DQE wrote:This comes across as a "contrast vs spatial resolution" dichotomy to me. Sometimes one can resolve (ie distinguish) very small objects that are close together at the expense of large-area contrast loss. In MTF terms, the system would have a poor low-frequency MTF but a relatively good high-frequency MTF.
Does such a description sound correct to you or is the Kingslake quote about something else?
I suspect you're thinking of the case that often appears with brightfield microscopy, where best contrast is achieved by stopping down but highest resolution is achieved at full aperture. In that case, the highest resolution still corresponds to the Rayleigh criterion for a perfectly corrected lens of the same aperture.
The situation that Kingslake describes is significantly different. Quoting from the introduction:
It is fairly well known among astronomers that on certain occasions double stars have been resolved whose separations are far below the theoretical limit of resolution of the telescope. The ultimate limit of resolution of any optical instrument depends on the size of the Airy disk, both as to the central dot and also the first diffraction ring; and if, therefore, by some means the size of the central dot can be reduced relative to the size of the first bright ring, then increased resolution of star images may be obtained.
Showing a little more of the article's summary than I did before, Kingslake writes that:
...thus we see from these experiments [and the accompanying theory] that the maximum visual resolving power for close double stars will be obtained when there is spherical aberration present to the extent of 1.5 times the Rayleigh limit.
This phrasing is not perfectly clear to me, but I believe he is saying that under "ideal" conditions the telescope has 1.5 times the resolution that you would expect based on its aperture.
I'm using "ideal" here in a rather strange way. Not only does the required amount of spherical aberration make the scope useless for viewing extended targets, but at the time of Kingslake's work, the spherical aberration would have been introduced accidentally and transiently as a result of temperature changes!
Your description in terms of the MTF sounds correct. But in the situation Kingslake describes, the tail end of the MTF is modified to be usefully above zero far beyond the Rayleigh limit. I suspect that it falls to zero at some frequency below that, then rises again, thus making it useful for double stars lying close together even though there are other coarser patterns that it would see as uniform gray.
--Rik
