objective back aperture equation

Posted by Nick Durr on
URL: http://confocal-microscopy-list.275.s1.nabble.com/objective-back-aperture-equation-tp3305776.html

Hi Everyone,
Pawley's confocal handbook (p. 239 in 3rd ed) and objective lens manufacturers
tell us that we can calculate the diameter of the clear aperture of an infinity
corrected objective lens (Dba) by the focal length of the tube lens (F_tube), the
numerical aperture (NA), and the magnification (M):
Dba = 2*F_tube*NA/M
I'm wondering if anyone knows where this equation comes from. If the
magnification is defined by M=F_tube/F_objective, then the equation can be
written as:
Dba = 2*F_objective*NA
From a geometrical optics argument, it seems like the the Dba should be dependant on the tangent of the focusing half angle (alpha=arcsin(NA/n)), not
the sine of the half angle. This would be especially important for high NA lenses.
Shouldn't this equation be more appropriate:
Dba = 2 * f_obj * tan(arcsin(NA/n))
Also, if anyone knows how to estimate where the back aperture is axially on the
objective lens, that would be good to know--is it safe to always assume it's
located at the first lens on the back of the objective?
Any help would be appreciated. Thanks,
-Nick