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SOFI Processing
MSSR Super-Resolution
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SOFI Theory
Super-resolution Optical Fluctuation Imaging (SOFI) extracts
sub-diffraction spatial information from temporal fluorescence
fluctuations of independently blinking emitters (quantum dots).
Key Principle
The fluorescence signal at pixel r is:
F(r,t) = Sum_k eps_k * s_k(t) * U(r - r_k)
The nth-order cumulant of intensity fluctuations yields an image
where the PSF is raised to the nth power:
C_n(r) = Sum_k eps_k^n * kappa_n[s_k] * U^n(r - r_k)
Since U^n is narrower than U, the effective
resolution improves by a factor of sqrt(n).
Resolution Improvement
Order
PSF
Resolution Gain
2
U^2(r)
1.41x
3
U^3(r)
1.73x
4
U^4(r)
2.00x
5
U^5(r)
2.24x
6
U^6(r)
2.45x
Cumulant Computation
For zero-mean fluctuations dF = F - <F> with
consecutive time lags:
C2:<dF(t)*dF(t+1)> (auto-covariance)
C3:<dF(t)*dF(t+1)*dF(t+2)> (3rd central moment)
C4: 4th moment minus products of 2nd moments (3 terms)
C5: 5th moment minus pair-triple products (10 terms)
C6: 6th moment minus pair-quartet, triple-triple, plus pair-pair-pair terms
Quantum Dot Blinking
QDots exhibit power-law distributed on/off times:
P(t) ~ t^(-alpha) with alpha ~ 1.5.
This stochastic blinking provides the temporal fluctuations
that SOFI requires.
Linearization
The nth-order cumulant scales as brightness^n, creating extreme
contrast. Taking the nth root |C_n|^(1/n) restores
linear brightness scaling.