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

When I get to the aperture stop, and

notice this is that 4D transform plane right behind the lens.

I would see each of the spectra,

the spatial 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 where the information is.

The extra bits of this Fourier transfer carry the shape 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 plot it here at

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

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

And this light is within plus or minus 2.5 millimeters, the size of the field.

I've imagined just the 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 is 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

spatial frequency extent of the object.

But it's at the object plane 0 position, yep that's right there.

While the chief ray bounds the positional extent of this bundle of information.

But it's at 0 angle, yep that's right there.

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

angular content of 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, and notice that's a unitless quantity,

from here down to here turns out to be 2000.