Hi Nick
Without trying to work it out for myself, I think you may have mixed up
the definition of the rear aperture of the lens with the exit bundle
diameter? For some (all?) high NA lenses the rear aperture is inside the
last lens(es) of the objective... In the first equation you give, it
looks like the Abbe sine condition is being used.
Hope I'm right and this helps.
Mark
Nick Durr wrote:
> 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
>
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