Limits To Resolution

February 8, 2010

Why jam extra megapixels into a compact camera, if its lens can’t resolve enough detail to use them?

Sampling a fuzzy image with an ever more finely-spaced pixel grid eventually stops adding information. After that, it merely balloons file sizes needlessly.

So it’s useful to check whether all of a camera’s pixels are capturing something real. Or do they simply hit a wall of lens aberrations, diffraction, and sensor noise?

I’ve had a chance to take some sample shots with the 8-megapixel Nikon Coolpix P60, using the resolution test target I posted last week. (Open a tab to remind yourself how the target is supposed to look.)

The P60 is assembled in China—perhaps even in a factory that doesn’t say “Nikon” over the door. Nonetheless, Nikon’s lens designers have an enviable reputation. And using a 9-element, 7-group design, its lens aberrations ought to be reasonably well controlled. So how well did the little Coolpix do?

As with my earlier post, I set up the target so that its squares with 40 divisions per inch match the pixel pitch of the sensor. At that magnification, ideally the camera should form an image of the 40-line target as a row of black pixels, then a row of white pixels, then black, etc.

The P60 shoots images that are 3,264 pixels wide. Dividing this by 40 tells us the subject field needs to be 81.6 inches wide overall—6 feet, 9–5/8 inches. Two reference marks at the proper spacing (black electrical tape on a sheet of plywood) helped me frame each shot with the right magnification.

Here’s a full-rez sample of what one complete test frame looks like. I turned off as many automatic settings as possible, to improve consistency (see notes* at end).

We’ll start with the best-case scenario: The lens is set at its sharpest focal length (at the wide end of the zoom range) and the target is in the center of the frame. The ISO is 80 (its lowest setting), for minimum noise. The aperture is wide open, for lowest diffraction:

f/3.6, 6.4mm focal length

200% View: f/3.6, 6.4mm focal length

Yes, this is the sharpest image I got in my tests.

While it’s startling to see the rainbow patterning in the 40-line sample, this is actually the “good” news. It means that enough resolution is being focused on the sensor for the test pattern to completely confuse the demosaicing algorithm.

We also see vertical and horizontal texture in the 50-line squares; but I believe this is “false texture” (aliasing), rather than true resolution.

(And please remember that most real-world subjects lack the kind of repeating patterns which make demosaicing totally freak out like this.)

The sharpness is not quite as good at longer focal lengths. Zooming to 14.3mm (corresponding to 81e) and backing away to maintain field size, things look like this:

f/4.1, 14.3mm f.l.

200% View: f/4.1, 14.3mm f.l.

The 50- and 40-line samples have lost most of their detail; also, the 30-line sample has begun to look a bit rougher. Note that the hairline border around the number boxes is virtually gone here—unlike the first shot which showed a hint of it.

We can also look at what happens towards the edges of the frame (where lens aberrations are generally not as well controlled). At a longer zoom setting of 23.3mm, a target at the photo’s right edge looked like this:

Edge of Frame: f/4.3, 23.3mm f.l.

Edge of Frame: f/4.3, 23.3mm f.l.

Well, there’s some rather troubling green fringing here. And even the 10-line sample has lost contrast noticeably.

But the other thing to notice  is how soft the vertical 30-line square has gotten. It’s hard to avoid the conclusion that 8 megapixels is plenty at this point; more finely-spaced pixels would not capture any additional detail.

Now, traditionally photographers have enjoyed the creative control of trading off shutter speed against aperture; e.g. using longer exposures at smaller f/stops, to yield a deeper zone of sharp focus.

And the P60 is theoretically aimed at the enthusiast end of the point & shoot market—folks who would appreciate manual controls like this.

But, in fact, its aperture is only “sort of” adjustable.

Nikon’s manual notes (somewhat cryptically),

  • Aperture: Electronically-controlled preset aperture and ND filter (–0.9 AV) selections
  • Range: 2 steps (f/3.6 and f/8.5 [W])

What happens when you “stop down” this lens is that an arm swings into place with a smaller hole in it. And after inspecting this with a magnifier, the hole does appear to be covered by a rectangle of neutral-density filter material.

Combined, the filter and the hole cut out about 2.4 f/stops worth of light. But diameter-wise, the aperture is seemingly just f/6.0 or so—not the f/8.5 stated (at the zoom wide end).

Why on earth did Nikon do this? Well, it’s because stopping down the lens increases diffraction, that’s why. (And given compact cameras’ teeny focal lengths, you rarely need more depth of field.)

Despite this throttled aperture range, we can still see diffraction having a blurring effect:

Diffraction: f/10.4 (nominal), 23.2mm f.l.

Diffraction: f/10.4 (nominal), 23.2mm f.l.

First, notice the overall drop in contrast. The 50- and 40-line samples are completely featureless. And the 30-line sample has slipped past the limit of resolution—you can no longer count all of the lines.

At this zoom setting, the (physical) aperture might measure f/7.0; this means an Airy disk more than 9 microns wide. With the P60’s sensor size, those blur disks spill across many pixels.

While sharpening by the camera’s processor can accentuate the bright peak at the center of the Airy disk, it can’t pull back detail that never existed. So, if we want the ability to close down the lens even by two stops, then a sensor with larger pixels, not smaller ones, is needed.

Note that we’ve been looking exclusively at ISO 80 here—the camera’s lowest sensitivity setting. But that’s not very realistic, considering how people actually use their cameras.

With a shirt-pocket compact, we would rarely feel like lugging around a tripod! So under anything but bright daylight, we’ll often need to use a higher ISO setting.

Fifteen years ago, films of ISO 400 were the most commonly purchased speed. So how does ISO 400 look here?

ISO 400 Test: F/4.1, 14.3mm f.l.

ISO 400 Test: F/4.1, 14.3mm f.l.

The 40-line sample does show some color tint from demosaicing; but the noise (and noise-reduction processing) are severe here. Neither the 40- or 50-line samples give any hint which direction the lines run.

The 30-line squares have once again passed the point where lines cannot be resolved completely. And there’s no sign of the hairlines bordering the number boxes.

At this level of resolution, we would hardly lose any detail if we substituted a 5 megapixel sensor of the same size. Plus in that case, each pixel would have 60% more light-gathering area—helping tame the noise.

In conclusion, the P60’s lens somewhat out-resolves the sensor under the most favorable circumstances. This is seen in the form of colored, “gritty” demosaicing artifacts.

But it doesn’t take long before real-world complications undercut the sensor’s inherent resolving power. And while we’ve treated aberrations, diffraction, and noise as separate, in practice several of these handicaps often come together in the same photograph (along with other factors such as camera shake).

This test is not definitive; it merely represents the performance of one, very average compact camera. However if we are seeing such flaws at “only” 8 megapixels, what sense does it make to drive up pixel counts even higher—to today’s 10, 12 or 14 Mp?

You can download a PDF of the target here. If you own a compact camera, I encourage you to try this test for yourself.

* Test setup: The camera was mounted on a tripod, with VR turned off. Unless noted otherwise, enlarged details are from the center of the frame, with the camera set at ISO 80 (best-case conditions).

I set ISO, aperture, and shutter speed manually. The white balance was set to “cloudy,” and the contrast setting was turned up to +1. I left sharpening and saturation at their mid setting, 0. A 2-second self-timer allowed vibrations to die out after I pressed the shutter release.

Autofocus used the central spot only; this included several of the target’s black squares. Two shots were taken at each setting, allowing the camera to re-focus each time (I never noticed any inconsistency between pairs of photos).

The 200% samples shown here were upsized using Photoshop’s “nearest neighbor” method, to avoid any additional artifacts. Any sharpening halos are from the camera’s own processing.


4 Responses to “Limits To Resolution”

  1. Chippets Says:

    What about the stair-stepping in the numbers? Is that in the test sheet as printed or produced by the sensor? I think this stair-stepping would suggest to many folks that more resolution could result in smoother diagonals. With the other degradations, this seems rather pointless, but I think this is something people would think of nonetheless.

    • petavoxel Says:

      The views onscreen here are enlarged 200% (one camera pixel becomes 4 screen pixels) in order to show the artifacts better. So that also makes the numerals look blocky.

  2. Chippets Says:

    Oh, I see that the numbers as printed do not have stair-steps. So the sensor resolution is visible in all cases it seems. I suppose it is possible to increase resolution to the point where these steps just blur out — but at a cost of more smearing and other ugliness.

  3. […] when aberrations & diffraction limit the pixel count which is actually useful, the argument becomes even stronger. Posted by petavoxel Filed in megapixel madness, […]

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