Frequency-Domain Near-Infrared Spectroscopy


Fig. 1: Example distribution of fluence (Φ) which may be thought of as photon density produced from the diffusion of many photons. An Example possible path of a single photon is shown as a white line.

To understand what Frequency-Domain Near-InfraRed Spectroscopy (FD-NIRS) is, we must first understand the optically diffuse medium. In an optically diffuse medium, light moves about by randomly changing the direction it's traveling. Particles representing packets of light are called photons. The act of these photons randomly changing direction is called scattering. Therefore, one says that an optically diffuse medium is one in which the behavior of photons is mostly described by their scattering. An example of a possible random photon path from scattering can be seen in Fig. 1. 

In reality, many media may be described in this optically diffuse way. For example, a cloud is optically diffuse. In a cloud, photons enter, randomly scatter within, and then exit. Due to the random scattering of the photons, your eye can not determine where a photon entered the cloud; thus, the cloud appears opaque or white. Expanding on this example, you may realize that, in general, what is described as an optically diffuse medium is seen as opaque. Examples are the aforementioned cloud, a glass of milk, or even biological tissue.

Scattering is not the only thing that may happen to a photon in a diffuse medium. A second common property that a diffuse medium has is absorption. This is when photons die when they interact with the medium. Take a black cup of coffee; this medium is primarily absorbing since photons die off as they travel through the liquid. But black coffee has little scattering since the photons do not change direction much.* If the coffee is strong and dark, we know it has high absorption, while if it is light and watery, we know it has low absorption. Now imagine we add milk to the coffee; this will make the coffee opaque as we have just added scattering, and the photons' directions within the liquid are now randomized. If we add cream instead of milk, we may notice the coffee is even more opaque since cream has a higher scattering compared to milk.

*Credit for this example goes to Prof. Steven Jacques.

Both absorption and scattering are probabilistic statements since every time a photon interacts with a piece of the medium, there is some chance that it will be absorbed, scattered, or neither. This is probabilistic because these events are associated with chance or probability, like when flipping a coin or rolling a dice. Since these interactions happen billions of times within the medium, the average behavior of the photons becomes rather predictable. In the coin-flipping analogy, this is the same as saying that if you flip a coin billions of times, we can predict that very close to half those times, it will come up heads. An example of this predictable average distribution of the photons can be seen in Fig. 1. This is, in some ways, amazing since we have started with random events and can draw predictable conclusions. Focusing on diffusion theory, a theory that describes an optically diffuse medium, this average behavior can be modeled using two optical properties that are associated with the absorption probability and probability of scatter in a random direction. These properties are named the absorption coefficient (μa) and the reduced scattering coefficient (μs').

Fig. 2: [Top] The average length of a path before a photon is absorbed (1/μa) versus optical wavelength (λ) in biological tissue. Long path-lengths allow for deeper light penetration, these regions are so-called optical windows and are shown in green. [Bottom] The typical absorption coefficienta) versus λ for typical biological chromophores (i.e. absorbers).

FD-NIRS essentially seeks to measure these two properties, the μa, and the μs', to describe a diffuse medium. In general, the absorption coefficient provides chemical information about the medium, like the strength of the coffee in the above example, and μs' provides structural information, like the number of fat droplets from cream in the coffee. A popular application of NIRS is in the measurement of biological tissues. In this case, μa may give us information about concentrations of blood. The μa of blood depends on the optical wavelength (λ), which can be thought of as the color of the light. A typical dependence of μa on λ is shown in Fig. 2. NIRS is called Near-InfraRed Spectroscopy because the technique focuses on a range of colors or λ starting from red and going to near-infrared,** with the former being visible by the human eye and the latter not. The reason for this choice of λ is that biological tissue tends to have lower absorption in this range; thus, photons can probe further into tissue. In fact, Fig. 2 shows the average path before absorption versus λ to show this so-called optical window of tissue. 

**This near-infrared optical wavelength (λ) range is approximately 600 nm to 1000 nm.

Now let us consider how NIRS measurements are physically done. In the most basic sense, some source of light is used to inject*** photons into a medium, then that light is detected at some other point at some source-detector distance (ρ).**** The way the source light varies in time describes the flavor of NIRS. This is either Continuous-Wave (CW), FD, or Time-Domain (TD). In the case of CW, the source light does not change with time; for FD, the brightness or intensity of the light oscillates as a sinusoidal wave,***** and finally, TD uses a source with a brief pulse of light. Focusing only on the interpretation of FD, the detected light will have some oscillation amplitude (i.e., Intensity (I)) and some time shift which is called its phase (φ) shift. This provides two pieces of information about the behavior of light within the medium which then may be translated into the two desired properties, the μa and the μs'. 

***By inject, we simply mean that photons are made to enter the medium; this can be as simple as shining a light at the optical medium.

****Source-detector distance (ρ) is typically on the order of 10 mm.

*****The modulation frequency is on the order of 100 MHz for FD.

As mentioned above, a notable application of diffuse optics and NIRS is on biological tissues [Fantini 2020, Bigio 2016, Scholkmann 2014]. However, diffuse optics finds a variety of applications in several other fields of study. In food science [Ozaki 2006], it may be applied for inspection [Johnson 2020] or evaluation [Kademi 2019]. In pharmaceutical manufacturing, diffuse optics may join other process analytical technologies, for example, to analyze and characterize particles [Razuc 2019] or powders [Stranzinger 2021]. A few other examples include archaeological soil analysis [Trant 2020], dendrology (study of wood) [Tsuchikawa 2015], and art authentication [Chen 2017]. In the study of biological tissue, diffuse optics finds applications in basic research, medical diagnostics, and physiological monitoring. Examples include clinical brain monitoring [Lange 2019], the study of brain activation [Agbangla 2017], breast imaging [Grosenick 2016], and muscle measurements in sports science [Perrey 2018]. This is by no means an exhaustive list of the possible applications of NIRS and diffuse optics.

Regardless of the application, a laboratory can purchase a commercially available FD-NIRS instrument for their research. These instruments provide FD measurements at multiple discrete λs and retrieve the I and φ of the detected FD light. Therefore, they can be used either for absolute measurement of optical properties μa and μs' or dynamic measurements of μa, which are interpreted as hemodynamics.


Fig. 3: Example of Frequency-Domain Near-InfraRed Spectroscopy (FD-NIRS) applied to the human brain. Temporal profile of source light in red and of detected light in blue.Symbols: Phase (φ), angular modulation frequency (ω), source Intensity (I), & detected Reflectance (R)

We conclude this introduction with a specific example of an FD-NIRS experiment applied to the human brain. When a person experiences some visual stimulus, it is expected that the visual portion of their brain will begin to utilize more oxygen. This causes the body to increase Blood-Flow (BF) to the visual cortex and so that more oxygen may be supplied there. An increase in BF is indicated by an increase in the concentration of Oxy-hemoglobin (O) and a decrease in the concentration of Deoxy-hemoglobin (D). Since these concentrations are connected to μa by Fig. 2, one may measure this change using FD-NIRS. Therefore, an experiment may be devised to make these so-called functional NIRS (fNIRS) measurements, as shown in Fig. 3. Here, sinusoidal light is injected into the subject's head, where it diffuses through the brain before being detected. The detected light's phase shift and amplitude are measured and may be converted to optical properties and blood concentrations. Through analysis, the changes in O and D may indicate BF and, thus, brain activity. This example is just one application in which FD-NIRS may be used to make measurements on tissue. The following dissertation will discuss details on how to collect and analyze these FD-NIRS data, including the case of this example experiment, as well as various other experiments and applications.