So, this system if I radiate out with a little square pixels here.

When I get to the aperture stop and

notice this is that Fourier transform plane right behind the lens.

I would see each of the spectra,

the spacial frequency spectra of those pixels laid out in space.

And the edge of the aperture stop would be right on the first null of that

sine x over x function.

And that's not a bad design principle because that's really what

the information is.

The extra bits of this Fourier transform carry the ship of the pixel, but

really this blob in the middle between the first nulls,

carries the information that there is a pixel there.

So what this Fourier space is, or this phase space, is I plotted here at

the plane of the object, where the light is in terms of position.

There's no light, then there's a lot of light, then there's none.

And this light is within plus or minus two and a half millimeters,

the size of the field.

I've imagined, just for clarity, I've turned one pixel right in the middle off.

So I have pixels that are on, and then the white line represents one pixel

that's off, and then the rest of the pixels are on.

And that's just sort of a convenient little marker.

And notice that, my marginal ray bounds the angular, or spacial frequency,

extent of the object, but it's at the object plane, zero position.

Yep, that's right there.

While the chief ray bounds the positional extent of this bundle

of information, but it's at zero angle.

Yep, that's right there.

So this phase space is a way of simultaneously looking at the spacial and

angular content on my beam of light.

And we see here in this nice telecentric case that we have this nice little box.

The area of that box, I noticed that's a unitless quantity

from here down to here turns out to be 2000.