Diffraction and Fraud in Digicams
January 19, 2010
There is a great article at cambridgeincolour.com about the role diffraction plays in digital-camera resolution.
The issue is that at microscopic scales, the wavelike nature of light makes it act in a slightly “squishy” way. Points of light brought to focus by a lens are smeared out by a certain irreducible amount—even if all lens aberrations are perfectly corrected.
Instead of a sharp pinpoint, light is actually focused into a fuzzy bulls-eye pattern. Its bright center is named the Airy disk, after the British scientist who first described it.
Interestingly, the diameter of the Airy disk is unaffected by lens focal length, or image size; it depends only on the f/ratio of the lens. As you stop down the aperture, a bigger fraction of the light fans outwards from its intended path, and so the wider the Airy disk blur becomes.
With lens aberrations, the opposite is true: they create the most blur at widest apertures. On stopping down, sharpness improves.
So most film-camera lenses give their sharpest images at the middle of the f/stop range—the “sweet spot” where the combined effects from diffraction and lens aberrations are lowest. That’s one way to interpret the old photography rule, “f/8 and be there.”
Anyway, it’s easy to figure out the Airy disk size. The diameter in microns is about 1.35 times the f/number (using the green wavelength our eyes see most brightly). So, for example, the Airy disk at f/4 is 5.4 microns across.
The shocking thing few camera-buyers realize is that these fuzzy blobs are often larger than the individual pixels in a digital camera sensor.
The problem is most egregious in the world of point & shoots. Everyone seems to want the highest possible megapixels, in a camera the size of a deck of cards. There’s no way to do this without making each pixel extremely tiny. While the pixels in a good DSLR sensor might be 5 microns wide, the latest megapixel-mad point & shoots shrink each one to 1.5 microns or less. You start to see the problem.
We need to be a little careful about relating Airy disk size to pixel size, though. Sensor pixels have a Bayer pattern of color filters over them; and the final RGB image pixels are the result of a demosaicing algorithm. Also, every digital camera applies some amount of sharpening. This can, to some extent, counteract the diffraction blur.
But you can’t generate detail that was never recorded to begin with.
My assumption is simply that when the Airy disk fully covers four sensor pixels (as shown above), you have reached the point where diffraction makes additional pixels useless—no additional detail can be extracted. (This is a more generous criteria than many other folks’ reckoning.)
Let’s consider a typical point & shoot. Although its lens might open to f/2.8 at the widest zoom setting, at a “normal” focal length the maximum aperture is more like f/3.7. At this f/stop, the Airy disk is 5 microns across; it would fully illuminate four pixels of 1.7 micron width.
So how many megapixels could you get, if a single pixel is 1.7 microns?
Take a typical P&S chip size of 5.9 x 4.4 mm (a size better known by the cryptic designation 1/2.3″). At 3470 x 2603 pixels, you’d have a 9 megapixel camera.
Adding more pixels will not capture more detail. Neither will improved chip technology—we’ve hit a fundamental limit of optics.
Remember, this is all at the lens’s widest aperture (i.e., the one giving the poorest lens performance). As you stop down from there, the diffraction just gets worse.
Yet today’s models continue their mad race to ever-higher megapixel counts. Ten, twelve—now even 14 Mp are being sold.
This is where I start using the word “fraud.” Customers are being sold on these higher numbers with the implication it will make their photos better. This is simply a lie. All the higher megapixels deliver is needlessly bloated file sizes.
People forget that “full” HDTV is only 2 megapixels (1920 x 1080). Or that a 6 Mp camera can make a fine 8″ x 10″ print. A camera with 2 micron pixels is just about the limit, in allowing you to stop down the lens at all. That means staying under 7 Mp, given typical point & shoot chip dimensions.
And the more important point is this: Shoppers shouldn’t give their money to companies who lie to them.