What We See
There has been a lot of nonsense promulgated over the so-called 3D qualities of Foveon / X3 images. I now understand (I think) what people have been talking about, but there really is no magic involved. There are also some issues that are relevant to the current version of SPP software.
•The SD1 does not have a blurring (anti-aliasing) filter. When used with a very good lens this allows extremely fine micro-detail to be recorded, creating prints and on-screen images (sometimes) with a feeling of greater depth and dimensionality. This isn't unique to the SD1 or other Foveon / X3 cameras because it isn't a function of this sensor technology; it is simply a result of not having a softened image caused by an AA filter. This is also seen with the Leica M8 / M9, which similarly do not have an AA filter, and which many users claim have a comparable 3Dish quality to their files. Indeed the absence of an AA filter is part of the appeal of medium format cameras and backs, and in the above comparison series is seen as well with the Pentax 645D.
•The X3 technology of the SD1's sensor means that there is no colour aliasing. Fine if you're shooting fabrics, but not that critical for most users. Where it does seem to play a role is in not requiring any Chroma noise reduction, since Chroma noise is an artifact of the Bayer sensor. Even at moderate to low ISOs there is some chroma noise, possibly even below normal visual sensitivity. But (and this is a conjecture on my part) its lack may play a role in the "look" that Foveon / X3 fans enjoy.
•It's worth noting that while a Bayer filter camera interpolates its image data, so too does a Foveon X3 sensor when one wants to make prints larger than native size. For the first time with the new SD1 model though, with its usable native 15MP size, up-ressing may not be needed when making all except large prints.
Direct Colour vs. Colour Filter Array
Other than sensors that use Foveon X3 technology all sensors (CCD and CMOS) use what is called a Bayer Matrix so as to be able to reproduce colour. Silicon photo sites are not able to record colour directly, and so various Filter Array technogies have been developed to make this possible. A Bayer matrix is by far the most common, and is used in virtually every camera on the market, from the smallest point-and-shoot to the largest medium format backs.
A Foveon sensor stacks R, G and B sensitive photosites vertically instead of horizontally. The advantages are that no colour array is needed, and this means that there is no colour aliasing. No colour aliasing means no need for a blurring filter (AA filter), and thus higher apparent resolution. And, though we are all used to counting the total number of photo sites in a Bayer sensor as contributing to spatial resolution, they don't. It's just that this is what we're used to.
Doing the Numbers
Bayer Filter Array Foveon X3
Over the years, since Sigma started championing (and now owning) the Foveon X3 technology, the world has had a problem with the way in which each sensor's megapixel count is stated. It is an understandable problem because in a Bayer sensor there may be, say, 20 million photosites but not all of them are used for luminance information. There are two greens for every red and blue combination and only the greens bare primary responsability for spacial resolution. The reds and blues are primarily for colour information. But, in an X3 sensors the sensors are stacked vertically and so each one contributes to luminance as well as colour information. So, take the new Sigma DP2M. It has a 46 Megapixel sensor according to Sigma. But since two thirds of these lie in the same spacial position as the other third there is no actual net grain in spacial resolution.
It's complicated though. A Bayer sensor doesn't record as much spacial resolution as its basic pixel count (say, 20MP) would indicate. It's actually about a third less than this, but since virtually every other sensor in every other camera on the market suffers the same handicap, no one fusses about it. It's a level playing field; well almost, if its weren't for Foveon and Sigma's X3.
Sigma made things problematic until recently by claiming that their sensor was 46 Megapixels. Yes, it is, but not when compared to a Bayer. With this new generation of cameras though Sigma needs to be given credit for, for the first time in their promotional literature, instead of just boldly stating 46MP, the say that this sensor is equivalent to a 30 Megapixel Bayer. While this is still a push, it's a lot closer to the truth.
The problem also comes in the Sigma X3 cameras do not have anti-aliasing filters. They don't need them because there is no colour aliasing because there is no Bayer matrix. This gives an X3 sensor a clear resolution advantage over any Bayer camera that does have an AA filter. Of course there are some Bayer cameras that don't have AA filters either, such as the Leica M9, S2, Nikon D800e and others, and so as you can see it isn't a simple discussion.
In the end this also isn't a discussion that I particularly care much about. It still riles up the debaters on net forums, but those are about the only ones still paying attention. Most serious photographers that I know are much more interested in a sensor / camera's real-world performance than just its megpixelage, because they know that there is a lot more to image quality than just numbers. In any event, once camera got above about 11 Megapixels only a relatively few photographers who make extremely large exhibition prints really cared any more. Yes, 40, 60 even 80MP is nice to have, but it's a sensor's other imaging qualities that make the real difference when it comes to IQ.
So, Sigma calls the DP2M a 46 Megapixel sensor but then qualifies it in the small print and says that it's roughly equivalent to a 30 Megapixel Bayer equipped sensor. The actual spacial resolution is 15 Megapixels (not at all shabby in its own right in an APS-C sized sensor). If I had to pick a number I would judge the DP2M to be roughly equivalent to about a 24–28 MP Bayer camera. But, as I wrote, this is the stuff of web forum fights, not something that serious photographers really spend that much time fussing about.