The sensel pitch of the D7100 is probably something like 3.917 micron. That means that at the Nyquist frequency of 127.7 cycles per millimetre, with f/14 diffraction (at 564nm wavelength) reducing the MTF to zero at 125 cy/mm, there is zero resolution left for such fine detail (regardless of its contrast) at the limit of the possible sensor resolution that can be achieved with wider apertures. Narrower apertures will reduce the absolute limit of resolution even more. A D800 (4.88 micron sensel pitch) would hit that zero contrast limit at 2/3rd stops narrower, at f/18.
Visible deterioration of microcontrast will start much earlier at wider apertures, assuming one uses the large number of pixels for large output or significant cropping. Downsampling of the image willobviously hide the lack of resolution.
Those figures seem about right to me. If the Canon 50D with a pixel pitch of 5.63 microns can continue to deliver discernibly higher resolution up to F16 (compared with a 40D with a pixel pitch of 5.63 microns), then one would expect a sensor with an even smaller pixel pitch of 3.92 microns (such as the D7100) to be limited to providing more detail up to and including F11 (approximately), compared with a camera such as the D7000 with a pixel pitch of 4.72 microns, especially considering that the D7100 has no AA filter, which must give it an additional slight resolution advantage however small that may be.
That you've calculated the theoretical cut-off point to be F14, implies there would probably be a discernible
improvement in detail up to F11 approximately. F13 would be too close to the cut-off point. But even at F11, one would expect such improved detail only to be discernible at 100% on monitor, or on very large prints at least 4ftx6ft, or on smaller prints of significant crops of the full image.
It is that last advantage of the potential of small crops that is of practical significance, so it's not surprising that Nikon have included a 1.3x crop mode on top of the already physically cropped-format of 1.5x, which results in a 14.4mp image, a faster frame rate of 7fps, and an equivalent focal length of 2x the 35mm-format focal lengths.
Just out of curiosity, I compared the DXOMark results at the pixel level (screen mode) for the 15mp Canon 50D, which I still use with my Canon 100-400 zoom, and the new Nikon D5200 which DXO have already tested.
Since the D5200 also has a 24mp sensor and 14 bit processing, just as the D7100 has, one would not expect the test results for the D5200 to be any better than the newer, more expensive and more professional D7100. In fact, one might reasonably expect the D7100 results to be at least very marginally better in some respects.
With this in mind, I was very interested to compare the D5200 pixel with the Canon 50D pixel. There's hardly any practical resolution difference between a 14.4mp image and a 15mp image, but there certainly is a difference between an effective 1.6x focal length and a 2x focal length. A 400mm lens on the 50D becomes effectively a 640mm lens, whereas a 400mm lens on the D7100, in cropped mode, becomes effectively an 800mm lens.
However, the D7100 pixel is significantly smaller than the 50D pixel (3.92 versus 4.68 microns) so I wondered whether such a 14.4mp crop would suffer any quality disadvantages compared with the full 15mp 50D image, such as lower SNR perhaps, or worse color sensitivity.
Wow! Was I surprised! Pleasantly surprised, of course. After scrutinising the charts and graphs comparing sensors at the pixel level, expecting to see at least some marginal benefit of the larger 50D pixel, at least in some respect, I could not find any improvement in any respect whatsoever, however marginal.
The best the 50D can do is approximately match the Tonal Range and 'SNR at 18%' results for the D5200 pixel, but only at ISOs of 200 and higher. For the other parameters of DR and Color Sensitivity, the smaller D5200 pixel is streets ahead, at all ISOs.
DR is a whopping 2 stops better at base ISO, as one might expect, but also 0.75EV better at ISO 6400. Color Sensitivity is a very significant 2 bits better at base ISO and about 1 to 1.2 bits better at all higher ISOs.
The more recent 18mp Can 7D is even worse at the pixel level. See for yourselves at:http://www.dxomark.com/index.php/Cameras/Compare-Camera-Sensors/Compare-cameras-side-by-side/(appareil1)/850%7C0/(brand)/Nikon/(appareil2)/619%7C0/(brand2)/Canon/(appareil3)/272%7C0/(brand3)/Canon
The bottom line for me is that I shall have no concerns at all about lower image quality in any respect (compared with my 50D), when using the cropped mode on the D7100 for a longer reach than I get with my Canon 50D, which is good news.
The bad news is that Nikon do not have a good quality, reasonably lightweight, 400mm/F5.6 prime or zoom that compares with the Canon offerings. I'm a bit reluctant to get the Sigma 150-500/F6.3 because of reports that this lens is sharpest only at F11, at the long end.