By Bob Atkins
OK, since the correct answer has been deduced by Jean-Baptiste Queru and Marijn Bezuijen It's time to reveal the answer! First here are the two images again
They were taken with:
The difference is that shot "A" was taken at the sharpest aperture of the lens (f5.6 I think) while shot "B" was taken at f22.
| Definitions: Nyquist limit the maximum frequency of a signal that can be measured with a method that samples the signal with a specific frequency, the sampling frequency. According to Shannon's sampling theorem, a signal must be sampled with a frequency at least twice the frequency of the signal itself. The maximum measurable frequency the Nyquist limit or frequency is thus half the sampling frequency. If the signal frequency is higher than the Nyquist limit, aliasing occurs. Aliasing - the spurious signal occurring when the sampling frequency is less than twice the frequency to be measured Thus for a digital sensor you need at least two pixels per cycle in order to record true information. If a sensor has 150 pixels/mm, the Nyquist limit of the sensor is 75 cycles/mm |
The Nyquist limit for this camera's sensor is around 75 cycles/mm which means that it cannot extract meaningful information from the image falling on it if the spatial frequency of that information if greater than 75 cycles/mm. Most sensors have an anti-aliasing filter ahead of them that tries to attenuate frequencies above the Nyquist limit and not affect frequencies below it, though such filters aren't very sharp. While you can make electrical filters with very steep edges, you can't make optical filters with similar properties.That means that in order to let as much information as possible through at 75 cycles/mm it has to let some information through above that frequency. It's the interpretation of that "information" that causes problems.
Now a good lens at f5.6 can transmit information out to around 285 cycles/mm and at, say, 80 cycles/mm it's MTF will be around 0.7 (70%). This means that some information will get through the anti-aliasing filter and cause the colored moiré type fringes which can be clearly seen in image "A". It's also responsible for the "blocky" and pixilated nature of the image at spatial frequencies close to the Nyquist limit. The plot below shows the MTF of a perfect lens at f5.6 (blue) and f22 (black). The red vertical line is the Nyquist limit.
From this plot you can see that at f22 a lens doesn't transmit any information above the Nyquist limit, so the anti-aliasing filter doesn't have to work so hard and there's no pseudo-information there to confuse things. However at f5.6 there's a load of information trying to force its way through the filter and that's what causes the problem. Some of it gets through and results in a spurious response above the Nyquist limit.
So is a lens at f22 "better" than a lens at f5.6? Well, if you're shooting a subject comprised mainly of fine detail at around 65-75 cycles/mm, the answer might be "yes". However on real world subjects the answer is "no". Overall image sharpness probably correlates best with the area under the MTF curve and as you can see, the area under the blue curve from 0-75 cycles/mm is larger than the area under the black curve. This translates to higher contrast and higher perceived "sharpness", even though the "resolution" is pretty much the same in each case, 75 cycles/mm.
How is all this relevant to real world picture taking? Well, it isn't really. You rarely see aliasing effects, but sometimes you do. Are they an indication of a problem? Well, yes and no. Clearly they aren't supposed to be there, so in that sense they are a problem. On the other had they go away with a less sharp lens, so unless you regard a sharp lens as a problem, maybe you could say that they're not a problem - or at least they don't always represent a camera "fault". Some cameras (like the Kodak DSLRs) don't use an anti-aliasing filter. They may give very sharp images, but they also can suffer badly from aliasing effects. You can totally eliminate alaising effects with a strong enough filter, but that will soften all the images significantly.
I suppose the lesson to be learned is that pixel peeping is a complex subject. You can't always tell what's going on, especially when you don't have all the facts together with the knowledge to accurately interpret them.
© Copyright 2004 Bob Atkins (www.bobatkins.com)