Monte Carlo analysis of two-photon fluorescence imaging through a scattering medium

Abstract

The behavior of two-photon fluorescence imaging through a scattering medium is analyzed by use of the Monte Carlo technique. The axial and transverse distributions of the excitation photons in the focused Gaussian beam are derived for both isotropic and anisotropic scatterers at different numerical apertures and at various ratios of the scattering depth with the mean free path. The two-photon fluorescence profiles of the sample are determined from the square of the normalized excitation intensity distributions. For the same lens aperture and scattering medium, two-photon fluorescence imaging offers a sharper and less aberrated axial response than that of single-photon confocal fluorescence imaging. The contrast in the corresponding transverse fluorescence profile is also significantly higher. Also presented are results comparing the effects of isotropic and anisotropic scattering media in confocal reflection imaging. The convergence properties of the Monte Carlo simulation are also discussed.

Multifocal multiphoton microscopy based on multianode photomultiplier tubes

“…The effects of photon scattering on image resolution and contrast in SMM have been investigated extensively by both Monte Carlo simulations [27][28][29] and experiments [30][31][32][33]. These studies examined the scattering effects on PSF ex [27,28,[30][31][32] and on the collection efficiency of emission light [29,31,33].…”

“…These studies examined the scattering effects on PSF ex [27,28,[30][31][32] and on the collection efficiency of emission light [29,31,33]. These studies focused on idealized specimens with homogenous fluorophore distribution and ignored pulse dispersion of excitation light with depth.…”

“…In practice, the decay coefficient is slightly higher than 2, because the average path length of excitation photons traveling to the focus is longer than the imaging depth for high NA objectives [31]. Within the depth range of a few times , (2) image resolution is not degraded, because the full-width-at-half-maximum intensity (FWHM) of PSF ex is not affected by photon scattering [28,31,32], and (3) image contrast is degraded mainly due to the decrease of excitation power as photon scattering effect. (4) Emission light becomes diffusive due to multiple scattering in the specimen.…”

Monte Carlo Simulation of Image Depth Improvement by Two-color Two-photon Fluorescence Microscopy

“…14,15) The Monte Carlo simulation is based on the optical properties of the sample tissue, which can be described by the following parameters: the refractive index n , the absorption coefficient a μ (defined as the probability of photon absorption per unit infinitesimal path length), the scattering coefficient s μ (defined as the probability of photon scattering per unit infinitesimal path length) and the anisotropy factor g (defined as the average of the cosine value of the deflection angle). For biological tissue, value of g usually ranges between 0.3 and 0.98, but in many cases g is ~0.9 in the visible spectrum, indicating that scattering mainly occurs in the nearly forward direction.…”

“…14) We choose the refractive index and the absorption coefficient as 1.37 n = and (1/ ) s μ λ ∝ . 15) Another assumption in our stimulation is that the highly scattering medium is infinitely wide and infinitely thick, which is reasonable because the beam size is significantly smaller than that of the tissue volume. A Cartesian coordinate system is used to record the trajectories of photons in three-dimensional space, as shown in Fig.…”