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Dear Esteban,

A simple ray-tracing diagram in combination with Snell's law will readily
give you the following formula:

Dz = Dz_motor * sqrt((n2^2 - NA^2)/(n1^2 - NA^2))

Where Dz is the actual axial displacement in the sample with refractive
index n2, Dz_motor is the axial displacement as indicated by the microscope
focus motor, n1 is the refractive index of the immersion medium and NA is
the numerical aperture of the objective lens.

Note that, as expected, for a perfectly matched system (n1=n2): Dz =
Dz_motor. Also, for small NA (NA<<n1 & n2) this leads to the much used
approximate correction n2/n1 as you have mentioned in your message. It is
not valid for large NA though.

I have used this formula with good results in my own studies. I seem to
remember there has been a publication during the 90's which compares this
formula with a more rigorous treatment starting from wave optics. I cannot
seem to find the reference, though. Maybe someone else on this list can ... 

Hope this helps.

Kevin



Kevin Braeckmans, Ph.D.
Lab. General Biochemistry and Physical Pharmacy
Ghent University
Harelbekestraat 72
9000 Ghent
Belgium
Tel: +32 (0)9 264.80.78
Fax: +32 (0)9 264.81.89

> -----Oorspronkelijk bericht-----
> Van: Confocal Microscopy List [mailto:[log in to unmask]]
> Namens G. Esteban Fernandez
> Verzonden: vrijdag 15 februari 2008 0:11
> Aan: [log in to unmask]
> Onderwerp: How to correct z distance in RI mismatch?
> 
> Hi everyone,
> 
> A user needs to measure the volume of fluid inclusions (mostly water)
> embedded in a clear mineral of RI ~2.4.  We did this by collecting
> z-stacks of reflected light on our LSM 510 confocal and rendering a 3D
> model, which turned out pretty reasonable.  We used an oil-immersion
> 63x Plan-Apo and oil on either side of the coverslip.
> 
> I know that the z distances are not accurate because of the grossly
> different RIs but I'm not sure how to correct them.  Can I just
> multiply the z step size by an n2/n1 factor to get the real Δz (with
> different factors for oil/mineral and mineral/water)?  In the
> literature I've seen less simplistic correction models that seem more
> accurate but no practical ways to implement them that I could decipher
> were presented.  Any help would be much appreciated.
> 
> Thanks,
> Esteban
> 
> --
> G. Esteban Fernandez, Ph.D.
> Associate Director
> Molecular Cytology Research Core Facility
> University of Missouri
> 1201 E. Rollins St.
> Columbia, MO 65211
> 
> 573-882-4895
> 573-884-9676 fax
> 
> http://www.biotech.missouri.edu/mcc/