Diffraction Calculator - Airy Disk Size Error?

[cpersons]

I am interested in typical Airy spot sizes achievable by high performance camera lenses. My search led me the tutorial "Understanding Diffraction: Pixel Size, Aperture and Airy Disks." In the diagrams under the section "Visual Example: aperture vs pixel size", were you accounting for the performance of the lens? Did you assume the "kit lens" that comes with each camera? Also, I may be misunderstanding what you're showing in general. Taking the Canon PowerShot G6 for example:

The equation for the Airy spot diameter is ~2.44*wavelength*F-number. So at 510 nm and f/32, the diffraction limited spot is 40 microns. You show that the pixel area is 5.46 microns^2, which implies the pixel width is 2.3 microns. So, the diagram should show 17 pixels across the width of the spot if the lens gives us diffraction limited performance, or even more if it does not. However, the diagram shows about 4 pixels across the width of the spot. I'd like to understand if I'm missing something here. Also, any info or websites you can point me to regarding typical spot sizes achievable by high performance camera lenses would be helpful.

[JonathanC]

The pixels are indeed about 2.3 micron, but the diagram seeks to show that the spot size changes with the f/ ratio.
This (the spot size in the tutorial) is the theoretical spot size and the real world spot size will be larger for several reasons. Firstly the theory assumes monochromatic light, which is unusual for real world situations. Secondly, most camera lenses aren't truly apochromatic so that the different colours focus at different points, on top of which zoom lenses can go either side of apochromatic as the focal length changes. Add in spherical abberation and you get into a can of worms.

Because of the above, the theory is rarely any use, other than to describe how diffraction works. This lets us understand the more empirical observations that stopping down below a certain aperture makes the image softer.
HTH

[McQ]

Glad you found the diffraction page helpful. The airy disks depicted in the diagram are the smallest theoretically possible, assuming an otherwise perfect (and ordinary) lens. A full simulation of the airy disk size (and shape) for most real-world lenses with multiple lens elements would be quite complicated indeed; I am not aware of anywhere else that has these calculations for consumer lenses.

However, it's arguable whether there would be any tangible benefit to such a simulation, because such a simulation would have to assume that the lens has been made exactly as designed. Practically speaking, design tolerances are often such that there's pretty substantial variation in optical characteristics from lens to lens -- even off of the same production line.

With regards to your specific example with the Canon G6 at f/32, I think what may have happened is that the aperture became accidentally reset or left at the default of f/11. In this case, everything would match up with what you are describing. It's easy to accidentally change these depending on where the mouse moves (without any clicks). When I changed it to f/32, the airy disk width matches with your rule of thumb calculation. However, a word of warning: when the airy disk becomes this big compared to the pixel size, using an absolute cut-off to define the radius can be misleading. circa 17 pixels is about right though, although this disk falls off gradually before and beyond this width.

Hope this clears things up.