Multiphoton Imaging Depth Calculator
Two-photon excitation depth penetration, resolution, and laser parameters.
Results
FWHM = 2√(ln 2)·ω; ω_xy = 0.320λ/(√2 NA) (NA ≤ 0.7) or 0.325λ/(√2 NA^0.91); ω_z = 0.532λ/(√2 (n − √(n² − NA²))) (Zipfel et al., Nat. Biotechnol. 21, 1369, 2003); the NA = 0.7 branch switch jumps ≈ 2 %, inherent to the fit.
Signal ∝ exp(−2µd) at constant surface power, µ = µ_a + µ_s | Depth = −ln(fraction)/(2µ)
Default µ_s = 6 mm⁻¹ (attenuation length ≈ 170 µm), a typical value for cortex near 800 nm. µ does not follow the wavelength input: enter the value for your wavelength (scattering falls at longer λ). At 1280 nm Kobat, Horton & Xu reached 1.6 mm in mouse cortex, near the depth limit set by out-of-focus background (J. Biomed. Opt. 16, 106014, 2011; Theer & Denk, JOSA A 23, 3139, 2006).
Signal & Excitation vs Depth
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 focus fit plus exp(−µz) attenuation with one extinction coefficient, counting ballistic photons only. The default µ_s = 6 mm⁻¹ is a typical cortex value near 800 nm; µ does not follow the wavelength.
- 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
- Kobat D., Horton N. G., Xu C. (2011). In vivo two-photon microscopy to 1.6-mm depth in mouse cortex. J. Biomed. Opt. 16, 106014. 1.6 mm at 1280 nm, near the fundamental depth limit. doi:10.1117/1.3646209
- Theer P., Denk W. (2006). On the fundamental imaging-depth limit in two-photon microscopy. J. Opt. Soc. Am. A 23, 3139–3149. Depth limit set by out-of-focus background. doi:10.1364/JOSAA.23.003139