Diffraction determined by entrance pupil or exit pupil?

Started 1 month ago | Questions thread
Jack Hogan Veteran Member • Posts: 7,432
Diffraction, Fourier and Focal Planes - Example

Jack Hogan wrote:

AiryDiscus wrote:

Jack Hogan wrote:

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?

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.

Goodman would beg to differ. Vectors are once again being placed wantonly and without thought, just like some of the others I lamented about earlier , QED.

Since no diagrams seem to be forthcoming here is mine, a 24mm prime at a working f/stop, from Bill's excellent optical bench page :

Goodman 3rd Edition, section 6.1.1, referring to the 'black-box' image shown a few posts ago (italics are mine)

  • Throughout this chapter we shall use the symbol [...] zi to represent the distance of the plane of the exit pupil from the image plane. The distance zi is then the distance that will appear in the diffraction equations that represent the effect of diffraction by the exit pupil on the point spread function of the optical system. We shall refer either to the exit pupil or simply to the "pupil" of the system when discussing these effects.

So zi, not focal length, is the distance to the Focal/Image plane to be used in Fourier Optics when propagating the complex field within the exit pupil plane to the image plane. With consequent implications for key parameters. I trust this was a worthwhile exercise.

BTW, what's effective aperture diameter D here?


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