Diffraction in Camera Lenses Explained
So what exactly is lens diffraction? Why do photographers hate it so much? How do you get rid of it? That’s the mystery that this article will unravel.
That evil Airy disc
Camera lenses, even if they’re built to absolute perfection, still make fuzzy images when you stop down their apertures too much. A pinpoint of light, after it travels through your lens aperture on its way to your camera sensor, gets ‘diffracted’ . Instead of hitting the sensor as a pinpoint, that spot of light ends up looking like the picture above. This light-dark-light circular pattern is called an ‘Airy disc’. In three dimensions, the Airy disc would look like ripples after a stone gets dropped into calm water.
A guy named George Airy (1801-1892) first developed the mathematics for this diffraction phenomenon, and from then on it’s been known as an ‘Airy disc’. Sir George Airy was a professor of mathematics at Cambridge University. He became an expert in Latin, ancient Greek, architecture, astronomy, and engineering, just to name a few of his skills. He even supervised the construction of London’s Big Ben chimes. But I digress.
If you look at the picture above, the exact size of the Airy disc is ambiguous. It just gets dimmer and dimmer at the fringes.
When a lens aperture is stopped down, the size of this Airy disc starts growing in diameter. The Airy disc diameter is only a function of the aperture f-number and the color (frequency) of light. When apertures are idealized as being a perfect circle, the Airy disc diameter, measured in microns, can be estimated to be 1.34 times the aperture f-number for green light (549nm or 0.549um). For blue light, for instance, the Airy disc diameter is smaller. Green light can be between 500nm and 600nm, but 549 was chosen here.
The Airy disc formula is:
Airy_disc_dia = 2.44 * frequency_um * F_stop
For the above,
frequency_um = 0.549
This is why integrated circuits that get made by projecting an image onto silicon use ultraviolet light. This very high frequency light (short wavelength) produces a really small Airy disc diameter.
The Airy disc is the culprit in making even ‘perfect’ lenses produce soft images, if they get stopped down far enough. For you to notice the image getting fuzzy, the size of this Airy disc has to grow until it covers more than a single pixel on your camera sensor. A rule of thumb is to start getting concerned about diffraction when the Airy disc grows to be two pixels across or more. For making prints, this rule can be loosened up considerably.
For camera sensors that have anti-alias filters (to help rid any Moire effects) the images are even fuzzier.
For an example, I’m going to pick on the Nikon Z9 camera, which has pixels that are 4.35 microns and NO anti-alias filter. Two pixels, then, cover 8.7 microns. We don’t care about the overall size of the sensor or how many megapixels it has, either; we only care about the distance between one pixel center and the next pixel center. If that pesky Airy disc covers a pair of pixels, then diffraction can be seen.
Diffraction versus F-stop
As shown above, when the lens (any focal length) gets stopped down to f/8 or narrower, the Airy disc diameter grows larger than two pixels (8.7 microns for Nikon Z9). As soon as this 2-pixel threshold is reached, some image softening starts.
At f/8, diffraction is barely noticeable. Diffraction starts growing in leaps and bounds by f/16, and image quality suffers. Don't even ask about f/32. You have to decide if getting that large depth of focus is worth it.
On cameras that support focus-stacking, it’s ideal to stick with f/5.6 or wider and take multiple shots to later combine them to get a large depth of field at optimal resolution. Just pick your lens’s sharpest aperture, and hope there’s no wind. Tripod required. You can manually re-focus between shots, if your camera doesn't have focus stacking. This is a trick to sidestep diffraction effects when there's no subject movement.
If you buy a camera with huge pixels, you might get away with one or two extra f-stops before diffraction rears its ugly head, but eventually it will show up.
When you hear the phrase “diffraction–limited”, it means that any lens aberrations except for diffraction have been essentially eliminated, so that any remaining aberrations all fit inside that darned Airy disc. Making the lens optics even more perfect is pointless. Diffraction is always lurking.
This lens fuzziness can’t be solved by money. It’s physics. Thanks, George (I guess).
