In FCS, the expression of diffusion coefficient is D=W2/4T(tau). But when I referred a paper for simplicity they had calculated the diffusion coefficient for 2D and had derived the above expression. As I know FCS is a 3D technique and we focus on a volume, then when in experiment we do consider a volume how do i justify that the term is 4 and not 6?
Dear Mithra,
This is an excellent question; I posed it to myself at some point in the past and came to the following answer: The confocal detection volume in an FCS experiment (conducted on a confocal microscope) is not spherical, but ellipsoidal. In the respective equation, you therefore usually just treat two directions, x and y, whereas the third, z, is not explicitly regarded, but just accounted for in the context of another parameter, often denonetd w or r, which is the aspect ratio of the ellipse. Hence, the two-dimensional form with a numerical factor of 4 needs to be used to calculate D from tau.
I don't have a supporting reference for this, this is just my personal throught. I will keep following this thread here, maybe some later post will highlight a reference that will help both of us.
Cheers,
Sebastian
Thanks a lot for the answer sir. I understood your idea of the explanation.Yes even when i was looking into the reference for the same i couldn't find any. I got the concept of the confocal detection volume and the reason for considering it 2D. I have one more doubt.While detecting we usually use a optical fiber. Does it collect the fluorescence intensity information in 2D or 3D. What is your opinion on this matter?
Mmh...from what I understand (again, this is just my personal understanding and nothing that I can support with a clear reference) the fiber transfers the information (i.e., the fluorescence light) that stems from the confocal volume to the detector (i.e., the photodiode), and the confocal volume has an ellipsoidal shape due to the NA of the objective lens, the specific tuning of the correction collar (if there is one), and the confocal pinhole diameter. By itself, the volume is of course a 3D object, but due to its ellipsoidal rather than spherical shape, the diffusive in- and outflux of fluorophores into it and from it is markedly affected only by its x and y extension, whereas the z extension is wider and therefore irrelevant...such thet a 2D equation for calculating D from tau is to be used in the end.
Have a look here, for a detailed derivation:
http://www.fcsxpert.com/classroom/theory/autocorrelation-diffusion-3d.html
You can look at it in the following way: there is a sqrt(1+2Dt/X) term per each spatial dimension, where X=w0 for the x and y axes (w0=x0=y0), and X=kappa*w0 for the z axis. The sqrt(1+2Dt/X) term comes out from the integration of the Gaussian propagator in each dimension.
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