Diffraction and Aperture Size: How Does It Affect Image Resolution?

[peter.ell]

Hi there, I understand somewhat how diffraction works in terms of the aperture of a camera lens and the resulting loss in resolution in the image, but my question is:

Is the degree of diffraction only dependent upon absolute aperture size, or the size of the entrance pupil? For example, f/22 shows noticeable diffraction with a wide-angle lens where the size of the aperture is, say, 1mm. But if I keep the f/22 but change the focal length to get longer on a zoom lens with a constant f/stop (it does this by magnifying the size of the entrance pupil to compensate for the longer focal length, essentially just a magnified virtual image of the aperture), then would I get less or the same amount of diffraction? I would guess it must be the same, but since the light passes through the 1mm aperture as if it were larger, perhaps there would be less diffraction?

Also, how is it that simply having a magnified virtual image of a small aperture give the same exposure as an aperture that is bigger? Why doesn't light just respond to the actual size of it?

And one more: I heard that diffraction in camera lenses is always present, but just begins to occupy a greater percentage of the total light hitting a sensor when the aperture is small. If this is true, then why is the airy disk smaller at larger apertures? Isn't diffraction just due to passing by the aperture blades, thus a larger aperture should either have the same sized airy disk or more since light would diffract over a greater area on a wider aperture?

Thank you so much or the enlightenment (pun intended).

 

[EWH]

Those are some hard questions with complicated answers, but this article:
http://www.clarkvision.com/articles/does.pixel.size.matter/index.html" by R. N. Clark should answer most of them. Particularly look at the sections from "Diffraction" to the "Apparent Image Quality" graph, but the whole article is very instructive about how all the pieces of an optical system contribute to the final image quality.

Short version: to a good first approximation the effect of diffraction on contrast and resolution depends on only the f-number of the whole optical system and the physical resolution of the sensor (the size of the pixels on the sensor).

"Also, how is it that simply having a magnified virtual image of a small aperture give the same exposure as an aperture that is bigger? Why doesn't light just respond to the actual size of it?"
With a wide field of view (short focal length compared to the sensor size) each pixel represents a wider angle than for a longer length lens, and thus more light for a uniformly light-emitting subject. To keep the amount of light per unit area hitting the sensor constant, the aperture must be larger (in mm) for the longer focal length. The f-stop numbering system allows for a constant metric to estimate exposure across lenses of any focal length.

"I heard that diffraction in camera lenses is always present, but just begins to occupy a greater percentage of the total light hitting a sensor when the aperture is small. If this is true, then why is the airy disk smaller at larger apertures?"
The issue is how well two closely spaced lines in the subject can be distinguished by neighboring pixels on the image plane. When the aperture occupies a smaller angle as seen from a pixel on the image plane, a smaller range of angles of light are allowed in, and a larger proportion of that range of angles will be partially occluded by the edges of the aperture. That proportion will be diffracted across neighboring pixels, reducing the contrast as light from a point on the subject is smeared across several pixels. So for a given pixel size and focal length, diffraction depends on the ratio of the aperture edge length to the aperture area.

The tradeoff is that when a wide aperture is used with a given focal length lens, light from a given point on the subject that has spread out over a greater range of angles is focused onto a given pixel on the sensor, and this degree of focusing (getting a given range of angles to a specific pixel) can only be done over a more restricted range of distances to the subject than is the case for a smaller aperture - that is, wide apertures give less depth of field than narrow apertures. With a smaller angle range admitted, changing distances to the subject varies the light angle less than when angles farther from the axis have to be focused, so narrower apertures have greater depth of field. (Depth of field is also inversely dependent on focal length - long lenses have less depth of field than short lenses with the same f-number, and this is independent of the field of view, so small sensors with a given field of view use shorter lenses and have greater depth of field at a given f-number.)