"Kurt Sutherland" <
[email protected]> wrote in message
news:
[email protected] om...
> Hello,
>
> I am trying to capture the motion of a mechanism with a high speed
> camera. The motion is a transient impact that reverses direction
> with about 100 g's of acceleration.
>
> I have the displacement curve as acquired from a laser doppler sensor
> and I'm
> reading it on an oscilloscope with very high sampling rate. However,
> the camera is a much slower rate (4000 fps). My question:
>
> How do you determine an adequate sampling rate for a transient event
> such
> as this? The Tektronix notes say you need a BW of 5 times the highest
> frequency content of your signal. They also try to relate bandwidth to
> rise time, but I don't know how that applies here.
>
> I will transform my displacement signal into the frequency domain to
> look at the frequency content next.
Kurt,
It looks like you have the right idea.
The displacement measurement, with its high sample rate, should give you
adequate information.
Another way to look at it was already suggested - how much displacement
error can you stand between frames?
Maybe instead of thinking about sampling in time we should be thinking about
sampling in space. Then you need to sample at a rate that is greater than
2x the spatial frequency or at a spatial interval that is less than 1/2 the
spatial separation of important features. Or, in your case, that is less
than the allowable position error of the measurement.
If you know the displacement as a function of time (sampled at a very high
rate) then perhaps you can relate the two:
Let's pose the question this way:
A high-speed object at velocity v0, at time t0, starts to decelerate at time
t0. It reverses direction and just reaches velocity -v0 = v1 at time t1.
What is the (maximum) displacement when the velocity reaches zero between t0
and t1?
How accurately must that displacement be measured?
There are two approaches that I'm sure someone will bring up:
1) You can sample the position with a camera and interpolate the position
from those frames. If you know a lot about the acceleration, you might do a
very good job with this approach. I'll not discuss this right now.
2) If you must brute force the measurement by only taking sample frames and
assume there is no interpolation, then consider this:
If you only sample at t0 and t1, then you haven't got a very good
measurement of the maximum displacement.
If you sample at intervals of (t1-t0)/2 then it could be much better but
only if you can register the samples at exactly t1 and t0 and only if the
acceleration is constant.
Assuming you can't do this we might assume that you are perfectly misaligned
with t1 and t0 - so it would be better to sample at intervals of (t1-t0)/4
and capture displacements at t0, t1 and [t0 + (t1-t0)/2] as well as at [t0 +
(t1-t0)/4] and at [t0 + 3*(t1-t0)/4]
But you can't know that you are perfectly misaligned either. So even the
approach above could yield position uncertainties as great as perhaps the
equivalent displacement to a time interval of (t1-t0)/8 (using linear
interpolation)
...... and so on.
You didn't say how you're going to use the frames. Given that you have the
high rate oscilloscope displacement data and know what you're going to do
with the frames, I'd say you already have enough information to decide what
to do with the camera.
It does appear that synching the camera with the "event" could help by as
much as a factor of 2 over the worst case arbitrary camera timing.
Also, if the experiment is repeatable, how about taking multiple frame
sequences with a variety of synch points relative to the "event" and
interleaving whole frame sets with appropriate temporal registration? The
result would likely be somehwat "noisy" but could have some benefit.
The latter could be viewed as follows:
What if the experiment were noiseless / repeatable and was actually
continuous and periodic. It just keeps happening over and over again with
the same frequency.
Then you could sample the periodic result at an interval that is slightly
shorter than the period - and not harmonically related ... like 3/pi of the
period. The longer samples are taken, the more "filled" in the period with
samples.
Now, this argues that the sample interval never has to be more than
slightly shorter than 2*(1/2) the period, no matter the frequency content of
the signal - as long as one can spend enough time sampling. That seems to
fly in the face of common thinking. I guess the "trick" is very accurately
knowing what the period is so that succeeding samples can be registered with
samples from preceding periods. Normally we don't allow ourselves to "know"
that in general DSP processing as compared to computing a Fourier Series.
Fred