- [Keith] Okay, hello everybody. I'm Keith Krause.

I'm also with the Airborne Observation Platform team.

I'm going to take what Tristan did,

and go a little more advanced.

I'm going to keep this presentation a little shorter than

the number of slides I have. So, fortunately,

Tristan covered several of my slides already,

and I'm going to try to introduce a little more

LiDAR theory, because it's kind of in the context

that hopefully will make sense of why our

waveform data looks the way it does.

Hopefully, that will make sense, and also talk a little bit

more about, you know, ask questions about

target detection and that sort of thing.

Some of that's going to come up a little more

in the waveform.

Tristan already kind of showed you Discrete LiDAR.

You're essentially finding returns or objects.

You get geolocations. That could be X, Y, Z

on a map. Intensity, other attributes.

That's great. But the hope is, with full waveform LiDAR,

you're actually measuring that entire signal

as a function of time.

The hope is that you can do more with that data.

We'll talk a little more about that.

One of the challenges in the past is that

full waveform LiDAR data just hasn't been

available to people.

There's a handful of groups that are working

with it right now, but you don't typically

see lots of papers or presentations on the subject.

We're hoping to change that.

At the current moment, we have LiDAR products

from some of our 2013 and 2014 flights.

That's available by request.

Unfortunately, we weren't able to collect any

waveform data last year, due to some instrument

hardware issues.

But we've been collecting it this year, in 2016,

and we're currently processing that data,

so it should be coming available, hopefully,

within the next couple of weeks.

As I mentioned, we hope more people get involved

with waveform LiDAR.

So, these are just more graphical representations

of what you've already seen from Tristan.

But I think the big thing in terms of waveform LiDAR

and what I'm going to talk about, just keep in mind right,

once again, you have this outgoing laser pulse,

some time goes by, and then you're able to record

some reflection of light as a function of time.

We're going to keep coming back to this change in time.

This is another form of one of the figures Tristan showed,

but from Texas A&M and Dr. Sorin Popescu.

We're going to zoom a little more into this plot here

in a second.

Once again, it's a 2D beam that's interacting

with objects as a function of time.

Keep in mind with LiDAR, time is distance.

Distance is time.

So, you have discrete return in full waveform.

Discrete return, there's usually onboard processing.

That realtime. We'll look at that signal and

try to do target detection, and then it does the ranging.

In Sorin's figure, he kind of talks about this idea that

depending on what sort of algorithm or hardware is used,

there could be a period of time where it detects an object,

and then might have to reset itself.

So, it can actually miss things.

The nice thing about the full waveform is,

you'll capture this entire signal as a function of time.

So, hopefully with post-processing,

you can go in and get more detail,

but as you'll see in a minute,

there are some complications too.

The hope is, looking at these waveforms,

just like with discrete data, you can start

to maybe imagine, based on the way the tree structure is,

that you might have overstory and some understory,

and maybe the ground.

You can start thinking about stratification of

either vegetation or other objects.

I'm not going to spend too much time here,

but just the general process of LiDAR is,

you fire your laser. You record your signal.

You do some sort of target detection.

Basically, once you've identified a target,

you can then look at the change in time

between that outgoing pulse and the received pulse.

You do some calculations that converts

that time-of-flight into a range.

Then from the range, you have your GPS IMU, and you can

figure out what direction the scan mirror is pointed at,

and then that gets you your coordinates.

So, just like discrete return points can have geolocation,

full waveforms can too.

You'll see with the product

that we include geolocation information.

In general, ranging follows kind of the basic

speed of light calculations from, I don't know,

a couple hundred years ago.

But essentially, in this case, we know the speed of light,

but you have the speed of light.

You have the change in time between

that outgoing and return pulse.

Remember the light has to travel there

and then also come back.

So the distance is actually half of that time.

And then, of course, you have the index of refraction

of air, because that laser light's actually going to

slow down a little bit traveling in air than say,

it would in space if you were in a vacuum.

So, that's just that absolute range.

You might also hear the term of range resolution.

Some people call this different, but Tristan mentioned,

you know, when objects get too close to each other,

you can't resolve them anymore,

and I'll show a figure of that.

But, essentially, that's going to be driven by

the outgoing pulse shape. So, these laser pulses don't

infinitely, or infinitesimally, jump up to a peak signal.

It does take time for it to ramp up, fire that laser,

and then ramp back down.

So, that shape will actually cause blurring,

and that's why you can't detect objects.

So, there are several different algorithms

for how you would do ranging.

Different manufacturers will use their different

proprietary algorithms.

I'm just going to show the really simple ones.

You can imagine that if you have your outgoing laser pulse,

then some time goes by. It reflects off,

in this case, probably the ground,

since you just get a single peak.

We're going to find the peaks, and then, in this case,

we're going to say, well, let's go and figure out

where the 50% energy is on the left side.

This would be called leading edge detection.

That's done in this case, mostly because,

if you look at the shape of this outgoing pulse,

it actually is kind of pushed more onto the right side.

So, it's not perfectly Gaussian.

Combination of, you have a sharper rise than you do a fall.

And then the other pieces.

This is the ground, so it's pretty simple,

but if you're interacting with the canopy,

you can imagine that that left edge

is going to be the top of the canopy,

so that might be where you actually want to range to.

I guess, one other thing to note.

The time between the outgoing pulse and the return pulse,

ends up being about 6500 nanoseconds.

When you do all the conversation, that comes out to about,

in this case, 983 meters.

You can imagine, if we're trying to fly

at about 1000 meters above the ground,

you have some terrain variation,

and there you're getting 983.

So, this may address your question a little bit,

but you can see, just with discrete and waveform,

you might get multiple peaks.

So, in this case, you could identify three objects,

and each of them has a leading edge.

So, you could identify in the discrete return,

three targets.

If you were just looking at the relative time difference

between these,

maybe you could say, this is the ground,

and this is the canopy top, and in this case,

the canopy would be 14 meters tall.

So, you can start to see, that might be one way that

you might analyze waveform data.

Rather than building a canopy height model on a raster grid,

you might be able to identify canopies and ground

within a single laser pulse, and now,

start looking at distance measurements that way.

So, a little more on range resolution and target separation.

This, hopefully illustrates what Tristan talked about.

In this case, I've just done a simulation,

and we're using a 10 nanosecond outgoing pulse,

which is typical of the Optech system,

I think at 70 kilohertz.

100 kilohertz might be a little wider,

so it would actually blur more.

But you can see in this case,

if you have a 10 nanosecond wide Gaussian,

and you take two ideal targets,

and put them 40 nanoseconds away from each other,

clearly you can see two peaks, and that's easy.

If you move them closer, you can see that the signal

starts to blend in the middle,

but you can still identify them.

Even here, no problem.

But you can see here, if you actually separate them

by exactly one of the full width half maxes,

to you and I, we still see kind of a double peak,

but actually a lot of algorithms might have a hard time

trying to determine where exactly those two peaks are,

and it might still say that there's one peak.

And as you get below,

if you get less than the full width half max,

you still had two targets in the original,

but you can see the signal sums into a single shape.

So, at this point, you've effectively lost your ability

to say there's definitely two objects there.

It could just be one object that was brighter.

And as you go even further, same kind of thing.

And you'll see, if we put some actual Gaussians on this.

At least in this case,

if you had a really sensitive algorithm,

you might say that, I only have one object,

but it's not a perfect Gaussian,

so maybe there's something else there.

But at this point, at half the full width half max,

you'd probably have no way of knowing

that there's two objects.

So, that's kind of the idea of range resolution.

You can imagine different branches in a tree,

if they're too close together, their signal is just

going to sum up and it's going to look like one big branch.

Not going to talk too much about this,

other than I do have a figure to kind of explain this.

But, one of the challenges with all these systems,

is being able to write the data fast enough to keep up.

Kind of as a comparison, the hyper spectral data.

You have a 640x480 array.

You're running it at 100 lines per second.

That's effectively equivalent to the data rate

the LiDAR runs at, at 100 kilohertz,

if we had 310 time bins that we were trying to save out.

Now, the difference is, the spectrometer has a fancy

computer, and I think it simultaneously writes

to four hard drives at the same time.

Whereas, the LiDAR, I think has a single hard drive.

So, there's kind of games you have to play,

making sure you're saving out that data fast enough,

or else the laser's going to keep firing,

and it'll just miss everything.

As an example, you might love to save the entire data space

from when you fired that outgoing laser all the way