SOFI QDOTS Super-resolution Optical Fluctuation Imaging

×

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.