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Dear confocalists,

I am confused about the correct formula for diffraction limmited 
resolution along the z-axis. Starting with conventional fluoresence 
microscopy:

I used to use the following formula given by Inoue in the first chapter 
of the Handbook

(1) z-min = 2*lambda*n /NA^2

where lambda is the wavelength in air, n the refraction index of the 
immersion medium, NA the numerical aperture of the objective and ^2 
means to the power of 2.
The text says that this is the distance from the center of the peak to 
the first minimum of the diffraction pattern.
The same is said by F Quercioli in Diaspro's "Optical Fluorescence 
microscopy".



In the new Murphy and Davidson (Fundamentals of Light Microscopy and 
Electronic Imaging, 2nd edition, page 109) I find the following formula:

(2) z = lambda*n /NA^2

Note that the "2" is missing, suggesting a resolution twice as good. 
However, this is not explained as Rayleigh criterion but as "depth of field"



Formula (2) is also given as "resolution in a conventional microscope" 
defined as "distance between points where the intensity is 80% of the 
peak intensity"  by Amos, McConnell and Wilson (Confocal Microscop, 
Chapter in Handbook of Comprehensive Biophysics), but only for cases 
with an NA <0.5. (Note that the clasical Rayleigh criterion in the focal 
plane leads to 73,5 % intensity at the minimum between peaks)

For high NA objectives Amos et al give the following Depth of field = 
80% limit:

(3) 0.51*lambda/(n-sqrt(n^2-NA^2))

This paper also gives a formula for theoretical confocal/two photon, 
although not for resolution but for FWHM, so that is a little different.


Example: 500 nm, NA=1.4, n =1.515, resolution according to the various 
formulas:

(1) 773 nm
(2) 386 nm
(3) 272 nm

This sounds very wrong and my gut feeling is I missed something. I'd be 
happy if you could clarify this for me.

Steffen
-- 
------------------------------------------------------------
Steffen Dietzel, PD Dr. rer. nat
Ludwig-Maximilians-Universität München
Walter-Brendel-Zentrum für experimentelle Medizin (WBex)
Head of light microscopy

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