Perspective on diffuse light in tissue: subsampling photon populations

Abstract

Significance: Diffuse light is ubiquitous in biomedical optics and imaging. Understanding the process of migration of an initial photon population entering tissue to a completely randomized, diffusely scattered population provides valuable insight to the interpretation and design of optical measurements.

Aim: The goal of this perspective is to present a brief, unifying analytical framework to describe how properties of light transition from an initial state to a distributed state as light diffusion occurs.

Approach: First, measurement parameters of light are introduced, and Monte Carlo simulations along with a simple analytical expression are used to explore how these individual parameters might exhibit diffusive behavior. Second, techniques to perform optical measurements are considered, highlighting how various measurement parameters can be leveraged to subsample photon populations.

Results: Simulation results reinforce the fact that light undergoes a transition from a non-diffuse population to one that is first subdiffuse and then fully diffuse. Myriad experimental methods exist to isolate subpopulations of photons, which can be broadly categorized as source- and/or detector-encoded techniques, as well as methods of tagging the tissue of interest.

Conclusions: Characteristic properties of light progressing to diffusion can be described by some form of Gaussian distribution that grows in space, time, angle, wavelength, polarization, and coherence. In some cases, these features can be approximated by simpler exponential behavior. Experimental methods to subsample features of the photon distribution can be achieved or theoretical methods can be used to better interpret the data with this framework.

Keywords: diffuse light; diffusion; subdiffuse light; tissue optics.

Fig. 1

Measurement parameters of light that are affected by the process of diffusion.

Fig. 2

Measuring the six parameters of light, where $t_i$ is the time, $x_i$ is the spatial position, ${\theta }_i$ the is the angular trajectory, ${\mathrm{OD}}_{\lambda }$ is the wavelength-dependent optical density, DOP stands for degree of polarization, and $\mathrm{\Delta }\mathrm{\Phi }$ is the difference in phase between light waves.

Fig. 3

The spread of light within a tissue in response to a very narrow collimated beam, where ${\mu }_s(1-g)$ is held constant while the scattering anisotropy parameter $g$ and scattering coefficient ${\mu }_s$ are varied. $g$ was varied as 0.5, 0.8, 0.9, and 0.95, whereas ${\mu }_s$ varied as 20, 50, 100, and $200{\mathrm{cm}}^{-1}$, such that ${\mu }_s(1-g)$ remained a constant $10{\mathrm{cm}}^{-1}$. The absorption coefficient was held constant at ${\mu }_a=1{\mathrm{cm}}^{-1}$; the tissue was semi-infinite; and the surface boundary was refractive index matched. The dashed line indicates an isoline at a constant fluence ($\phi$) of $10{\mathrm{cm}}^{-2}$, beyond which photon diffusion down concentration gradients acts as though the source were at $x$, $z=0.0$, 0.1 (i.e., the small, white circle at a depth of one transport mean free path). Colormap fluence field values were scaled logarithmically for improved visualization of the range.

Fig. 4

Venn diagram of a representative set of techniques of study in populations of photons, categorized by optical source-, detector-, and/or population-encoding scheme.