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

Summary

A technique utilizing wavelengths of 1150 and 1412 nm to measure the temperature of water surrounding an induction-heated small magnetic sphere is presented.

Abstract

A technique to measure the temperature of water and non-turbid aqueous media surrounding an induction-heated small magnetic sphere is presented. This technique utilizes wavelengths of 1150 and 1412 nm, at which the absorption coefficient of water is dependent on temperature. Water or a non-turbid aqueous gel containing a 2.0-mm- or 0.5-mm-diameter magnetic sphere is irradiated with 1150 nm or 1412 nm incident light, as selected using a narrow bandpass filter; additionally, two-dimensional absorbance images, which are the transverse projections of the absorption coefficient, are acquired via a near-infrared camera. When the three-dimensional distributions of temperature can be assumed to be spherically symmetric, they are estimated by applying inverse Abel transforms to the absorbance profiles. The temperatures were observed to consistently change according to time and the induction heating power.

Introduction

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.

Protocol

1. Experimental Setup and Procedures

Prepare an optical rail to mount a sample and optics for NIR imaging as follows.

1. Sample preparation.
   Note: When using water or aqueous liquid, do Step 1.1.1. When using an aqueous gel with high viscosity, do Step 1.1.2.
   1. Steel sphere setting in water.
      1. Fix a 2.0-mm-diameter steel sphere to the end of a thin plastic string using a small amount of glue.
      2. Hang the steel sphere at the center of the rectangular glass cell with an optical path length of 10.0 mm, a width of 10 mm, and a height of 45 mm (Figure 3).
      3. Pour filtered water into the cell carefully so as not to produce air bubbles.
         ​NOTE: A steel sphere can also be fixed to the tip of a thin plastic rod with a small amount of glue¹⁹.
   2. Steel sphere setting in aqueous gel.
      1. Heat an aqueous gel to reduce its viscosity such that it is low enough to be poured smoothly.
      2. Using a syringe, pour the aqueous gel into a rectangular glass cell with an optical path length of 2.0 mm, a width of 10 mm, and a height of 45 mm to half-full and leave it to cool.
      3. Place a 0.5-mm-diameter steel sphere in the center of the gel surface.
      4. Fill the cell with the aqueous gel.
         NOTE: Larger spheres (>~1 mm dia.) should not be used with a gel because they will move by gravitational and/or magnetic forces during induction heating.
   3. Set the cell in a plastic holder and mount it on the optical rail (Figure 3).
2. Preparation of NIR imaging system.
   1. Prepare a halogen lamp with a fiber light guide, and fix the end of the fiber light guide with a holder on the optical rail.
   2. Place a narrow bandpass filter (NBPF) with a transmittance peak at λ = 1150 nm or λ = 1412 nm between the fiber light guide and the cell (Figure 3).
   3. Interpose another bandpass filter (BPF), whose transmission wavelength range is wider than that of the NBPF, between the halogen lamp and the NBPF.
      NOTE: The BPF is needed to prevent thermal damage to the NBPF because it receives light directly.
   4. Interpose an iris diaphragm(s) in the light path between the NBPF and cell holder to reduce the stray light (Figure 3).
   5. Set up an NIR camera to detect the light transmitted through the cell (Figure 3). Connect the camera through a data transfer cable to a graphic board installed in a personal computer (PC) with image acquisition software.
   6. Set a telecentric lens between the cell and camera (Figure 3).
      NOTE: A common camera lens can also be used. However, a telecentric lens is better in terms of the selective detection of the light parallel to the chief ray for the IAT and reduction of the influence of diffraction.
      NOTE: The NBPF and BPF should not be placed between the cell and camera because, in doing so, the water temperature would increase via direct absorption of high-intensity light from the halogen lamp.
   7. Turn on the NIR camera and launch the image acquisition software.
   8. Light the halogen lamp and adjust its output power observing the image displayed on the monitor (Figure 4).
   9. Adjust the axis, position, and focus of the telecentric lens to obtain a fine image of the steel sphere.
      NOTE: If the adjustment is not complete, irregular intensity patterns will appear, leading to incorrect absorbances.
3. Preparation of induction heating system.
   1. Prepare an induction heating system consisting of a high-frequency generator (maximum output power: 5.6 kW; frequency: 780 kHz), water-cooled coil, and water chiller.
      NOTE: An induction heating system for brazing, welding, and soldering small metal parts is appropriate for this purpose; see Table of Materials.
   2. If possible, mount the coil on an XYZ movable stage to change its position.
   3. Place the coil near the cell such that the distance between the coil center and the steel sphere is approximately 15 mm (Figure 3). Ensure that there are no other metal parts near the coil.
      NOTE: The distance should be adjusted depending on the induction heating power and the sphere size.
   4. Circulate water for cooling.
4. Image acquisition and induction heating.
   1. Click "start" on the image acquisition software to store the images sequentially.
   2. Click "start" on the induction heating control software to commence the induction heating.
   3. After several seconds (depending on the conditions and purpose), click "stop" on the image acquisition software.
   4. Click "stop" on the induction heating control software.
   5. Save the temporally-stored images as a TIFF sequence (or other non-compressed format) on the image acquisition software.
      NOTE: If the temperature is high enough, the effect of light deflection will appear on the image⁷. The induction heating power must be decreased appropriately though experiments such that the increase in the temperature near the sphere is less than approximately 10 K, which can be confirmed in the following protocol steps for temperature estimation.

2. Image Processing and Temperature Estimation

Note: The saved sequential images are represented as I_i(x, z), where i is the sequential frame number. The coordinates, x, y, z, r, and r' are defined as are indicated in Figure 2; z is positive in the direction opposite to gravity. The outline of the following protocol steps is also illustrated in Supplement 1.

1. Absorbance image construction.
   1. Open I_i(x, z) with the image processing software.
   2. Reduce noise in I_i(x, z) by implementing 3 × 3 pixel averaging.
   3. Create an average image of I_i(x, z) over i = 1 to 5 (or more) before heating, and define it as the reference image, I_r(x, z).
      NOTE: This averaging reduces the noise to obtain a more reliable image than a single frame image.
   4. Construct the sequential images of the absorbance difference, ΔA_i(x, z), via the following equation:
         (1)
      NOTE: ΔA_i(x, z) is the variation in the absorbance, A_i(x, z), from the reference absorbance, A_r(x, z), before heating, and is derived as follows^{15,16,17,18,19}:
         (2)
      where I₀ is the intensity of incident light to the cell.
   5. Colorize the ΔA_i images using an appropriate color map such as blue-to-red.
      NOTE: The command script file for running Steps 2.1.2 through 2.1.5 for ImageJ is presented in Supplement 2.
2. Temperature estimation.
   1. Choose the time period during which ΔA_i(x, z) is circularly symmetric with respect to the center of the sphere by visually observing the images.
      NOTE: The circular symmetry is broken mainly by free convection. An image-based analytical judgement of free convection occurring is introduced in the previous work¹⁹; however, practically, the visual judgement is effective.
   2. Extract the ΔA_i(rʹ, θ) data along 360 radial lines (Δθ = 1˚) on the ΔA_i(x, z) images.
   3. Exclude the ΔA_i(rʹ, θ) data within the sphere and in its vicinity (Δrʹ≈ 0.2 mm). Note: The data are anomalously very small or large in the vicinity mainly because of the slight movement of the sphere.
   4. Average ΔA_i(rʹ, θ) over θ to determine the line profile, ΔA_i(rʹ).
      NOTE: The command script file for running Steps 2.2.2 through 2.2.4 for ImageJ is presented in Supplement 3.
   5. Approximate the ΔA_i(rʹ) data by the following multi-Gaussian function:
         (3)
      where a_j is the weighting factor, σ_j is the dispersion parameter, and R is the maximum of rʹ where ΔA_i(R) = 0 can be assumed.
   6. Calculate the absorption coefficient difference, Δµ_i(r), by substituting the obtained N, a_j, and σ_j into the following IAT of Eq. (3):
         (4)
      where erf is the error function.
   7. Convert Δµ_i(r) to temperature via the following equation:
         (5) 
      with the temperature coefficients of water, α_f, which are 2.8 x 10^-4 K^-1 mm^-1 for λ = 1150 nm¹⁹ and 4.1 × 10^-3 K^-1 mm^-1 for λ = 1412 nm¹⁷.
      Note: The command script file for running Steps 2.2.5 through 2.2.7 is presented in Supplement 4, where the Levenberg-Marquardt nonlinear least-squares algorithm^17,19 is employed for Step 2.2.5.

Results

Images of ΔA_i(x, z) at λ = 1150 nm for a 2.0-mm-diameter steel sphere in water and at λ = 1412 nm for a 0.5-mm-diameter steel sphere in maltose syrup are presented in Figure 5a and Figure 6a, respectively. In both cases, the sphere was located 12 mm below the bottom of the coil along its central axis. Figu...

Discussion

The technique presented in this paper is a novel one using the temperature dependence of NIR absorption of water and presents no significant difficulty in setting up the necessary equipment and implementation. The incident light can be easily produced by using a halogen lamp and an NBPF. However, lasers cannot be used, because coherent interference patterns would appear on the images. Common optical lenses and glass cells for visible-light use can be used, as they transmit an adequate amount of light at λ =...

Materials

Name	Company	Catalog Number	Comments
Induction heating system	CEIA, Italy	SPW900/56	780 kHz, 5.6 kW (max).
Coil	SA-Japan	custom	Water-cooled copper tube; two-turn; outer dia. 28 mm.
Water chiller	Matsumoto Kikai, Japan	MP-401CT
Halogen lamp	Hayashi Watch-Works, Japan	LA-150UE-A
Narrow bandpass filter for λ = 1150 nm	Andover	115FS10-25	Full width at half-maximum (FWHM): 10 nm.
Narrow bandpass filter for λ = 1412 nm	Andover	semi-custom	Full width at half-maximum (FWHM): 10 nm.
Bandpass filter for λ = 850−1300 nm	Spectrogon	SP-1300
Bandpass filter for λ = 1100−2000 nm	Spectrogon	SP-2000
NIR camera	FLIR Systems	Alpha NIR	InGaAs
Image acquisition software	FLIR Systems	IRvista
Image processing software	NIH	ImageJ	ver. 1.51r
Image processing software	MathWorks	Matlab	ver. 2016a
Telecentric lens	Edmond Optics	55350-L	X1
Steel sphere (0.5 mm dia.)	Kobe Steel, Japan		Fe-1.5Cr-1.0C-0.4Mn (wt %)
Steel sphere (2.0 mm dia.)	Kobe Steel, Japan		Fe-1.5Cr-1.0C-0.4Mn (wt %)
Maltose syrup as aqueous gel	Sonton, Japan	Mizuame	Food product