Hi Waldo,
I am going to try and avoid reproducing Born and Wolf "Modern Optics" in this post, but a little math is going to be necessary here...
The formula you are using for specifying resolution is effectively describing the width of the point spread function (PSF) of a simple lens system (a circular aperture with an ideal lens transform function) between its maximum and its first zero crossing (or the distance between the first negative and the first positive crossing, but that's not important).
An infinitely narrow (delta function) object imaged through this system will produce an image that simply reproduces this PSF. So this width is the best you can achieve given the diffraction pattern (PSF) of your system, hence its your diffraction-limited resolution. For two such delta functions, the Rayleigh resolution criterion specifies that you can "resolve" the 2 objects when their respective PSF "images" overlap so that the maximum of one falls on the first zero of the second. Runing through the math, this means that a diffraction limited system has a contrast (intensity difference between the maxima) of ~25% when that overlap occurs. This is the origin of the formula you are using, with a modification for the fact that your objective is being illuminated by light from the condenser, which we can ignore for now. I've attached a slide that shows this. The upper right figure shows 2 such PSF functions, one with 0.25 waves of spherical aberration, the other one ideal. The lower left hand figure illustrates the Rayleigh criterion. The dip in the middle is ~75% of the maxima on either side of it, or conversely, there's 25% contrast between the 2 peaks. If you had 2 ideal objects spaced at 0.61*L/NA where L is your wavelength, that's what you should see.
Clearly there are a large number of factors which affect the imaging system and prevent it from achieving this ideal PSF limit. You can describe any deviations from the ideal imaging condition using a variety of optical models (a good one for microscope objectives that is referenced and used a lot is by Fredrick Lanni and Sara Gibson, J. Opt. Soc. Am. A, 8(10), pp. 1601-1613, Oct 1991 if you are really curious). but basically you can think of any aberrations that degrade your diffraction-limited image as a deviation of the imaging rays from their ideal path. The size of the aberration is then a function of this distance, or more properly the product of the distance and the RI along the path. This is effectively why having a coverslip of a nonstandard thickness, or water instead of oil or RI=1.5 media induce spherical aberrations. Likewise a difference in path from the objective to the occular in a finite conjugte scope. There are many such sources of nonidealities in all of our scopes. A 4nm difference (from NA 1.35 to NA 1.40) in resolution can be inverted to obtain the effective path difference that produced this resolution change, be it from an aberration, or also from an NA difference. As you can imagine, the level of perfection that you'd have to attain in all your optics, including your sample, in order to see this difference in the "dip" contrast is simply unachievable. At least for anyone who is trying to get good pictures, not trying to get a physical review letter on some aspect of diffraction. By the way, as you can see from the upper left figure, one quarter wavelength (L/4) of spherical aberration is sufficient to lower the peak of the PSF to 80% of its value. For your 550 nm light, that's something like 137 nm...not accounting for RI etc...so imagine just what kind of heroic efforts you'd have to go through to shave another 4 nm off that PSF width.
Interestingly enough, a confocal scope has a narrower PSF than a regular BF socpe, so its PSF width is approx. 0.37L/NA to generate that 25% contrast, so for a given target, it will have a 25% "dip" at a smaller distance and hence has better resolving power by this criterion. Note the lower right figure though, no matter how much better the PSF may be, it still falls to zero at 2NA/L since the lens aperture is the limiting factor, and so you will get better contrast on your diatom pores with a confocal, BF or fluorescence, but you can't image what wont make it though the lens, so you can't see pore pitches finer than your NA limit (L/2NA).
Unfortunately, as soon as you are not using good old brightfield and switch to some kind of off-axis illumination (OAI, e.g. oblique) or DIC, the PSF is now different. That NA limit doesn't change though, but your contrast improves for certain targets. So you could get better contrast using a regular widefield scope if you tried some kind of OAI, depending on how the diatom's pores are aligned. But that PSF is for a different post.
Whew. Hope this has not left you in a coma.
David
p.s. this example is from a world apart from biological microscopy, so its using an NA of 2.1 and a wavelength of 1064 nm. The Rayleigh and Strehl ratios are all good though...
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