Modified FIR thermometry for surface temperature sensing by using high power laser

Ran Wang; Xinlu Zhang; Zhilin Zhang; Hujiang Zhong; Yujin Chen; Enming Zhao; Steven Vasilescu; Lu Liu

doi:10.1364/OE.25.000848

1. Introduction

All-optical temperature sensing has found numerous applications in engineering technology. The separation between the probe and receiver allows for remote temperature determination of machine components in motion [1]. In recent years, the demand for high spatial resolution temperature mapping has increased dramatically within biological and therapeutic industries. Applications benefitting from these improvements include photo-thermal therapy (PTT) systems (with feedback mechanisms) [2] and controllable drug delivery systems (temperature-dependent) [3,4]. Especially, high-resolution surface temperature sensing is of importance for PTT of skin cancer and monitoring of microcircuit.

Capable of satisfying the rigid requirements of biological and electromagnetic applications, upconversion FIR technique has excellent potential. This technique is not impacted by the fluctuation of laser power or the induction of surrounding electromagnetic environments [5]. In addition, upconverison processes using near infrared light as an incident source and thus yields high ratio of signal to noise compared to conventional down-conversion processes [6].

One main drawback of upconversion FIR technique is the heating effect of the incident laser which leads to a higher measured value compared to the ambient temperature. This error is unacceptable for situations that require a consistently high level of measurement accuracy; such as monitoring tissue temperature in vivo during PTT, in which overestimated temperature may result in a failure to eliminate cancer tissue via a lethal temperature.

In order to reduce the heating effect, low laser powers are usually used while measurements are taken [7]. However, low power producing weak signal decreases the sensing accuracy. In addition, the incident power needs to be higher sometimes. For instance, during the temperature sensing in vivo, higher laser power can compensate for the absorption and scattering of organic tissue and in doing so improves the number of detectable signals.

Revealing the principle behind the heating effect of laser may provide a solution for the problem at hand and allow a higher power to be used in FIR measurements, by bypassing the heating effect. Herein, temperature distributed on the sample’s surface is investigated, and a modified FIR formula is deduced. In addition, to verify this modified method, Er³⁺ doped Yttria ceramics are used to record the FIR behaviors.

2. Experiment

Y₂O₃ ceramics doped with Er³⁺ were prepared by a modified sol-gel process [8]. Upconversion spectral measurements were performed by irradiating the disks via a variable-power 976 nm diode laser with a spectral width of approximately 2.5 nm. The diameter of laser spot is around 1 mm. The emission was collected by a monochromator equipped with a photomultiplier tube. For temperature sensing, samples were attached to a heating stage (diameter of heating plate is ~10 cm) with resolution of 0.1 K. The structures of samples in powder form were identified by x-ray diffraction (XRD) using an X’Pert Pro diffractometer. The 2θ angle of the XRD spectra were recorded from 20° to 80° at a scanning rate of 4° / min.

3. Results and discussion

The XRD patterns of the Y₂O₃: xEr³⁺ (x = 0.5, 4, 12 mol%) ceramics are shown in Fig. 1(a). All the diffraction peaks of the phosphors coincide well with the standard data of highly crystallite cubic Y₂O₃ (JCPDS No. 05-0574).

Fig. 1 a) XRD patterns of Er³⁺ doped Y₂O₃ ceramics. b) Detailed energy levels of Er^{3+ 4}I_15/2, ⁴S_3/2, and ²H_11/2. Figures in the frames are the normalized upconversion spectra under low and high temperatures.

Download Full Size | PDF

Figure 1(b) shows the energy level distribution of Er³⁺ and the normalized spectra in the green emission. Based on the distribution of the sublevels, an averaged energy gap of $Δ \bar{E} = 862$ cm⁻¹ is given. Peak positions of emissions did not change with increasing the temperature, whereas the normalized intensity from the upper level ²H_11/2 increases clearly compared to that from the lower level ⁴S_3/2, leading to the variation of FIR value. FIR variation is governed by the equation

F I R = \frac{I_{2}}{I_{1}} = C \exp (- \frac{Δ E}{k T})

where I₂ and I₁ are the fluorescence intensity of ²H_11/2 and ⁴S_3/2 levels, respectively. C is a constant given by the properties of sample, ΔE the energy gap between the two levels, k the Boltzmann constant, and T the absolute temperature.

To reduce the heating effect of incident laser in FIR technique, lower laser power is commonly used [7]. One criterion of the sensing validity is that the incident laser power falls into the region in which FIR value hardly changes [9]. But this might lead to larger sensing errors than previously expected based on our experimental results.

Figure 2(a) shows the FIR dependence of laser power, which is characterized by a steady region in which the FIR value is almost unchanged. However, as shown in Fig. 2(b), temperature elevates with incident laser power even in the “steady region”. This indicates measurable heating effect always exists as long as sample was irradiated by laser. Note that the temperature of the sample increases with pumping power linearly, which is similar to the phenomena reported in other doping systems [10,11]. It appears this can be extended to other parts of sample’s surface because linear dependences shown in Fig. 2(b) are found in different positions (only two series data are given in the figure). Unfortunately, we cannot introduce this linear dependence into FIR expression so early, since the laser induced temperature should be a gradient distribution on the sample’s surface.

Fig. 2 a) FIR dependence of laser power. b) Temperature dependence of laser power, in which ‘nearest’ means thermal couple is beside the luminescent spot as close as possible without direct irradiation; ‘back’ means the probe is attached on the back position of the luminescent spot.

Download Full Size | PDF

Herein, COMSOL software is used to calculate the temperature distribution on the sample’s surface in order to reveal the tendency of heating effect, rather than to simulate the experimental data. Hence we only investigate the main features of temperature distribution under different incident laser power (0.1~1 W, according to our experimental setup) with several absorption coefficients (0.1~1, larger absorption coefficient represents higher doping level). We use thermal parameters of pure Y₂O₃ instead of Er³⁺ doped Y₂O₃ in the calculation due to the similarity between Er³⁺ and Y³⁺. Thus thermal parameters of materials, including sample (Y₂O₃) and heating plate (stainless steel 304) can be found in the software’s database.

A typical distribution is shown in Fig. 3(a). The maximal temperatures T_m, calculated by the software, can be well fitted by a linear line $T_{m} = α P + T_{0}$ [Fig. 3(b)]. Moreover, it is found that temperature increases with the absorption coefficient of material [Fig. 3(c)] as well as the laser power [Fig. 3(d)], whereas the shape of temperature distribution shows no substantial changes. Distributions under different pumping powers and absorption coefficients are normalized as shown in the insets of Figs. 3(c) and 3(d), respectively, where three series of data are almost identical. Comparing results in Figs. 3(b)-3(d), it can be concluded that the temperature of every point on the sample’s surface is proportional to pump power, which is consistent with the previous experimental results [Fig. 2(b)].

Fig. 3 Calculated results by COMSOL software. a) 3-D temperature distribution on the sample’s surface; b) Highest temperature T_m dependence of laser power; c)-d) Radial temperature distribution calculated by using different parameters. P denotes the laser power, α the absorption coefficient of sample. Insets are the normalized temperature distribution under different conditions.

Download Full Size | PDF

Due to the axial symmetry of temperature and upconversion luminescence, circular belt (denote as r, dr) is chosen as shown in Fig. 4(a), to deduce the modified FIR formula. Therefore temperature on the surface can be written as $T = T (r)$ and luminescence intensity as $I = I (r)$ , where r is the radial coordinate. Let dI₂ and dI₁ represent the fluorescent intensity of ²H_11/2 and ⁴S_3/2 level, respectively, from the circular belt (r, dr). According to Eq. (1), one can derive $d I_{2} / d I_{1} = C \exp (- Δ E / k T)$ . Since the spectrometer collects luminescent data emitted from the whole luminescent spot, the FIR can be rewritten in detail as follows.

F I R = \frac{I_{2}}{I_{1}} = \frac{\int_{0}^{R} d I_{2}}{\int_{0}^{R} d I_{1}} = \frac{\int_{0}^{R} C exp (- Δ E / k T) d I_{1}}{\int_{0}^{R} d I_{1}} = C \frac{\int_{0}^{R} exp (- Δ E / k T (r)) ρ_{G}^{n} (r) 2 π r d r}{\int_{0}^{R} ρ_{G}^{n} (r) 2 π r d r}

where

ρ_{G} (r) = exp (- B_{0} r^{2})

is the normalized Gaussian function and represents the distribution of laser power P, whose width is determined by B₀. Herein, radius of laser spot is around 0.5 mm, thus we arrive at

B_{0} \approx 1.7 \times 10^{7}

m⁻². Upconversion intensity is governed by

I \propto P^{n} \propto ρ_{G}^{n} (r) = exp (- B r^{2})

, where n is the photon number involved [8]. For green emission of Er³⁺, n is usually close to 2, thus

B = B_{0} n \approx 3.4 \times 10^{7}

m⁻² in the expression.

Fig. 4 a) Integrated element (r, dr) of luminescent spot, whose radius is equal to laser radius R; b) Calculated temperature distribution along the radial direction and fitted curve using Lorentzian function; c) Variation of parameter A₀ in the Lorentzian function with pumping power. A₀ determines the width of the Lorentzian curve; d) Comparison of fitted Lorentzian curve (temperature distribution) and Gaussian curve (laser power distribution).

Download Full Size | PDF

As shown in Fig. 4(b), distribution of temperature along the radial direction can be well fitted by the product of maximal temperature T_m and the normalized Lorentzian curve $ρ_{L} = 1 / (1 + A_{0} r^{2})$ . Note that these fittings are performed within the laser spot area, from $r = - 0.5$ mm to 0.5 mm, rather than across the whole sample (−5~5 mm), since only the area within laser spot is concerned. Also, distributions under other excitation power can be well fitted by the expression of $T (r) = T_{m} / (1 + A_{0} (P) r^{2})$ (data not shown), in which parameter $A_{0} = A_{0} (P)$ determines the width of Lorentzian curve, and increases with the pumping power. As shown in Fig. 4(c), A₀ in Lorentzian function is determined by fitting the calculated temperature distribution in the range of laser spot. A linear dependence $A_{0} = A P$ was obtained, where $A = 6.2 \times 10^{5}$ m⁻² is a constant. Therefore Eq. (2) can be further written as:

\begin{array}{l} F I R = C \frac{\int_{0}^{R} \exp (- Δ E (1 + A P r^{2}) / k T_{m}) \exp (- B r^{2}) r d r}{\int_{0}^{R} \exp (- B r^{2}) r d r} \\ \begin{matrix}  \end{matrix} = C \exp (- \frac{Δ E}{k T_{m}}) \frac{\int_{0}^{R} \exp (- (A P Δ E / k T_{m} + B) r^{2}) r d r}{\int_{0}^{R} \exp (- B r^{2}) r d r} \\ \begin{matrix}  \end{matrix} = C (\frac{A P Δ E}{k B T_{m}} + 1) \exp (- \frac{Δ E}{k T_{m}}) \end{array}

To simplify the above expression, we compare the Lorentzian and Gaussian curve fitted in this paper. It can be seen from Fig. 4(d), in which the T axis is extended, that Lorentzian curve is much broader than Gaussian one, which lead to far smaller A than B values (about two orders). Further an estimation of maximal value of ${(A Δ E / k B T_{m})}_{\max} = 7.5 \times 10^{- 2}$ W⁻¹ can be deduced, based on the average energy gap $Δ \bar{E} = 862$ cm⁻¹ and lowest $T_{m} = T_{0} = 300$ K (without laser excitation). Thus when laser power is lower than 1.3 W, we can usually omit the $A P Δ E / k B T_{m}$ term, due to its value being considered negligible (at least 10 times smaller compared to 1). Finally, based on the linear relationship shown in Fig. 3(b), we arrive at

F I R \approx C \exp (- \frac{Δ E}{k T_{m}}) = C \exp (- \frac{Δ E}{k (α P + T_{0})})

In this final expression, the fundamental reason for using maximal temperature T_m is based on the fact that the distribution of laser power (Gaussian curve) is much narrower than that of the temperature (Lorentzian curve) as shown in Fig. 4(d). This suggests the change of temperature within the luminescent spot is quite gentle and thus the temperature of different points within the luminescent spot can be treated as an average value for T_m. Thus it is indicated that Eq. (4) is valid only under the small laser spot situation. If the laser spot is large enough to make the distribution of temperature and laser power comparable, we cannot use the maximal temperature acting as the average. This is not a serious issue of concern as the small laser spot is the precondition for high spatial resolution temperature mapping. Another limitation of Eq. (4) is high laser’s power will challenge the validity of the omission mentioned above. This cannot happen in most cases since usually laser power of tens of milliwatts is high enough to stimulate strong signal which is much lower than the highest value (~1.3 W) estimated here. It should also be noted that excessive laser power leads to heating damage of the probe.

To verify the validity of this modified sensing method, FIR behaviors under different pumping powers are investigated through Er³⁺ doped Y₂O₃ ceramics. To calibrate the thermometer, the sample is attached on the heating plate set to different temperatures to simulate various ambient conditions. Note that actual temperature (T₀ in the above equations) of sample is lower than the setting temperature due to heat loss, as shown in Fig. 5(a).

Fig. 5 Experimental verification. a) Temperature dependence of heating power, in which horizontal axis represents the setting temperature of the heating plate, and the vertical axis is the actual temperature measured on the sample’s surface by thermal couple. Note that this measurement is carried out without laser excitation; b)-d) FIR dependences of temperature under different pumping power, fitting equations are given.

Download Full Size | PDF

To guarantee the generality, various laser powers and doping levels are used. Integrated intensity from 510 to 543 nm and 543-580 nm represent I₂ and I₁, respectively. As shown in Figs. 5(b)-5(d), the variation of FIR value fluctuates when using lower laser power, and tends to be smoother as power is increased. So a more accurate calibration would be expected in a higher pumping situation. Experimental data are fitted according to Eq. (4), in which T₀ and P are the independent variables; C, ΔE, and α are determined by the least square fitting of three series data obtained under different pumping powers. It is found that all the data are well fitted, and the fitted value of α increases from 0.07 to 0.26 with increased Er³⁺ doping concentration. Since α represents the transformation ability from incident photon into heat, it is quite reasonable that high doping sample possesses higher α value due to its stronger absorption. $Δ E / k$ are all close to the average value of $Δ \bar{E} / k = 1240$ , and C declines with doping concentration due to the structural change [12].

As a proof of concept, we use data obtained in a low doping sample to compare the sensing performance. Neglecting the laser heating under 132 mW excitation, a conventional calibrating expression of $F I R = 21.75 \exp (- 1250.23 / T)$ is obtained. If we use higher incident laser powers, as shown in Fig. 6, large deviations occur due to the boost of the heating effect. But through our modified method based on Eq. (4), quite precise sensing behaviors can be still guaranteed. Thus one can use a relatively high laser power to achieve not only strong light signal but also a higher sensing accuracy. In addition, absolute sensitivity reaches $1.1 \times 10^{- 3}$ K⁻¹, which is comparable to the state-of-the-art systems [13]. Note the precondition is the optical and thermal responses are still in the linear region.

Fig. 6 Comparison of sensing performance between the modified method proposed in this paper and the conventional method. a) 574 mW excitation; b) 1017 mW excitation.

Download Full Size | PDF

However, for real application of surface temperature mapping such as skin cancer therapy and microcircuit monitoring, the probe (upconversion nanocrystals) is likely to be dropt or sprayed onto the target’s surface. Thus density of the nanocrystals might be different with position, leading to measuring errors due to the change of thermal properties (different value of parameter α at different position). In addition, the surface of the target might be not flat, resulting in various energy distribution of laser power for non-collimating incident light, and finally decrease the sensing accuracy. To solve these problems, we further propose a dual-power measuring method as follows.

Let FIR₂ and FIR₁ denote the values measured under incident laser power I₂ and I₁, respectively, and ratio A = I₂ / I₁. We obtain the sensing temperature based on Eq. (4) as

T_{0} = \frac{1}{A - 1} (\frac{Δ E}{k \ln (F I R_{2} / C)} - \frac{A Δ E}{k \ln (F I R_{1} / C)})

Above expression is independent to the exact laser power and the thermal parameter α, thus can solve the aforementioned problems. To verify this dual-power measuring method, pork skin [Fig. 7(a)] is used as the biological tissue. 2Er/18Yb:NaYF₄ nanocrystals [Fig. 7(b)] diluted into cyclohexane are dropt onto the pork skin and dried naturally as the surface sensing probe. Different laser powers are used for calibration: 6 mW, 20 mW, and 37 mW represent low, medium, and high laser power, respectively. Calibration expression is shown in Fig. 8(a). The validity of this dual-power measurement by monitoring different positions on the pork skin is shown in Fig. 8(b).

Fig. 7 a) Photograph of the pork skin; b) TEM of sample, bar is 100 nm.

Download Full Size | PDF

Fig. 8 a) Calibration of thermometer; b) Surface temperature sensing of the pork skin at different positions by using the proposed dual-power method (20 mW and 37 mW).

Download Full Size | PDF

4. Conclusion

COMSOL software was used to investigate the heating effect of incident laser. It is found that the temperature distribution, within the luminescent spot, can be well fitted by a Lorentzian curve. The maximal temperature, which is proportional to the incident laser power, can be used as an average value in the modified FIR formula. Finally, the modified expressions were verified by experimental data. In conclusion, this work provides a valid solution for the removal of the laser’s heating effect in FIR technique, and can be incorporated into the therapeutic and industrial fields where accurate surface temperature mapping is imperative.

Funding

111 project (B13015); National Natural Science Foundation of China (11204048, 61377085); Natural Science Foundation of Heilongjiang Province (F201338); China Postdoctoral Science Foundation (2013M541340); Heilongjiang Postdoctoral Fund (LBH-Z13053).

References and links

1. L. Marciniak, K. Prorok, L. Francés-Soriano, J. Pérez-Prieto, and A. Bednarkiewicz, “A broadening temperature sensitivity range with a core-shell YbEr@YbNd double ratiometric optical nanothermometer,” Nanoscale 8(9), 5037–5042 (2016). [CrossRef] [PubMed]

2. X. Zhu, W. Feng, J. Chang, Y. W. Tan, J. Li, M. Chen, Y. Sun, and F. Li, “Temperature-feedback upconversion nanocomposite for accurate photothermal therapy at facile temperature,” Nat. Commun. 7, 10437 (2016). [CrossRef] [PubMed]

3. C. Kojima and K. Irie, “Synthesis of temperature-dependent elastin-like peptide-modified dendrimer for drug delivery,” Biopolymers 100(6), 714–721 (2013). [CrossRef] [PubMed]

4. S. He, G. Tourkakis, O. Berezin, N. Gerasimchuk, H. R. Zhang, H. Y. Zhou, A. Izraely, W. J. Akers, and M. Y. Berezin, “Temperature-dependent shape-responsive fluorescent nanospheres for image-guided drug delivery,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(14), 3028–3035 (2016). [CrossRef]

5. S. A. Wade, S. F. Collins, and G. W. Baxter, “Fluorescence intensity ratio technique for optical fiber point temperature sensing,” J. Appl. Phys. 94(8), 4743–4756 (2003). [CrossRef]

6. L. Prodi, E. Rampazzo, F. Rastrelli, A. Speghini, and N. Zaccheroni, “Imaging agents based on lanthanide doped nanoparticles,” Chem. Soc. Rev. 44(14), 4922–4952 (2015). [CrossRef] [PubMed]

7. M. Alencar, G. S. Maciel, C. B. Araújo, and A. Patra, “Er-doped BaTiO₃ nanocrystals for thermometry: Influence of nanoenvironment on the sensitivity of a fluorescence based temperature sensor,” Appl. Phys. Lett. 84(23), 4753–4755 (2004). [CrossRef]

8. L. Liu, H. L. Jiang, Y. J. Chen, X. L. Zhang, Z. G. Zhang, and Y. X. Wang, “Power dependence of upconversion luminescence of Er³⁺ doped Yttria nanocrystals and their bulk counterpart,” J. Lumin. 143, 423–431 (2013). [CrossRef]

9. Z. Chouahda, J. P. Jouart, T. Duvaut, and M. Diaf, “The use of the green emission in Er³⁺-doped CaF₂ crystals for thermometry application,” J. Phys. Condens. Matter 21(24), 245504 (2009). [CrossRef] [PubMed]

10. V. K. Tikhomirov, K. Driesen, V. D. Rodriguez, P. Gredin, M. Mortier, and V. V. Moshchalkov, “Optical nanoheater based on the Yb³⁺-Er³⁺ co-doped nanoparticles,” Opt. Express 17(14), 11794–11798 (2009). [CrossRef] [PubMed]

11. W. L. Lu, L. H. Cheng, H. Y. Zhong, J. S. Sun, J. Wan, Y. Tian, and B. J. Chen, “Dependence of upconversion emission intensity on Yb³⁺ concentration in Er³⁺/Yb³⁺ co-doped flake shaped Y₂(MoO₄)₃ phosphors,” J. Phys. D Appl. Phys. 43(8), 085404 (2010). [CrossRef]

12. R. Wang, X. L. Zhang, F. Liu, Y. J. Chen, and L. Liu, “Concentration effects on the FIR technique for temperature sensing,” Opt. Mater. 43, 18–24 (2015). [CrossRef]

13. B. Dong, B. S. Cao, Z. Q. Feng, X. J. Wang, and Y. Y. He, “Optical temperature sensing through extraordinary enhancement of green up-conversion emissions for Er–Yb–Mo:Al₂O₃,” Sens. Actuators B Chem. 165(1), 34–37 (2012). [CrossRef]

Modified FIR thermometry for surface temperature sensing by using high power laser

Abstract

1. Introduction

2. Experiment

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (8)

Equations (5)

Optics Express