Amplitude and phase of tightly focused laser beams in turbid media

Modeling nonlinear optical microscopy in scattering media, part II. Radiation from focal volume to far-field: tutorial

The development and application of nonlinear optical (NLO) microscopy methods in biomedical research has experienced rapid growth over the past three decades. Despite the compelling power of these methods, optical scattering limits their practical use in biological tissues. This tutorial offers a model-based approach illustrating how analytical methods from classical electromagnetism can be employed to comprehensively model NLO microscopy in scattering media. In Part I, we quantitatively model focused beam propagation in non-scattering and scattering media from the lens to focal volume. In Part II, we model signal generation, radiation, and far-field detection. Moreover, we detail modeling approaches for major optical microscopy modalities including classical fluorescence, multi-photon fluorescence, second harmonic generation, and coherent anti-Stokes Raman microscopy.

Modeling nonlinear optical microscopy in scattering media, part I. Propagation from lens to focal volume: tutorial

The development and application of nonlinear optical (NLO) microscopy methods in biomedical research have experienced rapid growth over the past three decades. Despite the compelling power of these methods, optical scattering limits their practical use in biological tissues. This tutorial offers a model-based approach illustrating how analytical methods from classical electromagnetism can be employed to comprehensively model NLO microscopy in scattering media. In Part I, we quantitatively model focused beam propagation in non-scattering and scattering media from the lens to focal volume. In Part II, we model signal generation, radiation, and far-field detection. Moreover, we detail modeling approaches for major optical microscopy modalities including classical fluorescence, multi-photon fluorescence, second harmonic generation, and coherent anti-Stokes Raman microscopy.

Aggregation-Induced Emission Luminogen with Near-Infrared-II Excitation and Near-Infrared-I Emission for Ultradeep Intravital Two-Photon Microscopy

Currently, a serious problem obstructing the large-scale clinical applications of fluorescence technique is the shallow penetration depth. Two-photon fluorescence microscopic imaging with excitation in the longer-wavelength near-infrared (NIR) region (>1100 nm) and emission in the NIR-I region (650-950 nm) is a good choice to realize deep-tissue and high-resolution imaging. Here, we report ultradeep two-photon fluorescence bioimaging with 1300 nm NIR-II excitation and NIR-I emission (peak ∼810 nm) based on a NIR aggregation-induced emission luminogen (AIEgen). The crab-shaped AIEgen possesses a planar core structure and several twisting phenyl/naphthyl rotators, affording both high fluorescence quantum yield and efficient two-photon activity. The organic AIE dots show high stability, good biocompatibility, and a large two-photon absorption cross section of 1.22 × 10³ GM. Under 1300 nm NIR-II excitation, in vivo two-photon fluorescence microscopic imaging helps to reconstruct the 3D vasculature with a high spatial resolution of sub-3.5 μm beyond the white matter (>840 μm) and even to the hippocampus (>960 μm) and visualize small vessels of ∼5 μm as deep as 1065 μm in mouse brain, which is among the largest penetration depths and best spatial resolution of in vivo two-photon imaging. Rational comparison with the AIE dots manifests that two-photon imaging outperforms the one-photon mode for high-resolution deep imaging. This work will inspire more sight and insight into the development of efficient NIR fluorophores for deep-tissue biomedical imaging.

Finite-difference time-domain analysis of increased penetration depth in optical coherence tomography by wavefront shaping

Multiple scattering in turbid media inhibits optimal light focusing and thus limits the penetration depth in optical coherence tomography (OCT). However, the effects of multiple scattering in a turbid medium can be systematically controlled by shaping the incident wavefront. The authors utilize the reciprocity of Maxwell's equations and finite-difference time-domain numerical analysis to investigate the ultimate performance bounds of wavefront shaping-OCT under ideal and realistic configurations and compare them with the conventional method. The results reveal that the optimized impinging wavefront significantly enhances the penetration depth of OCT.

Deep and high-resolution three-dimensional tracking of single particles using nonlinear and multiplexed illumination

Molecular trafficking within cells, tissues and engineered three-dimensional multicellular models is critical to the understanding of the development and treatment of various diseases including cancer. However, current tracking methods are either confined to two dimensions or limited to an interrogation depth of ∼15 μm. Here we present a three-dimensional tracking method capable of quantifying rapid molecular transport dynamics in highly scattering environments at depths up to 200 μm. The system has a response time of 1 ms with a temporal resolution down to 50 μs in high signal-to-noise conditions, and a spatial localization precision as good as 35 nm. Built on spatiotemporally multiplexed two-photon excitation, this approach requires only one detector for three-dimensional particle tracking and allows for two-photon, multicolour imaging. Here we demonstrate three-dimensional tracking of epidermal growth factor receptor complexes at a depth of ∼100 μm in tumour spheroids.

Existing single-particle tracking techniques are limited in terms of penetration depth, tracking range or temporal resolution. Here, Perillo et al. demonstrate three-dimensional particle tracking up to 200-μm depth, with 35-nm spatial localization and 50-μs resolution using multiplexed two-photon excitation.

Quantitative analysis of light scattering in polarization-resolved nonlinear microscopy

Polarization resolved nonlinear microscopy (PRNM) is a powerful technique to gain microscopic structural information in biological media. However, deep imaging in a variety of biological specimens is hindered by light scattering phenomena, which not only degrades the image quality but also affects the polarization state purity. In order to quantify this phenomenon and give a framework for polarization resolved microscopy in thick scattering tissues, we develop a characterization methodology based on four wave mixing (FWM) process. More specifically, we take advantage of two unique features of FWM, meaning its ability to produce an intrinsic in-depth local coherent source and its capacity to quantify the presence of light depolarization in isotropic regions inside a sample. By exploring diverse experimental layouts in phantoms with different scattering properties, we study systematically the influence of scattering on the nonlinear excitation and emission processes. The results show that depolarization mechanisms for the nonlinearly generated photons are highly dependent on the scattering center size, the geometry used (epi/forward) and, most importantly, on the thickness of the sample. We show that the use of an un-analyzed detection makes the polarization-dependence read-out highly robust to scattering effects, even in regimes where imaging might be degraded. The effects are illustrated in polarization resolved imaging of myelin lipid organization in mouse spinal cords.

Three-photon luminescence of gold nanorods and its applications for high contrast tissue and deep in vivo brain imaging

Gold nanoparticles can be used as contrast agents for bio-imaging applications. Here we studied multi-photon luminescence (MPL) of gold nanorods (GNRs), under the excitation of femtosecond (fs) lasers. GNRs functionalized with polyethylene glycol (PEG) molecules have high chemical and optical stability, and can be used as multi-photon luminescent nanoprobes for deep in vivo imaging of live animals. We have found that the depth of in vivo imaging is dependent upon the transmission and focal capability of the excitation light interacting with the GNRs. Our study focused on the comparison of MPL from GNRs with two different aspect ratios, as well as their ex vivo and in vivo imaging effects under 760 nm and 1000 nm excitation, respectively. Both of these wavelengths were located at an optically transparent window of biological tissue (700-1000 nm). PEGylated GNRs, which were intravenously injected into mice via the tail vein and accumulated in major organs and tumor tissue, showed high image contrast due to distinct three-photon luminescence (3PL) signals upon irradiation of a 1000 nm fs laser. Concerning in vivo mouse brain imaging, the 3PL imaging depth of GNRs under 1000 nm fs excitation could reach 600 μm, which was approximately 170 μm deeper than the two-photon luminescence (2PL) imaging depth of GNRs with a fs excitation of 760 nm.

Rapid computation of the amplitude and phase of tightly focused optical fields distorted by scattering particles

We develop an efficient method for accurately calculating the electric field of tightly focused laser beams in the presence of specific configurations of microscopic scatterers. This Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method computes the amplitude and phase of the scattered electric field in excellent agreement with finite difference time-domain (FDTD) solutions of Maxwell's equations. Our HF-WEFS implementation is 2-4 orders of magnitude faster than the FDTD method and enables systematic investigations of the effects of scatterer size and configuration on the focal field. We demonstrate the power of the new HF-WEFS approach by mapping several metrics of focal field distortion as a function of scatterer position. This analysis shows that the maximum focal field distortion occurs for single scatterers placed below the focal plane with an offset from the optical axis. The HF-WEFS method represents an important first step toward the development of a computational model of laser-scanning microscopy of thick cellular/tissue specimens.

Effects of light scattering on optical-resolution photoacoustic microscopy

The imaging depth of ballistic optical imaging technologies is limited by light scattering. To study the effects of scattering on optical-resolution photoacoustic microscopy (OR-PAM), the signals were divided into target and background signals. A method to simulate the point spread function (PSF) of the PAM system considering both optical illumination and acoustic detection was proposed, then the PSF was used to calculate the contribution of each class of signal at different depths of the focal plane (zf). How image contrast is degraded when there is a uniformly absorbing background as well as when there are small targets densely packed in the acoustic resolution cell were studied. By using the hyperboloid-focusing-based Monte Carlo method, optical focusing into a scattering medium was simulated. It was found that the lateral resolution provided by optical focusing is degraded by only 14% when zf=1.1 transport mean free path (l t'), compared with the case of no scattering. When zf=1.7 lt', the fluence at 50 μm radial distance away from the focal point is 93% of that at the focal point, which shows optical focusing is very weak at this depth. The method to simulate the PSF of PAM can be used in the future to optimize parameters so as to improve the system performance.

Digital optical phase conjugation of fluorescence in turbid tissue

We demonstrate a method for phase conjugating fluorescence. Our method, called reference free digital optical phase conjugation, can conjugate extremely weak, incoherent optical signals. It was used to phase conjugate fluorescent light originating from a bead covered with 0.5 mm of light-scattering tissue. The phase conjugated beam refocuses onto the bead and causes a local increase of over two orders of magnitude in the light intensity. Potential applications are in imaging, optical trapping, and targeted photochemical activation inside turbid tissue.

Numerical evaluation of temporal focusing characteristics in transparent and scattering media

Temporal focusing is a simple approach for achieving tight, optically sectioned excitation in nonlinear microscopy and multiphoton photo-manipulation. Key applications and advantages of temporal focusing involve propagation through scattering media, but the progressive broadening of the temporal focus has not been characterized. By combining a detailed geometrical optics model with Monte-Carlo scattering simulations we introduce and validate a simulation strategy for predicting temporal focusing characteristics in scattering and non-scattering media. The broadening of the temporal focus width with increasing depth in brain tissue is studied using both simulations and experiments for several key optical geometries, and an analytical approximation is found for the dependence of this broadening on the microscope's parameters in a transparent medium. Our results indicate that a multiphoton temporal focus has radically different broadening characteristics in deep tissue than those of a spatial focus.

Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues

The focal field distribution of tightly focused laser beams in turbid media is sensitive to optical scattering and therefore of direct relevance to image quality in confocal and nonlinear microscopy. A model that considers both the influence of scattering and diffraction on the amplitude and phase of the electric field in focused beam geometries is required to describe these distorted focal fields. We combine an electric field Monte Carlo approach that simulates the electric field propagation in turbid media with an angular-spectrum representation of diffraction theory to analyze the effect of tissue scattering properties on the focal field. In particular, we examine the impact of variations in the scattering coefficient (µ(s)), single-scattering anisotropy (g), of the turbid medium and the numerical aperture of the focusing lens on the focal volume at various depths. The model predicts a scattering-induced broadening, amplitude loss, and depolarization of the focal field that corroborates experimental results. We find that both the width and the amplitude of the focal field are dictated primarily by µ(s) with little influence from g. In addition, our model confirms that the depolarization rate is small compared to the amplitude loss of the tightly focused field.