Two-Photon Microscopy Calculator
Calculate resolution, excitation volume, peak intensity, and depth penetration for two-photon fluorescence microscopy.
Lateral FWHM (2P)
375 nm
1P equivalent λ 400 nm; Zipfel fit, NA > 0.7 branch
Axial FWHM (2P)
1.87 µm
Zipfel fit
Excitation volume
0.318 fL
π^(3/2) ω_xy² ω_z (1 fL = 1 µm³)
Peak intensity at focus
0.15 TW/cm²
At the focus depth, I_surface·e^(−µz); surface: 1.11 TW/cm²
Pulse energy
0.375 nJ
Peak power
3.52 kW
0.94 E/τ (Gaussian pulse)
Ballistic power at depth
4.06 mW
2P signal × 1.83e-2
Scattering length 1/µ
100 µm
Formulas (textbook approximation)
I²(r, z) ≈ exp(−r²/ω_xy² − z²/ω_z²), FWHM = 2√(ln 2)·ω
ω_xy = 0.320λ/(√2 NA) (NA ≤ 0.7), 0.325λ/(√2 NA^0.91) (NA > 0.7)
ω_z = 0.532λ/(√2 (n − √(n² − NA²))), V = π^(3/2) ω_xy² ω_z
I_peak = P_peak/(2π ω_xy²), P_peak = 2√(ln 2/π)·E/τ
P(z) = P₀ exp(−µz), 2P signal ∝ P(z)²
Gaussian fit to the squared focal intensity of a filled objective pupil: Zipfel, Williams & Webb, Nat. Biotechnol. 21, 1369 (2003). The peak intensity is within about 1 % of the Airy peak πNA²P/λ² (NA ≤ 0.8; the high-NA fit is 4–10 % lower at NA 1.0–1.4). The depth model counts only ballistic excitation photons; aberrations and out-of-focus background 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
Gaussian fit to the diffraction-limited focus of a filled pupil, with Gaussian pulses. The depth model counts only ballistic excitation photons; aberrations and out-of-focus background are not included.
- Zipfel W. R., Williams R. M., Webb W. W. (2003). Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369–1377. Gaussian fit to the squared illumination PSF. doi:10.1038/nbt899
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §8.5. Cambridge University Press. Exact paraxial Airy pattern the fit was checked against.