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An empirical approach
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How many megapixels do I want?
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There are countless forum threads around the web with people discussing whether digital cameras should have more or less megapixels.
The usual argument in favor of more megapixels is finer detail, while the "less megapixels" proponents argue that chips with bigger individual sensors deliver pictures with less noise. Then the "more megapixels" camp says that with more megapixels you do get more noise in a 100% crop, but that if you downsize your image to a "less megapixels" equivalent then noise should be comparable. The bitter discussion that ensues often leads to trolling and name-calling. Rinse and repeat. I've seen it countless times, and if you're reading this you probably have too.
The key of the discussion is the "more megapixels" argument that if you downsize your image the extra noise is averaged out. This argument requires many technical details that I'll leave out (no talking of gapless microlenses or backlit sensors here), let's just say that a "technically equivalent and state-of-the-art" condition should be imposed for all this discussion.
The thing is: "more megapixels" camp believes that this argument is true, the "less megapixels" camp believes it is not, and, given that we forum members can't build two totally identical sensors, but with different pixel densities, to test the argument, theories abound on why this should or should not be true, but none of them seems to be more than just simple speculation.
My approach here will be: it is true that we can't build those two sensors, but we can simulate them fairly easily, and that's what I've tried to do.
I have two relatively recent cameras at hand: one is a canon 500D (a DSLR with an APS-C sensor packing 15 Mpix), the other one is a Casio Z270 (a relatively cheap point-and-shoot with a tiny 1/2.5" sensor packing 10 Mpix). The 500D uses a 4.5 Mpix/cm2 CMOS sensor, the Z270 sports a 41 Mpix/cm2 CCD sensor. They are vastly different, but both were released in the first quarter of 2009, so I can guess they include similarly advanced technology. In any case, since the 500D cost nearly five times more, it should be expected to outperform the Z270 in all aspects, especially noise performance. That suits me well, as I'll try to give the "less megapixels" camp an advantage in every occasion I get; if that still leads to the Z270 delivering comparable or even lower noise than the 500D, I'll conclude that the "less megapixels leads to lower noise" argument is wrong.
The key to my empirical approach is to take two equivalent pictures using both sensors. The best way to do so would be to open up the Z270, take it lens off, adapt a DSLR lens in its place, then take a picture; now put the lens on the 500D, and take a picture with the camera in exactly the same position. Crop the center of the 500D image, and compare to a sampled-down version of the Z270 image.
I may try to do that in the future, but the main purpose for that would be different: if I ever do that, it will be to see whether more pixels mean more detail, given my lenses' resolving capabilities. For the purpose of noise analysis, I won't require both pictures to be taken with the same lens.
So this is what I have done:
1) Take my One Dollar Resolution Chart (a 70x50cm piece of white cardboard with a one dollar bill cut in half and pasted in the center and the top-left corner, read more about it here). Add a strip of black electric tape, a piece of blue cardboard, and a splash of grey paint, all close to the center. Now it looks like this:
2) Take a picture of my newly modified resolution chart with the 500D and a Tamron 17-50 lens (set at roughly 50mm full-frame equivalent) with standard noise-reduction and minimum sharpening. Crop the center of that picture, to get an area that is 1216x912 pixels, which means it was taken with the central 5.75x4.31 mm of the 500D's sensor.
3) Take a picture of the central 18x13cm area of the resolution chart using the Z270 (set at roughly 50mm full-frame equivalent). Correct white balance. Downsample by a factor of 3 (using a very common bicubic option), so the original 3648x2736 becomes 1216x912.
The results of 2) and 3) are two images that look like this:
And not only do they look the same, they both are 1216x912 pixels, and were created with a 5.75x4.31 mm sensor: in the case of 2), the central part of the 500D's 4.5 Mpix/cm2 sensor; in the case of 3) the full Z270's 41 Mpix/cm2 sensor. Oh, spap! What a nice coincidence! :)
I've repeated that process for ISO 400-800-1600-3200, and built some nice comparison tables that you can see by scrolling down, which contain 450x800, 100% crops from all those pairs of 1216x912 images.
And what do I see in those results?
First, more pixels can definitely mean more detail, but this is not a fair comparison in that respect, as the lens in the Z270, while being much, much worse quality than the Tamron 17-50, has a much easier job to do, working with a very tiny sensor. In order to see if more pixels really mean more detail, I'd need to pair the Z270's sensor with a DSLR lens. I'm not afraid of disassembling the Z270, I've done it before (I had to repair it after it fell down and the lens got stuck in a weird position), but that test will have to wait.
Second, on the topic of noise, at ISO 400 and ISO 800 the results show that a downsampled 41 Mpix/cm2 image can look astonishingly better than a straight-out-of-the-camera 4.5 Mpix/cm2 image. At ISO 1600 and ISO 3200, though, the Z270 is showing some big blobs of color, and, even worse, some ugly moire patterns, that can either be the result of bad processing on Casio's side (and thus avoidable), or natural artifacts created when a very small number of photons hit a very tightly packed matrix of very small individual sensors (each of which is, at most, 1.6 micrometers wide). Even so, I think they look slightly better than the ones from the 500D, and I'd place my bet on the "bad Casio processing" explanation, but still, this casts some doubts.
So, after all this, do I have a conoclusion? Well, kind of: it's not definitive enough, but I think that, all other things equal, I would be better off with a 130 Mpix APS-C sensor than with a 15 Mpix one. Of course, I don't need that much, and even the best lenses in the world may not be sharp enough for that; furthermore, that's a lot of data to process and store, which could create huge problems in the fps and rolling shutter areas, making this totally undesirable. But I think I've shown that more noise is not necessarily a reason to reject more pixels. I'm afraid that may not be conclusive enough, so this debate will live on; maybe if someone with access to newer and better cameras can do something similar to this and clear the mud once and for all...