Near-infrared window in biological tissue

Ange of wavelengths from 650 to nanometre

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The near-infrared (NIR) window (also known as optical window or therapeutic window) defines the range of wavelengths from 650 to nanometre (nm) where light has its maximum depth of penetration in tissue.[1] 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

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The absorption coefficient ( μ a {\displaystyle \mu _{a}} ) is defined as the probability of photon absorption in tissue per unit path length.[2] Different tissue components have different μ a {\displaystyle \mu _{a}} values. Moreover, μ a {\displaystyle \mu _{a}} is a function of wavelength. Discussed below are the absorption properties of the most important chromophores in tissue. The molar extinction coefficient ( ε {\displaystyle \varepsilon \,} ) is another parameter that is used to describe photon absorption in tissue. By multiplying ε {\displaystyle \varepsilon \,} by the molar concentration and by ln(10), one can convert ε {\displaystyle \varepsilon \,} to μ a {\displaystyle \mu _{a}\,} .

Figure 1: The molar extinction coefficients of HbO2 and Hb.[3]

Blood

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Blood consists of two different types of hemoglobin: oxyhemoglobin ( H b O 2 {\displaystyle HbO_{2}} ) is bound to oxygen, while deoxyhemoglobin ( H b {\displaystyle Hb} ) 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, H b O 2 {\displaystyle HbO2} shows its highest absorption peak at 410 nm, and two secondary peaks at 550 nm and 600 nm. As light wavelengths passes 600 nm, H b O 2 {\displaystyle HbO_{2}} absorption decays much faster than Hb absorption. The points where the molar extinction coefficient spectra of H b {\displaystyle Hb} and H b O 2 {\displaystyle HbO_{2}} intersect are called isosbestic points.

By using two different wavelengths, it is possible to calculate the concentrations of oxyhemoglobin ( C H b O 2 {\displaystyle C_{HbO2}} ) and deoxyhemoglobin ( C H b {\displaystyle C_{Hb}} ) as shown in the following equations:

μ a ( λ 1 ) = ln &#; ( 10 ) ε H b O 2 ( λ 1 ) C H b O 2 + ln &#; ( 10 ) ε H b ( λ 1 ) C H b {\displaystyle \mu _{a}(\lambda _{1})=\ln(10)\varepsilon _{HbO2}(\lambda _{1})C_{HbO2}+\ln(10)\varepsilon _{Hb}(\lambda _{1})C_{Hb}\,}

μ a ( λ 2 ) = ln &#; ( 10 ) ε H b O 2 ( λ 2 ) C H b O 2 + ln &#; ( 10 ) ε H b ( λ 2 ) C H b {\displaystyle \mu _{a}(\lambda _{2})=\ln(10)\varepsilon _{HbO2}(\lambda _{2})C_{HbO2}+\ln(10)\varepsilon _{Hb}(\lambda _{2})C_{Hb}\,}

Figure 2: The absorption spectrum of water.[4]

Here, λ 1 {\displaystyle \lambda _{1}} and λ 2 {\displaystyle \lambda _{2}} are the two wavelengths; ε H b O 2 {\displaystyle \varepsilon _{HbO2}} and ε H b {\displaystyle \varepsilon _{Hb}} are the molar extinction coefficients of H b O 2 {\displaystyle HbO_{2}} and H b {\displaystyle Hb} , respectively; C H b O 2 {\displaystyle C_{HbO2}} and C H b {\displaystyle C_{Hb}} are the molar concentrations of H b O 2 {\displaystyle HbO_{2}} and H b {\displaystyle Hb} in tissue, respectively. Oxygen saturation ( S O 2 {\displaystyle SO_{2}} ) can then be computed as

S O 2 = C H b O 2 C H b + C H b O 2 {\displaystyle SO_{2}={\frac {C_{HbO2}}{C_{Hb}+C_{HbO2}}}}

Water

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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  nm is shown in Figure 2. Although absorption is rather low in this spectral range, it still contributes to the overall attenuation of tissue.

Figure 3: The molar extinction coefficients of eumelanin and pheomelanin.[5]

Other tissue components with less significant contributions to the total absorption spectrum of tissue are melanin and fat.

Figure 4: The absorption coefficient spectrum of fat.[6]

Melanin

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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.[7] 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.[8] The molar extinction coefficient spectra corresponding to both types are shown in Figure 3.

Fat

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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.[9]

Figure 5: The scattering coefficient spectrum of biological tissue.[10]

Scattering properties of tissue components

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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.[11] Their dimensions range from 100 nm to 6 μm, and thus fall within the NIR window. Most of these organelles fall in the Mie scattering regime, and exhibit highly anisotropic forward-directed scattering.[12]

Light scattering in biological tissue is denoted by the scattering coefficient ( μ s {\displaystyle \mu _{s}} ), which is defined as the probability of photon scattering in tissue per unit path length.[13] Figure 5 shows a plot of the scattering spectrum.[14]

Effective attenuation coefficient

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Attenuation of light in deep biological tissue depends on the effective attenuation coefficient ( μ e f f {\displaystyle \mu _{eff}} ), which is defined as

μ eff = 3 μ a ( μ a + μ s &#; ) {\displaystyle \mu _{\text{eff}}={\sqrt {3\mu _{a}(\mu _{a}+\mu '_{s})}}}

where μ s &#; {\displaystyle \mu '_{s}} is the transport scattering coefficient defined as

μ s &#; = μ s ( 1 &#; g ) {\displaystyle \mu '_{\text{s}}=\mu _{s}(1-g)\,}

where g {\displaystyle g} 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 λ &#; 0.7 {\displaystyle \lambda \,^{-0.7}} .[15] The effective attenuation coefficient is the dominant factor for determining light attenuation at depth d {\displaystyle d} &#; 1/ μ eff {\displaystyle \mu _{\text{eff}}} .

Estimation

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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.

Figure 6 (a): Spectra for arteries (SaO2 &#; 98%).

Spectra for arteries (SaO&#; 98%).

Absorption coefficient: λmin = 686 nm; NIR window = (634&#;756) nm.

Effective attenuation coefficient: λmin = 690 nm; NIR window = (618&#;926) nm.

Effective attenuation coefficient: λ= 690 nm;= (618&#;926) nm.

Figure 6 (b): Spectra for veins (SvO2 &#; 60%).

Spectra for veins (SvO&#; 60%).

Absorption coefficient: λmin = 730 nm; NIR window = (664&#;932) nm.

Effective attenuation coefficient: λmin = 730 nm; NIR window = (630&#;) nm.

Effective attenuation coefficient: λ= 730 nm;= (630&#;) nm.

Figure 6 (c): Spectra for breast tissue (StO2 &#; 70%).

Spectra for breast tissue (StO&#; 70%).

Absorption coefficient: λmin = 730 nm; NIR window = (656&#;916) nm.

Effective attenuation coefficient: λmin = 730 nm; NIR window = (626&#;) nm.

Effective attenuation coefficient: λ= 730 nm;= (626&#;) nm.

Absorption spectrum for arteries

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In this case S a O 2 {\displaystyle SaO_{2}\,} &#; 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). 'cite: Anisotropic diffusion filter for dorsal hand vein features extraction &#; Sarah Hachemi Benziane, Abdelkader Benyettou'

Absorption spectrum for veins

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In this case S v O 2 {\displaystyle SvO_{2}\,} &#; 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).

Figure 7: : Effective penetration depth in breast tissue (StO2 &#; 70%). Effective attenuation coefficient: λmin = 730 nm; NIR window = (626&#;) nm.

Absorption spectrum for breast tissue

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To define S t O 2 {\displaystyle StO_{2}\,} (tissue oxygen saturation) (or T S I {\displaystyle TSI\,} (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.[16] Thus tissue oxygen saturation can be defined as S t O 2 {\displaystyle StO_{2}\,} = 0.2 x S a O 2 {\displaystyle SaO_{2}\,} + 0.8 x S v O 2 {\displaystyle SvO_{2}\,} &#; 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.

See also

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References

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1 - 15 of Optical Windows

What is an Optical Window?

Optical Windows are flat, optically transparent plates that are typically designed to maximize transmission in a specified wavelength range while minimizing reflection and absorption. They are often used to protect optical systems and electronic sensors from an outside environment. Because windows introduce no optical power into a system, windows should be selected based on the material transmission properties, optical surface specifications, and mechanical properties that match your application.

An optical window is an optical element that is transparent to a range of wavelengths, and that has no optical power. Windows may be flat or curved. They are used to block the flow of air or other fluids while allowing light to pass into or out of an optical system.

There are three optical windows as mentioned in the figure below 1st is at the 850 nm optical window, second is at nm, and lastly at nm. Optical window play a significant role in the design of optical system like in the above diagram the signal attenuation in the first optical window is different from the second and 3rd. for the 1st optical window the signal attenuation is 4 dB/km. However, at 2nd window the attenuation is only 0.5 dB/km and at the 3rd optical window the attenuation is only 0.2 dB/km, as seen from the curve. And therefore, for long distance communication the selection of optical window is very important. Also, optical window material has to be transparent to a wavelength range of interest but not necessarily to visible light. It is mechanically flat and sometimes it also is optically flat, depending on resolution requirements. An optical window is commonly parallel and is likely to be anti-reflection coated, especially if it is designed for visible light. An optical window may be built into a piece of equipment such as a vacuum chamber to allow optical instruments to view inside that equipment.

Material Properties

Material properties including the transmission, refractive index, and hardness of the window substrate can be critical for deciding which window is the best choice for the application. In optics, the refractive index or refraction index of an optical medium is a dimensionless number that indicates the light-bending ability of that medium. The figure below highlights the transmission regions of the different materials of optical windows.

Several other key properties for selecting the appropriate window for your application include the Abbe number, density, and coefficient of thermal expansion. The selection guide below lists the optical, mechanical, and thermal properties of our available window substrates as well as their size and thickness ranges.

Material

Index of Refraction

(nd)

Abbe Number

(vd)

Density

[g/cm3]

Coefficient of Thermal Expansion

[μm/moC]

Softening Temp

[oC]

Knoop Hardness

Size Range

Thickness Range

B270

1.523

58.5

2.55

8.2

533

542

5 - 75 x 75mm

1.0 - 3.0mm

Barium Fluoride (BaF2)

1.48

81.61

4.89

18.1

800

82

5 - 50mm

1.0 - 3.0mm

BOROFLOAT

1.472

65.7

2.20

3.25

820

480

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5 &#; 200 mm

1.75 - 6.5 mm

Calcium Fluoride (CaF2)

1.434

95.1

3.18

18.85

800

158.3

5 - 50mm

1.0 - 3.0mm

Germanium (Ge)

4.003

N/A

5.33

6.1

936

780

10 - 75mm

1.0 - 5.0mm

Gorilla Glass

1.509

N/A

2.44

7.88

843

5 - 200 x 200 mm

1.1mm

Magnesium Fluoride (MgF2)

1.413

106.2     

3.18

13.7

415

5 &#; 50 mm

1.0 - 3.0 mm

N-BK7    

1.517

64.2

2.46

7.1

557

610

5 - 75 x 75 mm

0.2 - 4.0 mm

Potassium Bromide (KBr)

1.527

33.6

2.75

43

730

7

13 &#; 50 mm

1.0 - 5.0 mm

Sapphire

1.768

72.2

3.97

5.3

2.5 &#; 75 mm

0.5 - 3.2 mm

Silicon (Si)

3.422

N/A

2.33

2.55

10 &#; 50 mm

1.0 - 3.0 mm

Sodium Chloride (NaCl)

1.491

42.9

2.17

44

801

18.2

13 &#; 50 mm

1.0 - 5.0 mm

UV Fused Silica

1.458

67.80

2.20

0.55

500

5 - 50 x 50 mm

1.0 - 5.0 mm

Zinc Selenide (ZnSe)

2.403

N/A

5.27

7.1

250

120

10 &#; 75 mm

1.0 - 6.0 mm

Refractive Index

The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in an optical medium, which describes how light slows down as it passes through the material. The refractive index for optical glasses (nd) is specified at the Helium d-line wavelength of 587.6 nm. Glasses with a low index of refraction are commonly referred to as crowns and glasses with a high index of refraction are referred to as flints.

Abbe Number

The Abbe number (vd) describes the material&#;s dispersion, or variation of the refractive index with wavelength. It is defined as

(nd-1) / (nf-nc)

Where, nF and nC are the refractive indices at 486.1nm (Hydrogen f-line) and 656.3nm (Hydrogen c-line), respectively. Low Abbe numbers indicate high dispersion. Crown glasses tend to have higher Abbe numbers than flints.

Density

The density of glass is important to consider because it helps determine the weight of the optical assembly, which is critical for weight-sensitive applications. Generally, the refractive index of a glass increases as the density increases. However, the relationship between refractive index and density is not linear.

Coefficient of Thermal Expansion

The coefficient of thermal expansion describes how the size of the glass will change with temperature changes. This property is a key factor in applications involving extreme temperatures and quick temperature differentials.

Koop Hardness

The Knoop hardness of a glass is a measure of its resistance to indentation i.e, a shallow hole or cut in the surface or edge of a glass. It is determined by using a fixed force with a given indenter and measuring the depth of the resulting indentation. The smaller the indentation, the higher the Knoop hardness. In general, materials with a high Knoop hardness are less brittle and can withstand greater pressure differentials than materials with a smaller Knoop hardness.

Optical Surface Specifications

The surface specifications of optical windows affect the optical performance and must be considered when selecting or specifying a window. It is important to make sure your optical window has the appropriate specifications to tightness to meet your application requirements, but over-tolerancing the window will unnecessarily increase the cost.

Surface Quality

The surface quality of an optical window is an evaluation of surface imperfections that may be caused during manufacturing or handling. These defects typically cause small reductions in throughput and small increases in scattered light, which have little to no adverse effect on the overall system performance in most imaging or light-gathering applications. However, some surfaces are more sensitive to these defects, such as surfaces at image planes, because surface defects are in focus. Windows with high power levels are also sensitive to surface defects because they can cause increased absorption of energy and damage the window.

Surface quality is often described by the scratch-dig specification in the U.S. Standard MIL-PRF-B. The scratch designation is determined by comparing the scratches on a surface to a set of standard scratches under controlled lighting conditions. This is not a direct measurement of the scratch dimensions themselves. On the other hand, the dig designation directly relates to the size of the dig. The dig designation is calculated by taking the diameter of the dig in microns and dividing it by 10.

Surface Flatness

Surface flatness measures the deviation of the window from a perfectly flat surface. The surface flatness of a test piece can be measured using an optical flat, which is a highly precise flat reference surface. When the surface of the test window is placed against the optical flat, fringes appear whose shape dictates the surface flatness of the window under inspection. The window&#;s surface is at least as flat as the reference flat if the fringes are evenly spaced, straight, and parallel. If the fringes are curved, the flatness error is indicated by the number of fringes between two imaginary lines: one tangent to the center of a fringe and one through the ends of that same fringe. Deviations in flatness are typically measured in values of waves (λ), or multiples of the testing light source&#;s wavelength. Every fringe corresponds to half of a wave. 1λ flatness can be used for typical applications, but high-precision applications such as high-power laser systems require flatness values down to λ/20. The diagram below demonstrates how an optical flat works.

Surface flatness is increasingly important when using a window at a viewing angle besides normal incidence. 

Transmitted Wavefront Error

Surface errors, refractive index inhomogeneity, and stress on the window can induce transmitted wavefront errors. This distortion of the transmitted wavefront causes degradation of image quality in image-forming systems and other performance losses in non-imaging systems. Transmitted wavefront error can be reduced by properly mounting the window and avoiding putting unnecessary stress on it. Transmitted wavefront error, along with surface flatness, describes the overall quality and surface characteristics of the window. To learn more about different types of wavefront errors, or optical aberrations, visit our Comparison of Optical Aberrations application note.

Anti-Reflection (AR) Coatings

Anti-reflection (AR) coatings are often put on optical windows to maximize transmission in the desired wavelength range. Most AR coatings are also very durable, with resistance to both physical and environmental damage. For these reasons, the vast majority of transmissive optics include some form of anti-reflection coating. When specifying an AR coating for your specific application, you must first be fully aware of the full spectral range of your system. While an AR coating can significantly improve the performance of an optical system, using the coating at wavelengths outside the design wavelength range could potentially decrease the performance of the system. The figure below shows the reflection plots of all the standard AR coatings we offer.

 Equivalent Glass Types

Many glass manufacturers offer the same material characteristics under different trade names and most have modified their products and processes to be ECO-friendly, the inclusion of ECO glasses differs by manufacturer. Once an item has been switched to ECO glass, Non-ECO-friendly glasses will not be utilized again. Based on availability, we reserve the right to substitute an equivalent ECO glass in our production runs. The table below shows the glass equivalents for common optical glasses.

In spectroscopy

Optical windows used for UV/VIS spectroscopy, are usually made from glass or fused silica. In IR spectroscopy, there is a wide range of materials that transmit light into the far infrared and can be utilized for the construction of optical windows, from barium fluoride (BaF2), calcium fluoride, potassium bromide, potassium chloride, sodium chloride, germanium (Ge), zinc selenide (ZnSe) and sapphire. These windows are either built into circular, elliptical, or rectangular configurations.

Applications

They are often used for isolating optical systems or components against detrimental influences from the environment. For example, most photodiodes and other kinds of photodetectors often contain an optical window above their light-sensitive area to protect it against dirt, corrosive influences, and mechanical damage. Similarly, the housings of lasers are often protected with optical windows to keep the housing free of any dust.

For the active tubes of gas lasers likehelium&#;neon lasers, optical windows are separating the inside low-pressure gas volume from the outside atmosphere. Similarly, windows are needed for multipass gas cells as used in spectroscopy. If such windows are not rigidly connected, one may require some suitable type of seals to get a housing reliably air-tight. There are special vacuum windows built into vacuum viewports, coming together with suitable seals and mounting parts.

Common optical materials used for optical windows are glasses like fused silica and BK7 for visible or near-infrared light. For infrared optics at longer wavelengths, one also uses various types of crystalline materials such as calcium fluoride, also semiconductors like zinc selenide, silicon, and germanium. Particularly for low-cost mass applications, some polymer materials are also often used, e.g. PMMA acrylic. They may be equipped with anti-scratch coatings for making them more resistant.

In some cases, an optical element such as a lens or a mirror can at the same time fulfill the function of an optical window, so no separate part is required for that. Note, however, that a separate optical window may be advantageous in rough environments, since it is both easier and cheaper to exchange it, compared with exchanging a high-quality optical element.

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