Near-infrared window in biological tissue
The near-infrared (NIR) window (also known as optical window or therapeutic window) defines the range of wavelengths from 650 to 1350 nanometre (nm) where light has its maximum depth of penetration in tissue. Within the NIR window, scattering is the most dominant light-tissue interaction, and therefore the propagating light becomes diffused rapidly. Since scattering increases the distance travelled by photons within tissue, the probability of photon absorption also increases. Because scattering has weak dependence on wavelength, the NIR window is primarily limited by the light absorption of blood at short wavelengths and  water at long wavelengths. The technique using this window is called NIRS. Medical imaging techniques such as fluorescence image-guided surgery often make use of the NIR window to detect deep structures. Absorption properties of tissue components. The absorption coefficient (formula_1) is defined as the probability of photon absorption in tissue per unit path length. Different tissue components have different formula_2 values. Moreover, formula_2 is a function of wavelength. Discussed below are the absorption properties of the most important chromophores in tissue. The molar extinction coefficient (formula_4) is another parameter that is used to describe photon absorption in tissue. By  multiplying formula_4 by the molar concentration and by ln(10), one can convert formula_4 to formula_7. Blood. Blood consists of two different types of hemoglobin: oxyhemoglobin (formula_8) is bound to oxygen, while deoxyhemoglobin (formula_9) is unbound to oxygen. These two different types of hemoglobin exhibit different absorption spectra that are normally represented in terms of molar extinction coefficients, as shown in Figure 1. The molar extinction coefficient of Hb has its highest absorption peak at 420 nm and a second peak at 580 nm. Its spectrum then gradually decreases as light wavelength increases. On the other hand, formula_10 shows its highest  absorption peak at 410 nm, and two secondary peaks at 550 nm and 600 nm. As light wavelengths passes 600 nm, formula_8 absorption decays much faster than Hb absorption. The points where the molar extinction coefficient spectra of formula_9 and formula_8 intersect are called isosbestic points. By using two different wavelengths, it is possible to calculate the concentrations of oxyhemoglobin (formula_14) and deoxyhemoglobin (formula_15) as shown in the following equations: Here, formula_18 and formula_19 are the two wavelengths; formula_20 and formula_21 are the molar extinction coefficients of formula_8 and formula_9, respectively; formula_14 and formula_15 are the molar concentrations of formula_8  and formula_9 in tissue, respectively. Oxygen saturation (formula_28) can then be computed as Water. Although water is nearly transparent in the range of visible light, it becomes absorbing over the near-infrared region. Water is a critical component since its concentration is high in human tissue. The absorption spectrum of water in the range from 250 to 1000 nm is shown in Figure 2. Although absorption is rather low in this spectral range, it still contributes to the overall attenuation of tissue. Other tissue components with less significant contributions to the total absorption spectrum of tissue are melanin and fat . Melanin. Melanin is a chromophore that exists in the human epidermal layer of skin responsible for protection from harmful UV radiation. When melanocytes are stimulated by solar radiation, melanin is produced. Melanin is one of the major absorbers of light in some biological tissue (although its contribution is smaller than other components). There are two types of melanin: eumelanin which is black-brown and pheomelanin which is red-yellow. The molar extinction coefficient spectra corresponding to both types are shown in Figure 3. Fat. Fat is one of the major components in tissue that can comprise 10-40% of tissue . Although not many mammalian fat spectra are available, Figure 4 shows an example extracted from pig fat. Scattering properties of tissue components. Optical scattering occurs due to mismatches in refractive index of the different tissue components, ranging from cell membranes to whole cells. Cell nuclei and mitochondria are the most important scatterers. Their dimensions range from 100 nm to 6 μm, and thus fall within the NIR window. Most of these organelles fall in the Mie regime, and exhibit highly anisotropic forward-directed scattering. Light scattering in biological tissue is denoted by the scattering coefficient (formula_30), which is defined as  the probability of photon scattering in tissue per unit path length. Figure 5 shows a plot of the scattering spectrum. Effective attenuation coefficient. Attenuation of light in deep biological tissue depends on the effective attenuation coefficient (formula_31), which is defined as where formula_33 is the transport scattering coefficient defined as where formula_35 is the anisotropy of biological tissue, which has a representative value of 0.9. Figure 5 shows a plot of transport scattering coefficient spectrum in breast tissue, which has a wavelength dependence of formula_36. The effective attenuation coefficient is the dominant factor for determining light attenuation at depth formula_37  ≫ 1/ formula_38. Estimation of the NIR window in tissue. The NIR window can be computed based on the absorption coefficient spectrum or the effective attenuation coefficient spectrum. A possible criterion for selecting the NIR window is given by the FWHM of the inverse of these spectra as shown in Figure 7. In addition to the total concentration of hemoglobin, the oxygen saturation will define the concentration of oxy and deoxyhemoglobin in tissue and so the total absorption spectrum. Depending on the type of tissue, we can consider different situations. Below, the total concentration of hemoglobin is assumed to be  2.3 mM. Absorption spectrum for arteries. In this case formula_39 ≈ 98% (arterial oxygen saturation). Then oxyhemoglobin will be dominant in the total absorption (black) and the effective attenuation (magenta) coefficient spectra, as shown in Figure 6 (a). Absorption spectrum for veins. In this case formula_40 ≈ 60% (venous oxygen saturation). Then oxyhemoglobin and deoxyhemoglobin will have similar contributions to the total absorption (black) and the effective attenuation (magenta) coefficient spectra, as shown in Figure 6 (b). Absorption spectrum for breast tissue. To define formula_41 (tissue oxygen saturation) (or formula_42 (tissue saturation index)), it is necessary to define a distribution  of arteries and veins in tissue. an arterial-venous blood volume ratio of 20%/80% can be adopted. Thus tissue oxygen saturation can be defined as formula_41 = 0.2 x formula_39 + 0.8 x formula_40 ≈ 70%. The total absorption (black) and the effective attenuation (magenta) coefficient spectra for breast tissue is shown in Figure 6 (c). In addition, the effective penetration depth is plotted in Figure 7.