If you follow the material through to the end, you will see that even I didn't get the answer to the question I posed on the net exactly right. My answer was that the optimum height for NVIS was somewhere between a quarter and a half wave above ground. (Given the choice, I would probably choose that height as a compromise solution -- sometimes you need NVIS, but I'd rather work DX.) But to maximize NVIS performance, 1/4 wavelength above ground is the right answer.
Here are a few caveats and clarifications of sections where the material (meant to accompany an oral presentation) is a bit sparse on text.
First off, NVIS is something of a secondary subject of this presentation. The main topic is the use of high vs. low fidelity ground models in NEC-2 antenna modeling. But NVIS is an area where ground model accuracy is particularly relevant, so there's plenty of NVIS discussion here.
Slides 12-17 probably need some further explanation. (Either that or they need to be skipped.) These slides are an attempt to explain the effect of dipole height above ground by viewing the dipole and its image in the ground as a two element array, but noting that unlike an ideal phased array, you have no independent amplitude or phase controls. Element spacing is the only available design variable.
Slide 23 is something I will not attempt to explain right now. If you really want to know what it's all about, ask and I can explain.
Slides 24-25. The answer to the question "what's wrong?" is that you can't maximize gain toward the zenith (i.e., the NVIS case) by laying your dipole on the ground, which is what the plots seem to imply: the lower to the ground, the higher the gain in the straight up direction. In these plots, this is the result of inaccurate modeling of ground losses.
Slides 30 and 31: 30 is the inaccurate result using the low fidelity ground model. 31 uses the more accurate ground model and is a realistic representation of the relative gains toward zenith at different antenna heights. There are no legends on these two plots, but the coloring scheme is consistent throughout the presentation. (See e.g., slide 25 or 29.) The intent of slides 30 and 31 was to toggle between the two for dramatic effect.
If you really want to dig deeper into the subject of NVIS antenna optimization, take a look at the Witvliet et. al., work cited in this presentation. I will provide that paper as well as the other cited work, the Kidder material from QST on ground models, via this mailing list under separate cover later today.
73 DE K7LU