Utilising ballistic light

When imaging in thicker biological samples, the optical radiation can be scattered, e.g. by heterogeneities in refractive index, and biological tissue is typically not transparent. Multiple scattering of photons can degrade image quality and limits the depth at which useful optical images can be obtained. There are a variety of approaches to address this challenge, most of which can be classified as ballistic light or diffuse light techniques. Optical scattering is a probabilistic process and the optical signal transmitted through a scattering medium such as optical tissue will include a fraction of unscattered or “ballistic” photons. This ballistic light signal will be attenuated according to  where I₀ is the incident ballistic light signal, z is the propagation distance and µ_S is the scattering coefficient, which is the inverse of the scattering mean free path (MFP). For biological tissue, this is of the order of 100 µm, which means that the ballistic light signal is reduced by e¹⁰ after propagating through 1 mm of tissue. Thus, when imaging through more than a few hundred microns of biological tissue, the optical signal will comprise a small fraction of ballistic photons and a much larger fraction of scattered photons. If an image can be formed using only the ballistic photons, then diffraction-limited resolution can be achieved and there are many biophotonics techniques that aim to form high resolution images using ballistic light. For example, ballistic photons retain their coherence with their source and so interferometric techniques, such as optical coherence tomography (OCT)¹ and holography, have been used to form ballistic light images in biological tissue.  OCT, which acquires images pixel by pixel, can detected ballistic photons backscattered from a depth of up to ~2 mm (or ~20 MFP). Holography, which entails wide-field detection, suffers from interpixel cross-talk (where scattered photons from one image pixel appear to detectors as having arrived in another pixel) and its ballistic light imaging depth is limited to less than 1 mm. Single point scanning multiphoton excited fluorescence microscopy and other nonlinear scanning microscopy techniques also provide ballistic light imaging since the beam focus is formed by ballistic photons and the scattering of the emitted photons does not impact the resolution since they all originate from the focus. Such techniques can image up to ~0.5 mm deep in tissue, depending on the incident power.

Utilising scattered light

The scattering of light in biological tissue is usually described using the mathematics of Mie scattering.  Biological tissue is predominantly forward scattering with a mean cosine squared scattering angle of . Effectively this means that singly scattered photons still convey some information about their original direction and for moderate scattering depths, detected photons tend to have been scattered along a snake-like path about their original trajectory. This snake light can be utilised to form images of intermediate quality. After ~30 scattering MFP² of biological tissue, photons are considered to have scattered sufficiently to lose all information about their original trajectory and are described as diffuse, such that their propagation can be modelled using the diffusion approximation³. Imaging is still possible with diffuse light but the propagation of photons is considered statistically and the image information obtained is based on the most probable trajectories of the detected photons. The resolution achievable with diffuse light as been estimated to be ~0.2L⁴ where L is the thickness of the scattering medium.

Diffuse light imaging can be modelled using Monte Carlo techniques to calculate the trajectories of individual photons, but this is computationally expensive. Alternatively, it is often analysed in terms of photon density waves that propagate in a manner analogous to electromagnetic waves but with much lower phase velocity and longer wavelengths. Detection can be steady-state or it can be time-resovled, using frequency domain or time domain detection. Essentially this exploits the fact that the earliest arriving light has taken the shortest path from source to detector and a measurement of the mean optical path can permit average optical absorption and scattering coefficients to be calculated.

Diffuse optical tomography using NIR radiation is a well-established approach to optical mammography, where it aims to detect tumours, particularly based on the detection of blood, and optical tomography of the brain, where it is used to map oxygenation as a means to detection haematoma in premature infants and to map blood oxygenation as a readout of neurological function. Diffuse fluorescence tomography has also been explored for mammography, utilising indocyanine green (ICG) as a contrast agent that is permitted to be used in patients, and for small animal imaging.

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¹ D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
² Bruce et al, APPLIED OPTICS 34 (1995) 5823
³ M. S. Patterson, B. Chance, and B. C. Wilson, ‘‘Time-resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,’’ Appl. Opt. 28, 2331–2336, (1989)
⁴ J. A. Moon, R. Mahon, M. D. Duncan, and J. Reintjes, ‘‘Limits for imaging through turbid media with diffuse light,’’ Opt. Lett. 18, 1591–1593 119932.