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>Hi all,
>
>I also have a very basic question on microscopy theory:
>
>The Rayleigh criterion states that resolution
>d=0.61*lambda/NA. Taking the condenser lens into
>account this (in the textbooks) becomes d=
>1.22*lambda/(NAo+NAc). But shouldn't it be d=
>0.61*lambda/NA with whichever NA is the smallest
>of the two?
>
>tia
>Stefan
>
>+++++++++++++++++++++++++++++++++++++++++++++++++++++++
>Stefan Gunnarsson
>Uppsala universitet Uppsala University
>Evolutionsbiologiskt centrum Evolutionary Biology Centre
>Enheten för biologisk strukturanalys Microscopy and Imaging Unit
>Norbyvägen 18A
>SE75236 Uppsala, Sweden Tel & Fax: +46 - 18 471 2638
>+++++++++++++++++++++++++++++++++++++++++++++++++++++++</x-flowed>
Hi all,
The Rayleigh Criterion is for telescopes and
works well for white stars on a black background.
Condensers were not relevant.
The Abbe version is for microscopes and you have
stated it above. The condensor is important in
transmission microscopy because light entering
the specimen at a steep angle can can produce
higher diffraction orders that might (repeat,
might) be accepted by the objective, than axial
light. However, you won't get all of this high
order diffraction because some diffracts the
"wrong" way and goes back towards the condenser.
As a result, smaller things can be seen with this
high angle illumination but the contrast is
pretty low.
It isn't "the lower of the two" because that
would only relate to undiffracted rays, and both
diffracted and undiffracted rays contribute to
the result.
Really both these equations are a bit of a 'con'
in terms of estimating the 'smallest thing you
might "see" (actually, the smallest distance
between two things) because they were developed
before either photons or pixels were recognized
as having a role to play in this process. And
visibility of white dots on black is very
different than the black dots on white scenario
present in most transmission LM imaging. (the
white background has more photons/pixel, hence
more Poisson noise, hence it is harder to see
small things in this noise.)
It is better to forget the equation and think of
the Contrast transfer plot, a downward sloping
line that relates the contrast in the image of
features of various sizes in the object. To make
the plot easier to draw, feature size is
expressed as spatial frequency (1/size). (See the
Chapter 1 by S. Inoue in the Handbook)
Big things are near the left axis and have 100%
contrast; things about Rayleigh/Abbe size have
about 25% contrast (or less if you are honest)
and things twice as bit as Rayleigh/Abbe have
about 60% contrast, etc.
In fluorescence microscopy, one is much more
likely to have ones "ability to distinguish two
closely-spaced features" limited by insufficient
photons (and hence big pixels and/or high Poisson
noise) than by Rayleigh/Abbe.
And then there is spherical aberration....
Abbe/Rayleigh assumed diffraction-limited optics which seldom occur.
Cheers,
Jim P.
--
****************************************
Prof. James B. Pawley, Ph. 608-263-3147
Room 223, Zoology Research Building, FAX 608-265-5315
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
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