Two Photon Excitation Calculation
This calculator provides an estimate of the two photon excitation focal volume and
excitation efficiency for a given 2P action cross-section, wavelength, laser power and numerical aperture.
For the fluorescent photons generated per second, the calculation assumes the concentration of the
fluorophore is a uniform concentration across the two-photon excitation volume.
The characteristic radii used (ωr and ωz) are 1/e radii of the two-photon excitation PSF
assuming an overfilled objective back aperture (i.e. at the diffraction limit). The calculator takes saturation into account,
assuming a simple saturation model (i.e. no triplet states), and is useful to estimate how the resolution is affected by the
excitation conditions. Note that the saturation model is a simplification and may not capture all the photophysical complexities
of all fluorophores.
The 2P excitation profile is modeled as a saturation function:
\[{\rm{Effective\ excitation\ volume = }}\int\limits_{ - 2{\omega _z}}^{2{\omega _z}} {\int\limits_0^{2{\omega _r}} {\frac{{a{e^{ - \frac{{{r^2}}}{{\omega _r^2}}}}{e^{ - \frac{{{z^2}}}{{\omega _z^2}}}}}}{{1 + a{e^{ -
\frac{{{r^2}}}{{\omega _r^2}}}}{e^{ - \frac{{{z^2}}}{{\omega _z^2}}}}}}\;} } rdrdz\]
The parameter a is given by:
\[a = \frac{{{\sigma _{2P}}{g_P}\tau I_0^2}}{{R{\tau _P}}}\]
where σ2P is the two-photon action cross-section, gP is the pulse shape factor
(0.58 for Sech-squared pulses), τ is the fluorescence lifetime, I0 is the peak excitation intensity,
R is the laser repetition rate, and τP is the FWHM of the excitation pulse.
After setting the parameters, click "Calculate" to see the results. The text in the results section can be
copied to the clipboard using the "Copy" button. The first two 2D plots show the spatial
distribution of the estimated number of fluorescence photons/sec along the lateral and axial axes
(assuming the 2P cross-section entered is the action cross-section, i.e. includes the quantum efficiency).
The third 2D plot shows the saturation curve for the current parameters. The saturation curve plots the
normalized excitation efficiency (relative to the non-saturated case) as a function of the saturation parameter a,
which is proportional to the peak excitation intensity squared.
To summarize - this calculator assumes:
Diffraction limited focus with no optical aberrations.
Simple two-state photophysical model.
Uniform concentration of fluorophores in the exciation volume.
The photons/sec generated do not take collection efficiency into account - a typical laser scanning microscope collects less than 10% of the total
photons generated, factoring in the solid angle of collection, filter transmission and PMT quantum efficiency.
The rate of fluorescence generation is in photons per second - you need to adjust for your pixel dwell time
(typically µs).
Set values and click Calculate...
2P Excitation Profile
Lateral & axial cross-sections through beam focus
Fluorescence photons/sec profile |
― ― FWHM of effective volume
Lateral profile (r)
Axial profile (z)
Focal Volume Saturation Calculator
I = 2π ∫∫ [ a·exp(−r²/ωr²)·exp(−z²/ωz²) /
(1 + a·exp(−r²/ωr²)·exp(−z²/ωz²)) ] · r dr dz
| \(V_\mathrm{gaus} = \pi^{3/2}\,\omega_{xy}^2\,\omega_z\)
I (integral)
—
\(V_\mathrm{gaus} = \pi^{3/2}\,\omega_{xy}^2\,\omega_z\) (µm³)
—
I / Vgaus
—
Method
—
\(\displaystyle a = \frac{\sigma_{2P}\, g_P\, \tau\, I_0^2}{R\, \tau_P}\)
I (integral)
a · Vgaus — linear (unsaturated) limit: I ≈ a·Vgaus when
σ2PI²τ ≪ 1
\(V_\mathrm{gaus} = \pi^{3/2}\,\omega_{xy}^2\,\omega_z\)
Current a