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.

Airy Disk versus Pixels

Pixels much smaller than the Airy Disk add no detail

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.


27 Responses to “Diffraction and Fraud in Digicams”

  1. […] 19, 2010 So, you’ve probably gotten the idea: I’m a bit outraged about ridiculous megapixel inflation in point & shoot cameras. But Is this just some […]

  2. Andrea Says:

    Hmmm… So if I read this right, it looks like the (coveted) Olympus EP-1 should be “safe” inasmuch as the sensor-to-MP ratio is much better: 17.3mm x 13mm sensor with 12.3m effective pixels.

    I can’t quite wrap my head around the arithmetic to figure out if my favorite Zuiko lenses would perform reasonably well, though it seems my beloved 65-200mm f4-f32 is best reserved for film. To say nothing of the 1200-1500mm monster zoom…

    • petavoxel Says:

      Yep, the E-P1 (and other current 12 Mp micro Four Thirds cameras) come in at about 5MP/sq. cm. That equals pixels about 4.3 microns across.

      This is a HUGE improvement over the typical point & shoot, although you’ll pay a lot extra for the privilege. My anecdotal impression is that they’re only about one f/stop’s worth of low-light performance behind a full-size DSLR.

      The µ4/3 sensor diagonal is half that of 35mm film; so yes, adapted OM lenses “act like” their focal length doubles.

  3. […] Here’s a nice blog post on why that is. Because of the wave-like nature of light, there is always some diffusion that occurs in a lens. The degree and size of this diffusion is fixed for a given aperture, and when it becomes significantly larger than the elements of your sensor, adding new pixels will not result in increased apparent sharpness. […]

  4. […] “Diffraction and Fraud in Digicams” “The Great Megapixel Swindle: An Example” […]

  5. Mike Says:

    Hm, so does this mean that those of us with too many megapixels can get away with lowering the picture resolution?

    I suppose it also depends on how the lower resolution is generated, if it’s by ignoring pixels or by doing some sort of filter to average pixels together.

    • petavoxel Says:

      If the camera gives the option to dial down the resolution, it’s quite likely you won’t lose any true image detail. Plus, you’ll be able to fit more shots onto the memory card. (Always use the best JPEG quality, though.)

      Try some sample shots at each resolution setting, and then compare them in whatever context is most representative for you: Onscreen, printed out at your usual size, etc.

  6. kjenwt97w2 Says:

    If the camera has the resolution to support them, a higher number of pixels is an advantage when you are photographing something like wildlife where it is hard to get close and you will have to crop the image to get a reasonably sized image of the main subject.

    • petavoxel Says:

      That’s quite true—but the pixels must contain real information, not mushy blur. If the need to crop heavily is part of someone’s camera requirements, then getting one with a larger sensor becomes mandatory.

      There are several entry-level DSLR kits that come with a second, telephoto zoom; that would be my suggestion for wildlife stalkers.

      • sdancer Says:

        I do not think any halfway ambitious wildlife stalker would be too happy with a lot of the kit telezooms. Optical quality is usually alright (I am still impressed by the pictures from a short kit lens that made the kit cheaper than the body alone), but build quality and aperture are not too good most of the time. Unless you are stalking in sunny, clean environments, you’ll either long for a faster lens very soon, or clog up the mechanics with dust, which will mean nasty noises in the best case scenario.

        Granted, fast (f/4 or better at the long end) telephoto or zoom lenses are very expensive, but sadly also the only way to handle even slightly suboptimal situations.

      • petavoxel Says:

        My point was that the casual birder or someone who takes zoo-animal shots will NEVER get good results by cropping a point & shoot image, no matter how many megapixels the camera claims.

        There are certainly some impressive pro-duty lenses available for wildlife shooting, but I think most people would have a hard time getting past their weight, size, and cost.

  7. Shad Says:

    Can you please comment on whether or not operating a pocket camera at one of its lower resolutions would help with image quality?

    For example, if I take a brand-new 12.0 megapixel camera and configure it to take 6.0 megapixel images, will I have higher image quality?

    My guess is “it depends” upon how the camera manufacturer interprets the individual physical pixel data and combines the data into individual final image pixels.

    • petavoxel Says:

      [I’m cutting & pasting my answer to a similar question elsewhere]

      This seems to be the most-asked question I’m noticing in the various comment threads.

      My answer is that it probably does not reduce real detail (check that out yourself, using the camera’s various res options); and you will save on file size.

      The answer is less clear about noise. When you look at a photo unmagnified on a computer screen, or make a normal-sized print, many individual noisy pixels get blended together. Doing that beforehand with the camera’s own processor won’t necessarily give any advantage. But it’s probably best to try it with your own camera and see if the image seems less speckle-y with the lower res settings. Blue skies in photos are a good place to look for noise.

  8. […] understand some of the background, though, you’ll want to read his or her other article about optical diffraction and Airy disks, which is very interesting, and then read his or her follow-up article where he (or she) addresses […]

  9. […] a technical viewpoint, this article is equally as interesting: it lays the groundwork as to why the image from the previous article is […]

  10. Fernando Says:

    I just bought a Sony alpha 850 am I fine or no?

  11. Cesar Says:

    Could someone clear up for me how to calculate micron sizes? For example, what about this camera? http://www.newegg.com/Product/Product.aspx?Item=N82E16830122218 I still don’t understand the mathematical conversion of sensor size to pixel size, but I know there are 1000 microns in an inch at least. 🙂 Thanks in advance!

    • petavoxel Says:

      Go to the specs tab for that Fujifilm S200EXR and you’ll see the sensor size is listed as 1/1.6″. As I wrote in my latest post, those “inches” numbers are completely unhelpful. But it means the real dimensions of the chip are about 8 x 6mm.

      That’s twice the area of a typical point & shoot CCD, which is good. But fitting 4000 x 3000 pixels into that means each pixel is 2.0 microns wide.

      You have to remember that even the cheapest DSLR will have a sensor with 5 to 8 times the area. (And, comparing cameras with equal megapixel counts, so will each individual pixel.)

  12. […] kind of a shaky job of explaining the technical issues, compared to my other ones about noise, and diffraction. There were also two followups that clarified some points, and decoded camera pixel sizes. But the […]

  13. Steve Dutch Says:

    This is great stuff, and I totally concur that anything over 5 Mpx is unnecessary, but it’s more complicated. I’m planning on incorporating this stuff into a class I’m currently teaching on Remote Sensing and I had just the cameras to test with. My good camera is a Canon Powershot and my backup pocket camera (relic of a failed attempt to get my wife into digital photography) is an HP Photosmart. I’ve already noticed that the HP has poorer performance, such as color fringing at the edges of pictures when blown up. Aha, says I, a perfect illustration.

    So I put a page of text on the floor and photographed it from chest high with both cameras (moderate zoom for cropping, plus flash). Sure enough, the Canon gave me crisp, contrasty text, even under high blowup. The HP was blurrier, lower in contrast and noisier. Both, however, were perfectly legible. Now all I needed was the specs to make the case.

    Shock! The Canon is 8 Mpx, the HP only 5. And BOTH have exactly the same size chip (1/2.5″ or about 4 x 6 mm). Both are pushing the envelope on pixel size and density, but the Canon is breaking the rules more than the HP! Yet when the pictures are blown up, the Canon blows the HP away.

    Wassup? I think it has to be the optics. Canon is and has long been a major player in lenses and I’d expect lenses in a Canon camera to be top notch. HP is originally a computer company crossed over into cameras and they get their lenses from who knows where? It’s like an SLR up against an Instamatic. Now for the record, disposable film cameras do an absolutely incredible job considering how the lenses are manufactured, but they will never equal a complex multi-element lens in performance. I think my Canon must just have a better lens than the HP.

    Then there’s also the software. It may be the Canon does a better job processing the image than the HP. Possibly the chip in the Canon collects more photons than the HP. Hard to tell.

    But the software issue raises a problem. If cameras continue to shrink pixels tinier than the Airy Circle, and it becomes impossible to find a consumer grade camera with fewer than 10 or 12 megapixels, will there be anything a user can do to safeguard picture quality? If the pixels are so tiny that the Airy Circle slops over onto adjacent pixels, and photons stray into the wrong pixel by the time they are recorded, the image will be incurably degraded. Opting for lower picture resolution will shrink file sizes, but won’t improve the quality of the pixels that are recorded.

    • petavoxel Says:

      Definitely a bad lens can undermine even the most “optimal” sensor. But also, when we compare different brands and generations of camera, there can be other complications.

      As time goes on, overall chip sensitivity improves (smaller wiring traces, better micro-lens coverage). Not every cameramaker adopts these enhancements at the same rate.

      Also, Moore’s law means that newer cameras throw greater processing horsepower at noise-reduction and sharpening algorithms. (You just cross your fingers that the processing doesn’t interact with the pixel noise in some ugly way.)

      Starting with more pixels, even “empty” ones, might enable the camera’s JPEG engine to create synthetically-sharp edges, even when there is no true optical detail behind it. This might look “punchy” subjectively, though it’s sort of a bogus gimmick.

      But ultimately diffraction, dynamic range, and noise mean that small pixels are a bad bargain.

  14. Steve Dutch Says:

    The more I ponder this, the more doubts I have about the physics.

    First, there are a number of indicators that 5 Mpx and a few microns in pixel size are about optimal. That’s about the size of human retinal cells (although we have about 100 million covering a much wider field of view than a chip). Also most films had resolutions around 100 line pairs/mm or 200 px, corresponding to about 5 microns. So I have no issue with 5 Mpx as a practical limit for digital cameras. HDTV is only about 2 Mpx and James Cameron shot Avatar at 2.2 (but with a huge lens and pixels like an ice cube tray, I’ll bet).

    On the other hand, nobody ever complained that film could have too high a resolution. Some microfilms allegedly had resolutions as high as 800 lp/mm. Eagles don’t seem to suffer from tighter packing of their retinal cells.

    More importantly, for every point beam that hits a pixel dead center there will be hundreds whose Airy disk overlaps the next pixel. That happens inevitably anyway even with large pixels. So if you have a point source bright enough to show the Airy disk and a couple of rings, tinier pixels would just record the pattern in more detail. Apart from the issue of tinier pixels capturing fewer photons and being noisier, I’m not sold that pixels tinier than the Airy disk inevitably degrade the image.

    Are there any advantages to tinier pixels? If two Airy disks partially overlap, tinier pixels might capture it. This happens in a telescope with very close double stars. If they are just at the limit of resolution, they will appear under perfect conditions as an elongated blob with tiny notches on either side. Astronomers call this a “notched double.” Tricky, huh? So there might be some extreme cases where tiny pixels help, but the least hand motion, departure from perfect focus, atmospheric distortion or optical imperfection would negate the advantage. Frankly, if it’s that critical, just zoom in.

    My conclusion: 5 Mpx is plenty and anything more than that is hype. Tiny pixels can hurt by increasing noise and they certainly lead to file bloat. I’ll keep the 8 Mpx on my Canon because it’s not hurting anything at the moment but if I have to buy a 10 or 12 Mpx model in the future I’ll limit picture width to around 2500 px. But I have serious doubts that, apart from noise, tiny pixels are inherently harmful until we get down to sizes where quantum effects become critical. I strongly suspect that the example on “The Great Megapixel Swindle – An Example” owes its poor quality not to small pixels but poor optics and processing.

    • petavoxel Says:

      Steve, take a look at my post from yesterday for a more sober analysis of the “best case scenario” using small-pixel cameras.

      One issue is simply to ask what megapixel count is sufficient for real-world uses. Needlessly large files mean the camera uses more battery power to process them, and takes longer to write & read them. (Plus the extra storage space required, although admittedly that keeps getting cheaper).

      Small pixels will always be handicapped in dynamic range (the ratio between the noise floor and the full-well capacity). The argument with respect to noise gets more complicated, because the extra noise at the 100% pixel view “ought” not be how we evaluate it. But my opinion is that higher pixel noise can interact with demosaicing and sharpening in unpleasant-looking ways; and the preferable solution is to reduce the noise in the first place. Only larger pixels can do that.

      I think diffraction is the issue which has not been publicized nearly enough. As you may know, astronomers use the “Rayleigh criterion” for when two point sources may be resolved—it’s a spacing about half the Airy disk diameter. That’s still in the neighborhood of 2.5 microns, for the typical maximum lens f/stops we see on compact cameras. But few lenses are truly diffraction-limited at their widest aperture.

      Up to a point “oversampling” the unresolved image may provide extra raw material for the camera’s postprocessing; but eventually you hit the limit of extractable detail. I think 1.4 micron pixels (e.g. in 14 Mp point & shoots) have clearly gone beyond that.

      If you’d like to read a much more technical discussion of pixel-size effects, start with R. N. Clark’s article here. He ultimately concludes that 5 micron pixels represent the optimum trade-off between image resolution and S/N ratios. But from there each photographer can elect whether to favor larger pixels (for high-ISO performance) or more resolution (e.g. if you mainly photograph detailed landscapes in bright light).

  15. phyllis ollari Says:

    so it seems the larger the sensor the better. It’s always been the lens that mattered, whether it be when cameras where metal boxes with a lens or a mini-computer. I would be interested in knowing that resolution of tech pan and ortho film as compared to digital. Also with film resolution are we only talking small format? What about medium and large format as well?

    • petavoxel Says:

      Diffraction has always been an issue for photography, regardless of format. But the blur disk diameter depends only on f/number, not the image size. Diffraction is tolerable at f/32 when you shoot 8×10″ sheet film!

      It’s the push for smaller sensors that has made the diffraction problem more severe. Now the range of f/stops that are usable (before the blur becomes much larger than the pixel spacing) is a serious restriction.

      Even an excellent Micro Four Thirds lens starts showing a drop in resolution when stopped down to f/8.

      A pixel size of 5 or 6 microns will probably resolve more detail than all but the most exotic film emulsions. The difference is that with digital, the resolution hits an absolute wall (the “Nyquist limit”); where film resolution just degrades towards lower contrast and more graininess as details get more finely spaced.

  16. […] document never once mentions the word “diffraction.” But as I’ve sputtered about before, with pixels the size of bacteria, diffraction becomes a serious […]

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