Three-Photon Microscopy Calculator
Calculate resolution, excitation volume, and depth penetration for three-photon excitation microscopy at 1300+ nm.
3P lateral FWHM
498 nm
2P at the same λ: 609 nm
3P axial FWHM
2.49 µm
2P at the same λ: 3.04 µm
Excitation volume (I³)
0.742 fL
(π/6)^(3/2) w² w_z (1 fL = 1 µm³)
Peak intensity at focus
5.6 TW/cm²
At the focus depth, I_surface·e^(−µz); surface: 111.6 TW/cm²
1P / 2P equivalent λ
433 / 650 nm
Pulse energy
100.0 nJ
Peak power 939.4 kW
Ballistic power at depth
4.98 mW
Scattering length 167 µm
Relative 3P signal at depth
1.23e-4
exp(−3µz), constant surface power
Formulas (textbook approximation)
I ≈ exp(−2r²/w² − 2z²/w_z²), w = 2ω_xy, w_z = 2ω_z (Zipfel radii)
FWHM of I^k = 2√(2 ln 2/k)·ω, so 3P = 2P × √(2/3)
V_3P = ∫I³dV/I₀³ = (π/6)^(3/2) w² w_z
I_peak = P_peak/(2π ω_xy²), P_peak = 2√(ln 2/π)·E/τ
3P signal ∝ P(z)³ = P₀³ exp(−3µz)
Gaussian fit to the squared focal intensity from Zipfel, Williams & Webb, Nat. Biotechnol. 21, 1369 (2003), extended to I³; against the exact paraxial Airy pattern the 3P lateral FWHM is about 1.5 % wide. The depth model counts only ballistic excitation photons.
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
Zipfel's Gaussian fit extended to the cubed intensity; its lateral FWHM is about 1.5 % wide against the Airy pattern. Ballistic depth model only; 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, extended here to I³. 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.