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>
>
>As for the sampling frequency at 2 or 2.3 or whatever, Shannon 
>calculated the entropy per letter in English text to be 2.3 bits per 
>letter, which may be the origin of that number.  But there is *no* 
>agreement on what the optimal sampling frequency should be.  This 
>was seen, for example, in the early days of CD players- 4x, 8x, 16x, 
>32x oversampling were all touted as providing "better" 
>reconstruction of the initial signal.


Dear Andy,

Do you really think that this information about CD players really 
fits the matter of sampling diffraction-limited microscope data?

My understanding was that multiple sampling was implemented in CD by 
using several photosensors at the confocal image plane so arranged 
that each "dot" on the disk was measured several times. In early 
players, the signal levels were low and the read noise was high, so 
by measuring the "same thing" 8 or 32 times, you could get a better 
estimate of whether is was a mark or a space. This was particularly 
important then as reading even a single "one" as a "zero" could 
produce an audible click until the error-checking algorithms 
improved in reconstructing computers.

It was not a matter of having smaller pixels, in either time or space.

Am I wrong about this?

And about the factor of 2 or 2.3 or 3, at the UBC course, we point 
out that it probably doesn't matter all that much which one you 
choose because one seldom knows the actual resolution of the optical 
system anyway. Although you do know it can't be much better than 
Abbe, even if you avoid spherical aberration, one counts so few 
photons that one can't really distinguish low contrast features and 
closely-spaced features always have low contrast. So we usually 
calculate the Abbe resolution and make the pixels half that size, on 
the assumption that the actual resolution on a living cell is 
probably about 20-50% less than we calculated.

Cheers,

Jim P.
-- 
               ****************************************
Prof. James B. Pawley,               		   Ph.  608-263-3147 
Room 223, Zoology Research Building,                         FAX  608-262-9083
250 N. Mills St., Madison, WI, 53706  [log in to unmask]
"A scientist is not one who can answer questions but one who can
question answers."  Theodore Schick Jr., Skeptical Enquirer, 21-2:39
"He who can get you to believe absurdities, can get you to commit atrocities."
						Voltaire.