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At 07:19 AM 9/12/2005, you wrote:
>Search the CONFOCAL archive at
>http://listserv.acsu.buffalo.edu/cgi-bin/wa?S1=confocal
>
>Hi all,
>
>I also have a  very basic question on microscopy theory:

This is also a question that is deceptively basic!


>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?

Ok, first let me state that performance metrics like "Rayleigh criteria", 
"Sparrow formula", "Modulation transfer function", "Point spread function", 
etc. etc. etc. all have limited descriptive abilities and are not absolute 
measures of the overall performance of an optical system.  This is because 
optics has a fundamentally incomplete conceptual foundation which I won't 
get into here, other than to say Emil Wolf has done a monumental job of 
partially reconciling- it has to do with describing how information is 
carried in a beam of light.

So: the Rayleigh criteria was developed for imaging distant stars (point 
objects) that are mutually incoherent- what happens to one star is 
independent of what happens to the other.  If I write your first formula as 
d = 1.22*lambda/(2*NA), you can see that in the case of the condenser and 
objective numerical aperture being equal, the two formulas agree. The 
factor 1.22 is the first zero of a Bessel function, which is the 
Fourier  transform (Hankel, actually- the integration is performed in polar 
coordinates) of a circle function.

Think of the formula as describing how the point spread function is carried 
from one lens to the other.  If one lens has a much lower NA than the 
other, the point spread function is much larger, and any 'benefit' of the 
high NA lens is lost: either one is subsampling a large PSF, or one is 
undersampling a high PSF.   Don't read too much into the formula- it's 
valid only for low NA lenses anyway.  Hope this helps!

If you want to discuss the further, email me directly,

Andy


Andrew Resnick, Ph. D.
Instructor
Department of Physiology and Biophysics
Case Western Reserve University
216-368-6899 (V)
216-368-4223 (F)