## Wednesday, 6 June 2012

### D800E versus diffraction

In a previous post (here), I have illustrated how diffraction through a circular aperture can be modelled either in the spatial domain as a point spread function (PSF), or in the frequency domain as a modulation transfer function (MTF). I will now put these models to use to investigate the influence of diffraction on the resolution that can be achieved with the D800E at various apertures.

### Simulating the effect of diffraction

I will not go into the maths behind the diffraction MTF; this was discussed in another post (here). For now, it is sufficient to understand that we can combine the diffraction MTF with the sensor's MTF through multiplication in the frequency domain.

Assume for the moment that the D800E effectively does not have an AA filter (in practice, this might not be entirely true, i.e., the D800E may just have a very weak AA filter compared to other cameras). This allows us to model the pixel's MTF curve as a sinc(x), as was shown in a previous post. Next, we assume that the lens is diffraction limited, i.e., the other lens aberrations are negligible, and thus the lens MTF is just the diffraction MTF.
For a D800(E) pixel pitch of 4.88 micron, and an aperture of f/8, we obtain the following combined MTF curve:
 D800E combined MTF at f/8
The dashed grey curve represents the sensor's MTF, and the black curve represents the diffraction MTF. The blue curve is the product of these two curves, and represents the combined diffraction-and-sensor MTF.
At f/8, our peak MTF50 value will be 0.344 c/p, or 70.4 lp/mm. Note that this is still higher than what I measured on a D7000 at f/5, which peaked at about 0.29 c/p (61 lp/mm), but the D7000  has an AA filter.

Moving to even smaller apertures will cost us resolution, thus at f/11 the curve looks like this:
 D800E combined MTF at f/11
At f/11, MTF50 peaks at only 0.278 c/p, or 57 lp/mm. This is still extremely crisp, although you might barely be able to see the difference compared to f/8 under ideal conditions. Pushing through to f/16:
 D800E combined MTF at f/16
Note how close the combined MTF curve and the diffraction MTF curve have now become; this indicates that diffraction is starting to dominate the MTF curve, and thus also resolution. At f/16, MTF50 has dropped to 0.207, or about 42.3 lp/mm, which is not bad, but quite far from the 70 lp/mm we achieved at f/8.

What about going in the other direction? Here is what happens at f/5.6:
 D800E combined MTF at f/5.6
MTF50 now reaches 0.412 c/p, or 84.4 lp/mm. At f/4 (not shown as a plot) we get 0.465 c/p (95.3 lp/mm), and so on. Below f/4 we will start seeing the residual aberrations of the lens take over, which will reduce effective resolution. I have no model for those yet, so I will stop here for now.

Ok, so I will go one step further. Here is the MTF plot at f/1.4, but keep in mind that for a real lens, other lens aberrations will alter the lens MTF so that it is no longer diffraction limited. But this is what it would have looked like if those aberrations were absent:
 D800E combined MTF at f/1.4
Off the charts! MTF50 will sit at 0.557 c/p, or 114.1 lp/mm. The pixel MTF and the combined MTF are now very similar, which is to be expected, since diffraction effects are now almost negligible. Now if only they could build this lens ...

### In closing

These results seem to support the suggestions floating around on the web that the D800E will start to visibly lose sharpness after f/8, compared to what it achieves at f/5.6. But this does not mean that f/11 is not sharp, since 57 lp/mm is not something to be sneezed at! Even more importantly, there is no "magical f-stop" after which diffraction causes the resolution to drop; diffraction will lower resolution at all f-stop values. The balance between diffraction blur and blur caused by other lens aberrations tends to cause lens resolution to peak at a certain aperture (around f/4 to f/5.6 for many lenses), but even at f/1.4 you will lose resolution to diffraction, just not a lot.

There are also some claims that the D700 was usable at f/16, but now suddenly the D800E will not be usable at f/16 any more. This is not true. If we compare a hypothetical D700E with our hypothetical D800E above, we see that the D800E attains an MTF50 value of 42.3 lp/mm at f/16, and the hypothetical D700E would reach only 37.2 lp/mm.

The real D700 has an AA filter. If we approximate the strength of this filter as a Gaussian with a standard deviation of 0.6246, then the D700 would only reach an MTF50 of 25.6 lp/mm at f/16. A similar approximation of the AA filter for the D800 would produce an MTF50 of 34.4 lp/mm at f/16. So the D800 (or D800E) will always capture more detail than the D700 at all apertures. The D800E is perfectly usable at f/16, and more so than the D700.

[Incidentally, the diffraction + Gaussian AA filter approximation used here appears to be quite accurate. Roger Cicala's Imatest results on the D800 and D700 with the Zeiss 25 mm f/2 (see here) agree with my figures. From Roger's charts, we see the D800 at f/5.6 achieves 1200 lp/ph, or about 50.06 lp/mm, compared to my figure of 50.7 lp/mm. The D700 at f/5.6 attains roughly 750 lp/ph (31.38 lp/mm) in Roger's test, and my model predicts 31.9 lp/mm.]

The catch, though, is that the D700's MTF50 at f/16 is 0.216 c/p (25.6 lp/mm), whereas the D800's MTF50 at f/16 is 0.168 c/p (34.4 lp/mm). The apparent per-pixel sharpness of the D700 will exceed that of the D800 at 100% magnification on-screen. If you view them at the same size, though, the D800 will be somewhat sharper.