Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

A technique to measure temperature near a small heat source within a medium is required in many scientific research fields and applications. For example, in the research on magnetic hyperthermia, which is a cancer therapy method using electromagnetic induction of magnetic particles, or small magnetic pieces, it is critical to accurately predict the temperature distributions generated by the magnetic particles^1,2. However, although microwave^3,4, ultrasound^5,6,7,8, optoacoustic⁹, Raman¹⁰, and magnetic resonance^11,12-based temperature measurement techniques have been researched and developed, such an inner temperature distribution cannot be accurately measured at present. Thus far, single-position temperatures or temperatures at a few positions have been measured via temperature sensors, which, in the case of induction heating, are non-magnetic optical fiber temperature sensors^13,14. Alternatively, the surface temperatures of media have been remotely measured via infrared radiation thermometers to estimate the inner temperatures¹⁴. However, when a medium containing a small heat source is a water layer or a non-turbid aqueous medium, we have demonstrated that a near-infrared (NIR) absorption technique is useful to measure the temperatures^{15,16,17,18,19}. This paper presents the detailed protocol of this technique and representative results.

The NIR absorption technique is based on the principle of temperature dependence of the absorption bands of water in the NIR region. As is shown in Figure 1a, the ν₁ + ν₂ + ν₃ absorption band of water is observed in the 1100-nm to 1250-nm wavelength (λ) range and shifts to shorter wavelengths as the temperature increases¹⁹. Here, ν₁ + ν₂ + ν₃ means that this band corresponds to the combination of the three fundamental O-H vibration modes: symmetric stretching (ν₁), bending (ν₂), and antisymmetric stretching (ν₃)^20,21. This change in the spectrum indicates that the most temperature-sensitive wavelength in the band is λ ≈ 1150 nm. Other absorption bands of water also exhibit similar behavior with respect to the temperature^{15,16,17,18,20,21}. The ν₁ + ν₃ band of water observed within the range λ = 1350−1500 nm and its temperature dependence are shown in Figure 1b. In the ν₁ + ν₃ band of water, 1412 nm is the most temperature-sensitive wavelength. Thus, it is possible to obtain two-dimensional (2D) temperature images by using an NIR camera to capture 2D absorbance images at λ = 1150 or 1412 nm. As the absorption coefficient of water at λ = 1150 nm is smaller than that at λ = 1412 nm, the former wavelength is suitable for approximately 10-mm-thick aqueous media, while the latter is suitable for approximately 1-mm-thick ones. Recently, using λ = 1150 nm, we obtained the temperature distributions in a 10-mm-thick water layer containing an induction-heated 1-mm-diameter steel sphere¹⁹. Moreover, the temperature distributions in a 0.5-mm-thick water layer have been measured by using λ = 1412 nm^15,17.

An advantage to the NIR-based temperature imaging technique is that it is simple to setup and implement because it is a transmission-absorption measurement technique and needs no fluorophore, phosphor, or other thermal probe. In addition, its temperature resolution is less than 0.2 K^15,17,19. Such a good temperature resolution cannot be achieved by other transmission techniques based on interferometry, which have often been used in heat and mass transfer studies^22,23,24. We note, however, that the NIR-based temperature imaging technique is not suitable in cases with considerable local temperature change, because the deflection of light caused by the large temperature gradient becomes dominant¹⁹. This matter is referred in this paper in terms of practical use.

This paper describes the experimental setup and procedure for the NIR-based temperature imaging technique for a small magnetic sphere heated via induction; additionally, it presents the results of two representative 2D absorbance images. One image is of a 2.0-mm-diameter steel sphere in a 10.0-mm-thick water layer that is captured at λ = 1150 nm. The second image is of a 0.5-mm-diameter steel sphere in a 2.0-mm-thick maltose syrup layer that is captured at λ = 1412 nm. This paper also presents the calculation method and results of the three-dimensional (3D) radial distribution of temperature by applying the inverse Abel transform (IAT) to the 2D absorbance images. The IAT is valid when a 3D temperature distribution is assumed to be spherically symmetric as in the case of a heated sphere (Figure 2)¹⁹. For the IAT calculation, a multi-Gaussian function fitting method is employed here, because the IATs of Gaussian functions can be obtained analytically^{25,26,27,28,29} and fit well to monotonically decreasing data; this includes experiments employing thermal conduction from a single heat source.