FCS Calculator
Fluorescence Correlation Spectroscopy — diffusion time, concentration, and confocal volume.
Results
Autocorrelation curve
Model
V_eff = π^(3/2) w₀² z₀, N = c·N_A·V_eff, D = w₀²/(4τ_D)
G(τ) = (1/N)(1 + τ/τ_D)⁻¹(1 + τ/(κ²τ_D))^(−1/2) [1 + T/(1 − T)·e^(−τ/τ_T)]
SNR = ε √(Δτ · T_meas) / √(1 + 1/N)
3D Gaussian detection volume (Hess & Webb 2002) with the triplet term of Widengren, Mets & Rigler (1995); T is the mean fraction of molecules in the triplet state, so G(0⁺) = 1/(N(1 − T)). The SNR is Koppel's (1974) shot-noise limit for the shortest lag channel (εΔτ ≪ 1, ε²Δτ τ_D ≪ 1): it grows with the brightness per molecule and, for N ≫ 1, does not depend on N. Background light, afterpulsing and the deviation of a real confocal volume from a Gaussian (larger at high NA or with a mismatched pinhole) are not included.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
3D Gaussian detection volume with free diffusion and one triplet state. The SNR is Koppel's shot-noise limit at the shortest lag; background, afterpulsing and non-Gaussian confocal volumes are not included.
- Hess S. T., Webb W. W. (2002). Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy. Biophys. J. 83, 2300–2317. Effective volume π^(3/2) w₀² z₀ and the 3D Gaussian G(τ). doi:10.1016/S0006-3495(02)73990-8
- Widengren J., Mets Ü., Rigler R. (1995). Fluorescence correlation spectroscopy of triplet states in solution: a theoretical and experimental study. J. Phys. Chem. 99, 13368–13379. Triplet factor 1 + T/(1 − T)·e^(−τ/τ_T). doi:10.1021/j100036a009
- Koppel D. E. (1974). Statistical accuracy in fluorescence correlation spectroscopy. Phys. Rev. A 10, 1938–1945. SNR set by the counts per molecule, independent of N. doi:10.1103/PhysRevA.10.1938