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> I have a few questions about phase contrast microscopy:
>
> 1. Can a phase-contrast microscope see a single Rayleigh-scattering
> particle, for example, a 40 nm glass bead suspended in water?
> http://en.wikipedia.org/wiki/Rayleigh_scattering

It is possible to see, but it will be small blip (positive or negative
depending on the sign of phase delay in the phase ring) on a large
background.  You will need high dynamic range camera (e.g., 16-bit
sCMOS) so that the intensity modulation because of the bead spans
three bits. The shading in illumination can make things worse. It
should help to move the bead out of the view, acquire background, and
then subtract the background from the image with the bead in the view.
 It may be easier to start with dark-field to locate the bead and then
switch to phase-contrast. I am assuming you are interested in optical
assessment rather than practical use.

>
> 2. Suppose you've etched a perfectly smooth square trough (or a raised
> square ridge) into your coverslip surface, perhaps one micron high and
> 20x20 microns wide. I'm confident the edges of the trough/ridge would show
> up nicely under phase-contrast microscopy; would the middle of the
> trough/ridge appear to be a different brightness than the surrounding
> coverslip?
>

Yes, the middle of the square will approach the background. This is
because of shade-off artifact
(http://www.microscopyu.com/tutorials/java/phasecontrast/shadeoff/).
It is because some low spatial frequencies diffracted by the specimen
get modified by the phase-ring in objective.

>  I'm primarily interested in first-hand experience rather than theoretical
> predictions, so if you know the answers for similar-in-spirit but not
> identical samples, please let me know.
>
> I have followup questions, assuming the answers to 1 and 2 are
> straightforward.

Best
Shalin