Real Life Beamforming with substandard arrays. Need help forming some sort of solution.

Hi,
I'm doing a very simple beamforming/phased array project for a bit of
fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
200kHz.
I'm having problems formulating a simple delay and sum beamformer.
When I do quite simply delay by so many samples and sum, what I get
are answers which are reasonable but wrong. So I cant quite figure out
what step I'm missing.

The data received are 4 Gaussian shaped sinusoids from a reflection
that is about head on (broadside).  If I add them up without delay I
get a nice big gaussian sine wave.  If I delay the data slightly then
the gaussian reduces but when I delay it enough so that the 4 signals
are about back in phase again (actually 360 degrees out) I get a big
gaussian again.  This makes total sense.  So what am I doing wrong?

I thought about retrieving the envelope of the gaussian then doing the
delay and sum, although I havent tried yet.  That should work, but I
dont think it is optimal in any sense.

Thanks for any responses.

Phil

On 25 Jun, 12:55, Phil Winder <philipwin...@googlemail.com> wrote:
> Hi,
> I'm doing a very simple beamforming/phased array project for a bit of
> fun. &#4294967295;What I have is 4 40kHz ultrasonic transducers being sampled at
> 200kHz.
> I'm having problems formulating a simple delay and sum beamformer.
> When I do quite simply delay by so many samples and sum, what I get
> are answers which are reasonable but wrong. So I cant quite figure out
> what step I'm missing.
>
> The data received are 4 Gaussian shaped sinusoids from a reflection
> that is about head on (broadside). &#4294967295;If I add them up without delay I
> get a nice big gaussian sine wave. &#4294967295;If I delay the data slightly then
> the gaussian reduces but when I delay it enough so that the 4 signals
> are about back in phase again (actually 360 degrees out) I get a big
> gaussian again. &#4294967295;This makes total sense. &#4294967295;So what am I doing wrong?
>
> I thought about retrieving the envelope of the gaussian then doing the
> delay and sum, although I havent tried yet. &#4294967295;That should work, but I
> dont think it is optimal in any sense.
>
> Thanks for any responses.
>
> Phil

I can think of a few main reasons for the problems:

1) Sampling synchronisation. Sampling the different channels
   with the required accuracy is a big deal. Are you sure
   your system is sufficiently precise?

2) Sensor directivity.  Ideally, array sensors ought
   to be omnidirectional. Unless a sensor has been designed
   to be used in an array, it is likely that the directivity
   is far from omnidirectional.

3) Reflections. Arrays that are used in multipath
   environments behave weirdly. One diagnostic is that
   some perform well only  at/near broadside.

And then there are implementations of the delay operator.
Unless you sort out how to implement fractional delay,
you might get weird problems.

One possible way of testing the hardware would be to
use a sinusoidal steady-state signal. Record the
signal for some time with the source at different
angles. Then compute the (f,k) spectrum of the signals
and see that the spike in the spectrum moves along
the k axis.

Rune

Phil Winder wrote:


> I'm doing a very simple beamforming/phased array project for a bit of
> fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
> 200kHz.

That looks like pretty coarse time resolution.

> I'm having problems formulating a simple delay and sum beamformer.
> When I do quite simply delay by so many samples and sum, what I get
> are answers which are reasonable but wrong. So I cant quite figure out
> what step I'm missing.
> 
> The data received are 4 Gaussian shaped sinusoids from a reflection
> that is about head on (broadside).

How the envelope of the pulse compares to the beamforming delays?

>  If I add them up without delay I
> get a nice big gaussian sine wave.  If I delay the data slightly then
> the gaussian reduces but when I delay it enough so that the 4 signals
> are about back in phase again (actually 360 degrees out) I get a big
> gaussian again.  This makes total sense.  So what am I doing wrong?
> 
> I thought about retrieving the envelope of the gaussian then doing the
> delay and sum, although I havent tried yet.  That should work, but I
> dont think it is optimal in any sense.
> 
> Thanks for any responses.

Try increasing the sample rate and use CW sine.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Jun 25, 3:14 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> Phil Winder wrote:
> > I'm doing a very simple beamforming/phased array project for a bit of
> > fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
> > 200kHz.
>
> That looks like pretty coarse time resolution.
>
> > I'm having problems formulating a simple delay and sum beamformer.
> > When I do quite simply delay by so many samples and sum, what I get
> > are answers which are reasonable but wrong. So I cant quite figure out
> > what step I'm missing.
>
> > The data received are 4 Gaussian shaped sinusoids from a reflection
> > that is about head on (broadside).
>
> How the envelope of the pulse compares to the beamforming delays?
>
> >  If I add them up without delay I
> > get a nice big gaussian sine wave.  If I delay the data slightly then
> > the gaussian reduces but when I delay it enough so that the 4 signals
> > are about back in phase again (actually 360 degrees out) I get a big
> > gaussian again.  This makes total sense.  So what am I doing wrong?
>
> > I thought about retrieving the envelope of the gaussian then doing the
> > delay and sum, although I havent tried yet.  That should work, but I
> > dont think it is optimal in any sense.
>
> > Thanks for any responses.
>
> Try increasing the sample rate and use CW sine.
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultanthttp://www.abvolt.com

Hi, thanks for the replies.
@Rune:
Synchronisation is not a big problem here, since all the targets and
the array are static.  Results taken are always the same.
I havent seen any multipath in my setup, the walls are quite far away.
The delay operator is simply having the data pointer at incremented
intervals.  E.g. A[0], B[2], C[4], D[6].  What do you mean by
fractional delay? Do you mean I would have to interpolate the data so
that I could do A[0], B[0.5], C[1], D[1.5] ??
And that is all I am really doing with this test, although I am
creating the signal on the same board so I do rely on reflections.
Thanks.
@Vladimir:
Yeah I know, but unfortunately thats as fast as my ADC will go on the
microcontroller.  Like before, I could interpolate?
The envelope is very long compared to the delays.  Hence the 360
degree in-phase problem.
What ido you mean by "CW Sine"?

Thanks,
Phil

On Jun 25, 3:55 am, Phil Winder <philipwin...@googlemail.com> wrote:

> Hi,
> I'm doing a very simple beamforming/phased array project for a bit of
> fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
> 200kHz.

You  haven't said what the array shape is. Is it a line equally
spaced? If so, how far apart are the elements?

> I'm having problems formulating a simple delay and sum beamformer.
> When I do quite simply delay by so many samples and sum, what I get
> are answers which are reasonable but wrong. So I cant quite figure out
> what step I'm missing.

> The data received are 4 Gaussian shaped sinusoids from a reflection
> that is about head on (broadside).  If I add them up without delay I
> get a nice big gaussian sine wave.

That's good.

> If I delay the data slightly then the gaussian reduces

That's good

> but when I delay it enough so that the 4 signals
> are about back in phase again (actually 360 degrees out) I get a big
> gaussian again.  This makes total sense.

True

> So what am I doing wrong?

You have failed to recognize that you have rediscovered spatial
aliasing.

>
> I thought about retrieving the envelope of the gaussian then doing the
> delay and sum, although I havent tried yet.  That should work, but I
> dont think it is optimal in any sense.
>
> Thanks for any responses.
>
> Phil

Most of the linear array beamforming literature deals with arrays
where the element separation is less that or equal to half a
wavelength at the highest frequency of interest. This is the same as
being at or below the Nyquist frequency for the spatial sampling.
Where does your array fit in?

Dale B. Dalrymple

On 25 Jun, 19:20, Phil Winder <philipwin...@googlemail.com> wrote:
> On Jun 25, 3:14 pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
> wrote:
>
>
>
>
>
> > Phil Winder wrote:
> > > I'm doing a very simple beamforming/phased array project for a bit of
> > > fun. &#4294967295;What I have is 4 40kHz ultrasonic transducers being sampled at
> > > 200kHz.
>
> > That looks like pretty coarse time resolution.
>
> > > I'm having problems formulating a simple delay and sum beamformer.
> > > When I do quite simply delay by so many samples and sum, what I get
> > > are answers which are reasonable but wrong. So I cant quite figure out
> > > what step I'm missing.
>
> > > The data received are 4 Gaussian shaped sinusoids from a reflection
> > > that is about head on (broadside).
>
> > How the envelope of the pulse compares to the beamforming delays?
>
> > > &#4294967295;If I add them up without delay I
> > > get a nice big gaussian sine wave. &#4294967295;If I delay the data slightly then
> > > the gaussian reduces but when I delay it enough so that the 4 signals
> > > are about back in phase again (actually 360 degrees out) I get a big
> > > gaussian again. &#4294967295;This makes total sense. &#4294967295;So what am I doing wrong?
>
> > > I thought about retrieving the envelope of the gaussian then doing the
> > > delay and sum, although I havent tried yet. &#4294967295;That should work, but I
> > > dont think it is optimal in any sense.
>
> > > Thanks for any responses.
>
> > Try increasing the sample rate and use CW sine.
>
> > Vladimir Vassilevsky
> > DSP and Mixed Signal Design Consultanthttp://www.abvolt.com
>
> Hi, thanks for the replies.
> @Rune:
> Synchronisation is not a big problem here, since all the targets and
> the array are static. &#4294967295;Results taken are always the same.
> I havent seen any multipath in my setup, the walls are quite far away.

Famous last words...

You need to consider the duration of the pulse (T) and the
speed of sound in the medium (c). The spatial scale is
determined by the length (in meter) of the pulse, computed as

L = c*T.

So if the pulse lasts for 0.1 s and the medium is air with
sound speed 340 m/s, the length of the pulse is 34 meters.
If there is any reflecting surface (walls, ceilings, floors,
ground) in your setup is closer than that, you are de facto
dealing with multipath propagation.

> The delay operator is simply having the data pointer at incremented
> intervals. &#4294967295;E.g. A[0], B[2], C[4], D[6]. &#4294967295;What do you mean by
> fractional delay? Do you mean I would have to interpolate the data so
> that I could do A[0], B[0.5], C[1], D[1.5] ??

Yes.

The time delay td between consecutive elements in uniform
linear arrays is given by the direction of arrival as
something like (writing off the top of my mind, might
not be 100% correct)

td = D*cos(theta)/c

where D is the distance between sensors, c is the speed of
sound, and theta is the direction of arrival relative to
the array axis.

So if you constrain yourself to integer delays you will
only be able to steer the beam in a few directions. If
you can implement arbitrary delays you can steer the
beams in any direction.

Rune

"Phil Winder" <philipwinder@googlemail.com> wrote in message 
news:ea3868f4-81b2-4721-99a3-1ce0c5dab835@m73g2000hsh.googlegroups.com...
> Hi,
> I'm doing a very simple beamforming/phased array project for a bit of
> fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
> 200kHz.
> I'm having problems formulating a simple delay and sum beamformer.
> When I do quite simply delay by so many samples and sum, what I get
> are answers which are reasonable but wrong. So I cant quite figure out
> what step I'm missing.
>
> The data received are 4 Gaussian shaped sinusoids from a reflection
> that is about head on (broadside).  If I add them up without delay I
> get a nice big gaussian sine wave.  If I delay the data slightly then
> the gaussian reduces but when I delay it enough so that the 4 signals
> are about back in phase again (actually 360 degrees out) I get a big
> gaussian again.  This makes total sense.  So what am I doing wrong?
>
> I thought about retrieving the envelope of the gaussian then doing the
> delay and sum, although I havent tried yet.  That should work, but I
> dont think it is optimal in any sense.

Phil,

Vladmir suggested higher temporal resolution.  You should get into the 
numbers if you want to think this through:

- you are currently sampling 5 times per cycle.  That amounts to samples 
that are 360/5 = 72 degrees.  That's a lot of phase shift.  Thus the 
comments you get regarding fractional delays.  The simple solution is to be 
able to beamform without fractional delays.  What is the minimum phase shift 
you need in the implementation?

You didn't really say what beamforming implementation other than delay and 
sum you're using.  You didn't say what "reasonable but wrong" means to you. 
By my reckoning, if everything is perfectly aligned in time according to 
your description, the first steered beam you could form would be with phase 
shifts of 0, 72, 144, 216 degrees - assuming an integral number of samples 
to form a delay using 0, 1, 2, 3 sample shifts.

You didn't say what the spacing between elements is.  The sum of the 
elements has a beam pattern determined by the spacing.  As you delay the 
element outputs this has an affect for everything that's not broadside. 
This is a big deal so you can't overlook it.  The beams that are formable 
depend on the element spacing.  You need to relate the electrical phase 
angles (delays) to the mechanical phase angles (the beam steering direction) 
somehow.

Consider this:  let's put the element spacing at 360 degrees of phase - the 
same as 5 samples.  That means they are 0.0281 feet apart for 40kHz.
OK - so now even if you don't delay any of the elements there will be beam 
pattern peaks at broadside and at endfire.  And, when you delay each element 
in increments of 5 samples they will all be in phase again. 90 mechanical 
degrees is the maximum steering angle for a line array because the beam is 
"conical" and 75 degrees and 105 degrees are on the same conical beam that's 
formed. ..... well, conical in a perfect sense which this isn't.  There will 
be big sidelobes.

And, if you have this spacing then you can steer the beam in increments of 1 
sample delay (theoretically).  I think this works out to beams that are 
spaced 22.5 degrees apart.

Now, if the target is always broadside then how are you testing the 
beamformer?  At best you will get an attentuation as you steer the beam away 
from broadside.  There will be sidelobes that will have less attentuation. 
All this in a perfect world.

But, you don't get the gaussian shape?  There are two key reasons for this 
that I can think of:

1) Beamformers by their nature create constructive and destructive 
interference of the received waveforms.  If you have strong destructive 
interference in the middle of the waveform for a particular beam steering 
direction then that will definitely change the envelope.  This will 
definitely happen if you steer a null toward the target.  The middle of the 
gaussian (if it's long enough) will be zero and all you will see are the 
leading and trailing edges. ... just like a FIR filter transient response.

2) If there is any multipath then that acts a bit like a set of additional 
delays laid on top of each element/delay and you can get what's described in 
#1.  Lloyd's Mirror is a simple example of this where peaks and nulls are 
formed as a function of frequency.

Fred 

Phil Winder wrote:
> Hi,
> I'm doing a very simple beamforming/phased array project for a bit of
> fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
> 200kHz.
> I'm having problems formulating a simple delay and sum beamformer.
> When I do quite simply delay by so many samples and sum, what I get
> are answers which are reasonable but wrong. So I cant quite figure out
> what step I'm missing.
> 
> The data received are 4 Gaussian shaped sinusoids from a reflection
> that is about head on (broadside).  If I add them up without delay I
> get a nice big gaussian sine wave.  If I delay the data slightly then
> the gaussian reduces but when I delay it enough so that the 4 signals
> are about back in phase again (actually 360 degrees out) I get a big
> gaussian again.  This makes total sense.  So what am I doing wrong?
> 
> I thought about retrieving the envelope of the gaussian then doing the
> delay and sum, although I havent tried yet.  That should work, but I
> dont think it is optimal in any sense.
> 
> Thanks for any responses.
> 

You haven't told us about the geometries, distances, medium (water?) 
etc. As Vladimir mentioned a 1/5th cycle delay granularity is rather 
coarse. Us medical ultrasound guys usually shoot for 1/20th or better. 
So you may have to increase your sample rate.

Find out what the ultrasound propagation speed in your medium is. Then 
calculate the delay between target and each transducer. Multiply times 
two (often forgotten in the heat of the game ...) and see how much delay 
you need for each. That should always jibe.

Of course, 40kHz easily gets into frames, surfaces and so on and then 
you end up having one big transducer instead of four. They need to be 
somewhat isolated and have good backing material. Fixing all four onto a 
hard surface with some epoxy won't likely cut it. Mounting and backing 
is a whole science to itself, we often have special materials engineers 
just for that.

-- 
Regards, Joerg

http://www.analogconsultants.com/

"gmail" domain blocked because of excessive spam.
Use another domain or send PM.

On Jun 26, 2:03 am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:
> "Phil Winder" <philipwin...@googlemail.com> wrote in message
>
> news:ea3868f4-81b2-4721-99a3-1ce0c5dab835@m73g2000hsh.googlegroups.com...
>
>
>
> > Hi,
> > I'm doing a very simple beamforming/phased array project for a bit of
> > fun.  What I have is 4 40kHz ultrasonic transducers being sampled at
> > 200kHz.
> > I'm having problems formulating a simple delay and sum beamformer.
> > When I do quite simply delay by so many samples and sum, what I get
> > are answers which are reasonable but wrong. So I cant quite figure out
> > what step I'm missing.
>
> > The data received are 4 Gaussian shaped sinusoids from a reflection
> > that is about head on (broadside).  If I add them up without delay I
> > get a nice big gaussian sine wave.  If I delay the data slightly then
> > the gaussian reduces but when I delay it enough so that the 4 signals
> > are about back in phase again (actually 360 degrees out) I get a big
> > gaussian again.  This makes total sense.  So what am I doing wrong?
>
> > I thought about retrieving the envelope of the gaussian then doing the
> > delay and sum, although I havent tried yet.  That should work, but I
> > dont think it is optimal in any sense.
>
> Phil,
>
> Vladmir suggested higher temporal resolution.  You should get into the
> numbers if you want to think this through:
>
> - you are currently sampling 5 times per cycle.  That amounts to samples
> that are 360/5 = 72 degrees.  That's a lot of phase shift.  Thus the
> comments you get regarding fractional delays.  The simple solution is to be
> able to beamform without fractional delays.  What is the minimum phase shift
> you need in the implementation?
>
> You didn't really say what beamforming implementation other than delay and
> sum you're using.  You didn't say what "reasonable but wrong" means to you.
> By my reckoning, if everything is perfectly aligned in time according to
> your description, the first steered beam you could form would be with phase
> shifts of 0, 72, 144, 216 degrees - assuming an integral number of samples
> to form a delay using 0, 1, 2, 3 sample shifts.
>
> You didn't say what the spacing between elements is.  The sum of the
> elements has a beam pattern determined by the spacing.  As you delay the
> element outputs this has an affect for everything that's not broadside.
> This is a big deal so you can't overlook it.  The beams that are formable
> depend on the element spacing.  You need to relate the electrical phase
> angles (delays) to the mechanical phase angles (the beam steering direction)
> somehow.
>
> Consider this:  let's put the element spacing at 360 degrees of phase - the
> same as 5 samples.  That means they are 0.0281 feet apart for 40kHz.
> OK - so now even if you don't delay any of the elements there will be beam
> pattern peaks at broadside and at endfire.  And, when you delay each element
> in increments of 5 samples they will all be in phase again. 90 mechanical
> degrees is the maximum steering angle for a line array because the beam is
> "conical" and 75 degrees and 105 degrees are on the same conical beam that's
> formed. ..... well, conical in a perfect sense which this isn't.  There will
> be big sidelobes.
>
> And, if you have this spacing then you can steer the beam in increments of 1
> sample delay (theoretically).  I think this works out to beams that are
> spaced 22.5 degrees apart.
>
> Now, if the target is always broadside then how are you testing the
> beamformer?  At best you will get an attentuation as you steer the beam away
> from broadside.  There will be sidelobes that will have less attentuation.
> All this in a perfect world.
>
> But, you don't get the gaussian shape?  There are two key reasons for this
> that I can think of:
>
> 1) Beamformers by their nature create constructive and destructive
> interference of the received waveforms.  If you have strong destructive
> interference in the middle of the waveform for a particular beam steering
> direction then that will definitely change the envelope.  This will
> definitely happen if you steer a null toward the target.  The middle of the
> gaussian (if it's long enough) will be zero and all you will see are the
> leading and trailing edges. ... just like a FIR filter transient response.
>
> 2) If there is any multipath then that acts a bit like a set of additional
> delays laid on top of each element/delay and you can get what's described in
> #1.  Lloyd's Mirror is a simple example of this where peaks and nulls are
> formed as a function of frequency.
>
> Fred

Wow, thanks for all the time guys.  Well thought out posts there.
Well firstly I will answer some general questions that some of you
put:

Spacing: Yes, I am using 1 wavelength seperation, or 360 degrees.
This is purely a mechanical constraint.  I figured the wavelength to
be 8mm.  Now the transducers are 15mm wide so I had to mount them in a
-_-_ format so that the element spacing will be constrained.  I
believed that this would introduce a vertical directivity, but not
affect the horizontal.  This is acceptable.

Medium: Air.

Receive Pulse Length: About 6mS = 2m.  Plus its not quite gaussian.
Its more like the transmission signals you see. Curved up then decay
down.

@Dale: I think that most people agree that there is not enough
resolution here so I will try and implement something a bit more fine
scale by interpolating.  I dont really want to use an external ADC to
keep it simple.  I will try and get it working this way, and if it
doesnt then I might give it a try.

@Rune: Ah yeah, never thought of it that way. Well you could argue
that the spreading in the pulse is in some part due to multipath.
That will only affect the temporal resoultion, so I not too fussed
about that yet.  I want to get some sort of directivity first.   And
yes, I will try and interpolate and see if that helps.

@Joerg: Yes it is very course.  It is a constraint of my hardware and
its at it's maximum already.  I could get an external ADC but this
would complicate things further.  As for distance, I'm trying to go as
far as possible.  At the moment its about 2m, but I'm hoping to get
more when I swap to a better microcontroller.  My test object is about
30cm away.
Yes thats a good idea, just to have a look at the times.  I'll try
that.
And transducer frame coupling, bit too advanced yet.  In any case I am
only steering the receive at present. Not the transmit.  But yes that
could be a problem.  In the future I will test for that.  Thanks.

@Fred: Long post!  Yes I agree that the conversion is slow.  10
degrees of accuracy would be great, but for now 45 degrees would make
me go yaaaay.  But I disagree that increasing the conversion rate
would be simplest.  It means extra hardware and extra coding.  If I
did it in software then its not going to be strictly true, but its
only coding.  A lot simpler.
Beamforming, is delay and sum.  Thats it.  The transmit is currently
firing a broadside pattern (assuming that it doesnt become one big
coupled transducer from Joerg).  By resonable I meant that the signals
go from being in phase out of phase then in phase again although the
envelope has clearly moved causing a large signal again.  But I think
interpolating and making sure that I dont go over 180 degrees should
fix that.
I did some simulations on the beam width, and its wide.  Very wide
about 30 degrees, but it is directional.  And that is the aim at the
moment.  Beta 1 as it were.  Plus because of the 1 wavelength spacing
there were some nasty side lobes around the end fire.  But because of
the directionality of the transducers (vaguely directional) I thought
that these would compensate slightly for the bad side lobes.  But
obviously I wouldn't be able to get anything on or near to end fire.
I am not scanning the transmit, only the receive.  And Im doing that
in software.  So yes I agree that the sidelobes would have something
nasty to say, but I want to see more of a distinction.  I think
interpolation is the way to go.
And finally, yes I do get the Gaussian shape.  Its due to the
transmission medium and the fact that I am putting a squarewave in to
drive the transmitters.  The pulse would get "smoothed" out because of
the transducers mechanical resistance and then due to multipath and
scattering the pulse comes back as described.

Thanks to all of you that have replied.  Any more thoughts then feel
free to answer back, but for the mean time I am going to give the
interpolation a go.
Best Regards,
Phil

Phil Winder wrote:

[...]

> @Rune: Ah yeah, never thought of it that way. Well you could argue
> that the spreading in the pulse is in some part due to multipath.
> That will only affect the temporal resoultion, so I not too fussed
> about that yet.  I want to get some sort of directivity first.   And
> yes, I will try and interpolate and see if that helps.
> 

Interpolation after the acquisition won't yield that much. Since it 
seems you are bent on using a small uC you could try this:

a. Fire -> Acquire at 200ksps.
b. Fire one MCLK cycle delayed -> Acquire at 200ksps.
c. Fire two MCLK cycles delayed -> Acquire at 200ksps.
d. ...
.
.
.

Stop after you are one MCLK cycle away from a 360 turn on your 200kHz 
ADC clock. Now stitch together all the information gathered. Now if your 
uC begins to choke under all that data you could loosen the spec a bit, 
maybe step several MCLK cycles each time but you need to get into the 
vicinity of at least 1MSPS.

This is pretty much how digital scopes work in equivalent time sampling 
mode, where their ADC isn't fast enough for the signal. It requires that 
the signal doesn't move, or in your case that the targets don't move too 
much.

[...]

-- 
Regards, Joerg

http://www.analogconsultants.com/

"gmail" domain blocked because of excessive spam.
Use another domain or send PM.