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The question of whether or not to include an anti-aliasing (AA) filter on digital cameras comes up quite often in these fora. The dLSR by Foveon does not use an AA filter and neither does the Leicas nor the medium format cameras. The question of how to “reconstruct” a continuous signal from its samples was addressed by Claude Shannon and others, leading to a theoretical approach that is widely taught in signal processing courses. We are talking about how you can “know” the signal EXACTLY at any point, even though you measure at only a finite number of points. Very powerful. Under Shannon’s assumptions, he showed that undersampling the signal will produce a distorted reconstructed signal, with parts of the signal above the Nyquist frequency mixed back in at lower frequencies. This is called aliasing. In the case of high frequency repetitive patterns, the attendant distortions are called Moire patterns, like those seen in images of fabrics. According to this sampling theory, there is no principled way to remove the aliasing. Therefore, the AA filter is there to remove the high frequency information from the signal before it is digitally sampled by the dSLR sensor.
It would seem that it is a no brainer to keep the AA filter. In fact, companies like Canon and Nikon take pains to design and include AA filters. These are costly to manufacture and you would think that they would omit them if they could make the camera better and incur lower cost, to boot. Maybe including them in a medium format camera would be too expensive. On the other hand, the case of the RGB digital camera isn’t exactly what Shannon analyzed. The correlations between the RGB color channels make the problem more interesting and it is apparently possible to do better than would be predicted from the sampling theorem. But this is all pretty murky; if you leave out the AA filter there are conditions in which you can have noticeable aliasing (moiré). In fact, you will have aliasing in virtually any scene. And many observers may think that the aliased image is sharper and prefer the camera without the AA filter. There are lots of claims but very little real data by advocates of removing the AA filter. It always comes down to look at how good my image looks. Never a comparison of the same camera lens combo with and without AA filter.
There are two basic parts in the imaging chain, the lens and the sensor. When the lens has high resolution and the sampling of the sensor is low, you will have the potential for serious aliasing. As the sensor sampling (more densely packed pixels) increases the need for an AA filter decreases. One potential solution is to use a sensor that is oversampled for the available lenses. Collect all the incident photons, accepting that each sensel will have collected fewer photons. Apply a digital filter to the raw image to remove the high frequency details and then resample to a smaller matrix, thus restoring the signal-to-noise ratio. Perhaps something like this solution could be implemented and we could have the best of both worlds, no optical AA filter and no aliasing.