Re: Pupils: Planes vs Curves

Jack Hogan wrote:

AiryDiscus wrote:

Jack Hogan wrote:

bclaff wrote:

Jack Hogan wrote:

...

Entrance and Exit pupils are virtual planes - and images of each other related by pupil magnification, so either will work. ...

A couple small points, since this is the PS&T forum.

We generally treat them as planes but they are in fact normally curved.

We generally only consider them viewed on-axis; off-axis they often move and rotate.

Yeah, I've been thinking about that, I believe this is the source of many incorrect assumptions and conclusions, at least on my part. My current understanding, which comes in large part from Goodman, is that whether they are plane or curved depends on the definition one uses, which depends on the intended purpose.

No, their meaning is never ambiguous. The entrance and exit pupils are clearly and strictly defined as the images of the aperture stop, viewed through the front or rear member of a lens.

That may very well be for you and your cohorts. As for me, I've been confused aplenty by many pictures in supposedly respected papers and texts that show incorrectly located vectors representing distance to the imaging and/or focal plane. For a lens focused at infinity the arrow jumps arbitrarily from gaussian sphere to principal plane to exit pupil at the whim of the writer as if they were all the same, though they clearly aren't.

Would you like to link something?

A 'member' is all optical elements in front of or behind the stop.

When dealing with diffraction in Fourier Optics one takes the complex-lens as black-box approach, where the Entrance and Exit pupils represent the terminal properties of a complex lens simplified down to just those two elements.

No, this is not what the pupil is in physical optics. Physical optics inherits all elements, assumptions, and definitions from geometric optics. Superset, not alternative set.

That may very well be, but In Fourier optics the source I mentioned is pretty clear, referring to the terms in italics above (Goodman ch. 6):

... the "terminals" of this black box consist of the planes containing the entrance and the exit pupils.

This text does not appear in chapter six of the current edition of the book. I will assume you're using an illegally acquired copy of the second edition, which is easy to find online.

If you look in the appendix of that edition, which you are directed to do mere words away from what you quoted, you find a definition that is not in any material way different to what I described;

The entrance pupil of the optical system is defined as the image of the most severely

limiting aperture, when viewed from the object space, looking through any optical

elements that may precede the physical aperture. The exit pupil of the system is also defined as the image of the physical aperture, but this time looking from the image

space through any optical elements that may lie between that aperture and the image

plane.

So, "in Fourier optics the source you mentioned" is pretty clear, indeed, and it is in discord with your representation of what it says.

The diffracting aperture is assumed to lie in a plane and the field within it is what is propagated to the image plane. Any deviations from the ideal (including aberrations) are assumed to be phasor differences built into that field. So in this case I believe the pupils are planes.

No, the aperture is assumed to lie at the instantaneous transition between collimated and focusing space. Your exact interpretation of where this is depends on the assumptions you make. If you assume your system is described by paraxial optics of slow F/#, then this is (approximately) a plane. If the F/# is fast, then it is almost certainly the surface of a paraboloid.

As I mentioned earlier, that may very well be if you take a different perspective. But Goodman says clearly above that that's not the case in Fourier Optics.

See above.

The assumption there is that the exit pupil is a plane containing a flat phase shifting plate representing all abnormalities.

You put too many buzzwords in there to make sense. If you're saying the pupil is a binary object that may contain some phase change, that is not true either. Nonbinary pupils are covered in some depth in the good book, and are 'widely' used for coronagraphy.

The pupil and plate have only x and y dimensions, not z. If another interpretation of Goodman's words is possible, I'd be happy to hear it.

The pupil function P (!= pupil, again) must exist in a plane. The pupil must not. See the paragraph I quoted.

For the typical black box treatment, we use a pupil function which is not precisely the same as a pupil. The pupil function exists in a plane and has amplitude and phase such that it is equivalent to the pupil, with all of its complexity. It cannot capture pupil aberrations, for example.

The way I read it, Goodman makes different assumptions for his purposes and therefore uses the terms differently.

No, he does not.

In the meantime I have a skill-testing question for you or anyone interested:

Let's say you have such an exit pupil and related function, a lens of focal length f and f-number N, focused at infinity. You use Fourier Optics to propagate the field at the exit pupil to the focal plane. How far precisely is that from the exit pupil? From the principal plane?

Be precise, show your assumptions and your work.

Depends on your assumptions and approach.

In the case that you wish to use a plane to plane (free space) propagation to move from the XP to the image, you would use whatever the distance is between the pupil and the image. The principle plane is not necessary to be considered. There is not really any work to show for this. You are asking to move from one plane to another, so you must propagate the distance between them. You must apply a quadratic phase at the XP with this approach.

In the case that you wish to invoke the Fourier transforming property of a lens and use what I would call a focusing propagation, simply taking an FT, then the distance is one focal length.

There is, again, no work to show (this is the fourier transforming property of a lens), unless you would like me to recreate proofs that have been known for what is now a very long time.

I encourage you to read the whole book, and not skim it around formulas you want to lift without context. Or take a course in the topic.