Now let's use the next capability of the program,

which is to analyze the performance of the lens.

If you notice, the next tab after setup is analyze.

And the first set of analysis tools along the toolbar,

are actually the ray diagrams that we've been looking

at already, particularly the cross-section.

After that we see things like rays and spots.

So let's go to the standard spot diagram.

And what this does,

drag it over here.

Is it gives you a view of a set of

nested cones of rays and how they land in our image plane here.

So this view is just basically looking at,

as if there's a piece of paper in the image point here,

and every ray when it landed made a little spot,

and each of these are the spots that it made.

So there's nested cones of rays that are launched into the lens.

Of course in this cross-section view we're almost seeing a slice through those cones.

And most of them land near the axis,

near the optical axis near the origin, and that's just what you want.

And an ideal lens would put all of the rays there.

But of course, we've already seen that these rays launched through the edge of

the aperture stop are falling far off of the perfect image position.

And so we see those as circles that are expanding away from that perfect spot.

So the reason I wanted you to see this is later

on we'll ask the program to calculate an average,

or effective spot size,

perhaps through a root mean square,

or a mass calculation,

and that can be used then to drive optimization,

to make the lens bigger.

What we see here basically we got,

rays that have landed in a big cone far from the ideal focus.

Now to get a better picture of that,

let's call out the ray aberration diagram.

And this is my favorite of all of the analysis tools.

It's the same thing again,

but just presented little more quantitatively.

What we have here is two views in the x and y planes.

They're identical because this system is symmetric.

The P coordinates here Px and Py,

basically tell you where the ray landed,

where it went through the stop P zero.

P equals zero is at the origin on the optical axis,

and one is right through the edge.

The coordinate this way is,

once again what we're going to call the ray error later on in the course,

it's how far off the ideal position did the ray land.

So an absolutely perfect lens,

would have straight blue lines right through the origin here.

And that would be all of the ray errors were zero.

All of the rays launched into

the lens landed exactly at the same position at the upper plane here.

And what we see here which is very typical,

is that near the axis,

we'll call this paraxial for near the axis later on.

The lens performs pretty well,

because there all the rays are landing where they should be,

with a ray error of zero.

But as we launch rays farther and farther from the axis into the stop,

we see greater and greater ray error.

Later on the course we're going to learn that the shapes of these ray error curves,

these aberration curves, tell us what kind of aberration we have.

This particular one is a spherical aberration.

So this gives you a flavor that there's all sorts of tools here.

We just dipped our toe into them,

but there's various ways of looking at the performance of the lens,

and having it calculate in real time how the lens is doing.

And by in real time,

I mean if we went up here and changed this to be a less powerful lens,

less curved surfaces, maybe 70 millimeters, these recalculate.

This plot has rescaled.

It looks kind of the same, but it's rescaled the axis.

And this lens is actually working a little bit better.

And we can kind of see that here,

because that spread of rays down near the focus is not quite so big.

So the point is, we now have a way of analyzing the performance of lenses.

And what we primarily learned is that even

this super simple lens that's a pretty weak lens,

these surfaces aren't very curved,

doesn't actually perform very well and that's an important point.

Lenses in general are difficult to make work

well and that is why optical designers have jobs.