Aliasing and anti – aliasing

Manufacturers go to great lengths to reduce the appearance of noise in images by building anti - aliasing filters into their cameras. To understand how they work, we need to know something about the rature of sampled systems, as Professor Bob Newman explains. WITH the release of Nikon D800E with its (deliberately) ineffective anti - aliasing fi ter, there has been a renewed interest in the benefits (or otherwise) of omitting the anti - aliasing filter altogether. The lure is greater resolution, but the question is: Can you get something for nothing7 The answer is, of course, ’. Anti - aliasing filters are built into a camera for a reason. They are expensive optical components, and camera manufacturers would gladly omit them if they were not necessary. The fashion for photography - filter’comes from their common omission in medium - format cameras. The reason for that is simple: the cost of the size of filters needed for those cameras is very high, and it is difficult for the low - volume manufacturers to source them. Nonetheless, the lack of a filter adds a top - end cachet to a camera. To understand what lies behind the filter cioice, itnecessary to know something aoout the nature of sampled systems.  Aliasing and anti - aliasingSAMPLING SYSTEMS Digital cameras are  discrete  or sampled systems. That is, they capture a signal by taking regular measurements or samples of that signal. These systems were analysed in the 1940s by Claude Shannon and Harry Nyquist of Bell laboratories. Translated into the spatial rather than temporal domain by replacing the temporal frequency (in events per second) with spatial frequency (features per metre), for photographic use their famous theorem states:  If a function(x) contains no frequencies higher than E features per metre, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) metres apart. Completely determine’means to te able to completely reconstruct from the sampled data. For example, if we wish to completely reconstruct an image projected on the sensor with features of 1/10,000m, then we must sample it no less than every 1/20,OODm. Now, if we consider this theorem in reverse, we can see that if the function does contain frequencies higher than B features per metre and we only sample at 2B samples per metre, then we will not be able to reconstruct the original function. This is what causes ’. The frequency 2B samples per metre, or half the sampling frequency, is known as the Nyquist frequency.

ALIASING

Consider the set of sampled values in Tig 1. The two functions shown fit the same set of samples. From that data we cannot tell which is the true function. In theory, for continuous functions there could be an infinite njmber, which fit the same set of samples, so it is impossible to select the correct one without a prion knowledge of which one is right. In the context of imaging this means that an image that is sampled at toe low a frequency will be interpreted differently from the original scene. To demonstrate this, I have created a severely aliased file by sampling a photograph without removing features smaller than twice the sampling distance. The photograph sampled properly is shown in Fig 2, as is the aliased image. At first sight, the full aliased image appears to be a great deal sharper than the original, and indeed this is one of the draws of the filter - free camera. However, on a close-up comparison of the two images, we can see that much of the apparent additional detail corresponds to features that are not really there. The two enlarged crops compare the aliased and unaliased versions. Often aliasing is identified with  moire , but this is only one of the visible types of aliasing artefact. The others are to do with this false ’detail that occurs. Some people prefer the aliased look, but for those who wish their images to be a close approximation of the original scene, it is not a desirable effect.

 Aliasing and anti - aliasingANTI - ALIASING

The solution to aliasing is to remove any spatial frequency that is greater than half the sampling frequency, or in the spatial domain to remove from the image any feature that is smaller than twice the sample (pixel) distance. This requires a filter that acts on the image itself. Effectively, it is a blurring filter, but one that is designed to give a very controlled amount of blur. The most common construction uses a material called lithium niobate, which has an optical quality known as birefringence. This means that differently polarised light takes a different optical path through the material. Thus a ray of light passing through a piece of lithium niobate will be split into two slightly diverging rays, one vertically and one horizontally polansed (Fig 3). By controlling the thickness of the material, the amount of divergence can be manipulated. The end result is that a point in the image will be spread into two points. A second such filter at right angles splits the two points again, resulting in four points. The designer should define the filter such that the spread of points in the horizontal and vertical position just matches the pixel size, thus ensuring that no feature smaller than two pixels can be presented to the sensor. The result of such a filter is an MTF curve (Fig 4). It can be seen that this is not a perfect filter. For a start, it degrades the contrast of features someway below the Nyquist frequency, and it has a lobe of transmission above that frequency. In practice, the upper pass band is counteracted by the resolution fall-off of lenses, but it still results in visible aliasing, even in cameras with anti - aliasing filters. The fall-off before Nyquist is handled by applying a corrective filter in processing, Usually using a sharpening or mask’operation, a process that has become a cie rigueur part of tie digital workflow.

TO FILTER OR NOT TO FILTER?

The Nikon D800E, with the effectiveness of its anti - aliasing  liter removed, has proved attractive to many. They are beguiled by the visibly sharper images that the camera seems to offer. But, as we have seen, this sharpness is mostly illusory, and what is seen is not an accurate representation of the scene, at least in the fine details. However, this is not in itself a reason for an individual not to choose the filterless option. Photography is not entirely about accuracy, and we are used to colour films becoming popular due to offering a  better than rear colour rendition (Fujichrome Velvia comes to mind). Thus, if the  crunchy  sharpness of the aliased image is preferred, then there is no reason not to select that option. It should be realised, though, that having selected the aliased option, there is no way, at least in theory, of finding out which of the infinite possible renderings of that image corresponds to the real scene. At best, editing can restore the semblance of reality, based on human knowledge of what the image ought to look like. If a photographer prefers a realistic rendering, or has customers who do, then it is probably wiser to stick with the filter.

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