diameter, and it has a 2D Gaussian intensity profile. This doesn't matter if the beam is stationary and aimed straight at the detector. But if the beam is sweeping, and especially if it's spread out, the voltage on the PD will rise and fall as it's swept past because the intensity will be constantly changing. A pinhole or slit could constrain it, e.g. to a central area, but diffraction will just spread the beam out again into the same basic shape anyway. So I'm not sure it works again.

Duncan, are you proposing that the mirror will sweep a small angle? That has the same intensity profile problem, but it's lessened in that it doesn't spread the beam out like the cylinder does - only the laser's own divergence would occur. And you wouldn't even need to dig a hole: A vertically-mounted mirror (i.e., at the side of the rod) to reflect in the direction of swing would accomplish the same thing. Similarly, a prism or right-angle mirror could reflect the light from the side up the pendulum, too (that might be the most practical orientation). Interesting and more promising!

Edited By S K on 11/08/2023 00:42:42

I thought of this a while back, and proposed it in some thread here somewhere, but then I decided it wouldn't work. The reason is that a cylindrical mirror will widen the beam exactly as much as the lever arm extends, and the two kind of cancel each other. So yes, the beam may sweep 10x faster out at some distance, but it will be widened and dimmed by 10x too. No?

But now I feel like something along these lines could still work as long as the laser is strong enough. Maybe I'll print up another holder with an angle between the laser and sensor to just try it empirically. My flag is my rod, which is shiny enough. I wonder what an optimal angle would be? I guess 60 degrees sounds OK.

Edited By S K on 11/08/2023 00:15:20

I don't need a comparator yet. For now I'm looking at the analog output straight from the photodiode. What I want to know is what the photodiode's own signal is doing so I gain an understanding of what an op-amp, etc., would have to work with. (The photodiode is definitely not close to saturating.)

So: I increased the load resistor to 10k, which significantly increased the I-to-V gain, in order to compensate for the reduced illumination through the slit. I also narrowed the slit a little more. I think I could go narrower still with some care.

The net result at present is roughly 80 mV signal and about a 3 ms rise/fall time. The rise and fall times are currently dominated by the speed of the flag, which causes the voltage to rise as more of the photodiode is illuminated or fall as more is covered.

I tried to use my counter to compute an RMS value for the period, but it would not work reliably with this signal level, so an op-amp will be needed to make more progress. Adding a comparator, Schmitt trigger, etc., can speed up the edges almost arbitrarily, but while that looks good, it says basically nothing about timing resolution of everything that came before.

If the slit technique is the best improvement that can be made, I could buy a precise one. These are available down to 3um and probably lower, but they are quite expensive. With a very narrow slit, a more powerful laser might help too.

Can you elaborate?

A lens focusing the beam to a spot right at the flag would help. But I don't think it would help more than an equivalently-narrow slit.

I was hoping for something like a lever-arm that could be arbitrarily long.

Edited By S K on 10/08/2023 21:48:36

I have some results - mostly anecdotal thus far - from testing a laser and photodiode combination. The setup is seen below.

The photodiode (Thor Labs FDS010) is silicon, and was selected for its small active area of 0.8mm^2 (1mm diameter). The small area means a small capacitance and hence high speed (quoted 1ns rise/fall time, presumably with a 50 Ohm load), plus a flag should spend less time traversing the surface during a pendulum swing.

The laser is a Thor Labs PO204, 635nm, Class 2 (<=1mW), with a lens and a round beam of about 3mm across. This wavelength is somewhat close to the photodiode's peak wavelenth sensitivity of 730nm. A Class 2 laser is generally safe, and is as bright as likely needed for this application, as it is indeed very bright: absolutely do not stare into the beam (with your remaining good eye)!

I have mounted a slit, made from two razor blade shards, vertically in front of the photodiode (the mount is very cheesy, but it works for now), with explanation below.

The photodiode is being run with a 5V reverse bias purely for convenience (10-20V would be better). A 380 Ohm load resistor is used to provide a detectable voltage while still maintaining a fast speed of operation.

I used my gravity pendulum as a test vehicle, and an oscilloscope to observe the output. The combined capacitance of the photodiode and the scope probe is slightly under 20pF. In combination with the 380 Ohm load resistor, this should be a very fast sensor.

But, without the slit, the rise and fall times were about 50 ms! This is very long, and at first I was confused (also by the linear slewing that was observed), but the reason is simple: it takes about that long for the pendulum to sweep across the ~1mm detector. I predicted this effect notionally (hence the small detector), but my mistake was not calculating how bad it would be!

Using the slit (not measured, but it's pretty small) reduced this to ~7ms, which I still consider to be very slow. And since it blocks a lot of the light, it also reduces the signal amplitude considerably:

There's a fair amount of noise in the signal, which I should track down.

Here's the dilemma: Pendulums are just too slow for good timing! Even with a narrow slit, the rise and fall times are much slower than I was hoping. The problem is that the slope of the rise/fall times is slow enough for noise to cause a fair amount of jitter in a comparator's output.

At this point, I am not at all surprised at the ~5us RMS noise in the Sharp sensor's output, and it's not clear to me that much better can be achieved without trickery. For now, I don't recommend that people spend the money on the above sort of combination. But for those using the Sharp opto-interrupter, a slit in front of the photodiode may help. Also, it's best to detect the swing at BDC, where it's moving the fastest.

To be continued after I spend some time in thought. Some way to optically amplify the speed of the pendulum is needed. Any ideas?

Edited By S K on 10/08/2023 21:12:55