1. Introduction

The existing medical research results have demonstrated that cytopathic effect can affect routine metabolic activities and thus induce the change in the temperature field in the cell. Exploring a method or a tool that can accurately monitor three-dimensional (3D) temperature gradient distribution in cells and tissues or even on subcellular level and detecting subtle change in local temperature can greatly enhance the detectability of tumors and local inflammation and provide a more precise monitoring tool for hyperthermia.

High-sensitivity thermocouples have been developed for temperature measurement, leading to the concept of micro-calorimetry since the 1970s. The development of micro-calorimetry has reached the peak in the 1990s. Owing to its high sensitivity and capability of measuring slow processes, micro-calorimetry has aroused widespread attention of many scholars in life sciences mainly including pharmaceutical chemistry and pharmacology [1–3], mitochondrial energy metabolism and the related change rules [4], bacterial growth rules and the related influencing factors [5,6] and bio-toxicity of quantum dots [7]. Nevertheless, current micro-calorimetry techniques lack specificity and can only be used for the investigations on a whole at macroscopic level. For example, micro-calorimetry now has been employed for investigating the whole flora, but fails to examine the bio-thermal effect of a single bacterium or a single cell (especially in the cell).

Great progress in nanometer material science and bioengineering over the past years has provided a novel technique of real-time temperature monitoring on molecular level. At present, temperature measurement on micro-nano scale is mainly based on non-contact optical temperature measurement principle, and traditional fluorescein or fluorescent tracer particles are used as thermal probes. Using these thermal probes, temperature can be indirectly detected by investigating the particle’s fluorescent information such as fluorescence intensity, lifetime, and peak wavelength). Gota et al. measured the temperature in the cell using a hydrophilia fluorescent nano-gel thermometer with fluorochrome [8]. Chapman et al. detected the temperature of a single living cell using an exogenous fluorescent probe [9]. Zohar et al. and Suzuki et al. employed transition-metal ions for accurate measurement of temperature of a single cell [10,11].

However, the above-described innovative work can only measure the mean temperature of each cell and impose intensified requirements on experimental conditions. In addition, the detection probes are easily affected by surroundings, poor in light resistance and stability, and thus cannot achieve continuous monitoring for a long time.

In addition to many essential characteristics of nanoparticles, quantum dots also exhibit incomparable fluorescent characteristics in contrast with traditional organic fluorescent dyes, so that the fluorescence spectra of the marked biomolecules can be easily distinguished and identified. Currently, quantum dot has been applied to many domains including quantum dot display screen [12,13], quantum dot light emitting diode [14,15], quantum dot solar cell [16,17], quantum dot laser [18], and quantum dot biomarker [19–24]. The fluorescence switch property of N-GQD was explored by alternate addition of Al³⁺ and EDTA. The probe was also utilized for detecting Al³⁺ in living cells owing to its excellent biocompatibility [25]. Kumari et al. synthesized green fluorescent carbon quantum dot by recycling the wasted polyolefin residues and explored the applications to Cu²⁺ sensing and living cell imaging [26].

Temperature can induce the changes in quantum dot forbidden bandwidth, size as well as the connection strength between the surface ligand and shell and thereby affect some parameters including fluorescence intensity, half-peak width, peak wavelength, and fluorescence lifetime. Accordingly, quantum dot cannot only serve as a type of non-invasive temperature probe for the temperature detection in electronic components on micron scale [27], but also can be modified by bioactive groups on the surface for examining thermal imaging and temperature distribution in biological tissues and cells [28] as well as monitoring real-time pressure and temperature on the surface of the wind tunnel in aeronautics and astronautics [29,30].

Glen et al. scattered CdSe/ZnS quantum dot in lauryl methacrylate and investigated the temperature characteristics of fluorescence spectra in the temperature range 100–315 K [31] and found that the fluorescence intensity changed linearly with temperature with a correlation coefficient of −1.3%/°C. Javier et al. realized alternate deposition of CdTe quantum dot and PDDA thin film in hallow optical fibers by means of electrostatic self-assembly technique, investigated the fluorescence intensity in the temperature range 20–90 °C and temperature characteristics at the peak wavelength, and successfully applied these conditions for fiber temperature sensor [32].

Although the peak wavelength and half-peak width of the synthesized CdTe quantum dot fluorescence spectra in the solution exhibit favorable linear relationship with temperature during heating and cooling processes, the reproducibility of thermal cycling process is poor and irreversibility appears, which are very unfavorable for the preparation of the temperature probe. Thus, improving the stability of CdTe quantum dot fluorescence spectra during the thermal cycling process is necessary. In contrast, the space is narrow and the conditions are quite complex around the cell. The quantum dot in the solution should have appropriate carrier to avoid the agglomeration and oxidation of quantum dot during temperature monitoring. Moreover, quantum dot should also be as light as possible so that the effects on cell metabolism can be minimized.

When using quantum dot as a temperature measuring probe, another key to achieving 3D temperature measurement in the space on micro-nano scale lies on the spatial positioning of the probe. Currently, common methods for spatial positioning of particles mainly include laser scanning confocal microscopy, defocused imaging positioning, and dual-helix point spread function for positioning.

Quantum dot has also been used as a temperature measuring probe for two-dimensional (2D) temperature measurement. Li et al. injected CdTe quantum dot into the cell and measured the fluorescence spectra using a spectrometer to measure planar temperature in the cell [33]. The most critical point in 3D temperature measuring on micro-nano scale is to achieve 3D positioning of the probe, in which maintaining the particle’s axial positioning remains a difficulty. Shen et al. summarized the algorithms behind, and practical applications of single particle tracking (SPT) [34]. King et al. realized the positioning in living cancer cells by utilizing the fluorescence effect of iridium (Ir) nanoparticles [35]. Ballister et al. presented a new technique to rapidly and reversibly control protein localization in living cells with subcellular spatial resolution using a cell-permeable, photoactivatable chemical inducer of dimerization [36].

In recent years, dual-helix point spread diffusion has become the research hotpot regarding axial positioning, which is achieved by establishing the relationship between the defocusing distance and imaging. By using dual-helix point spread function in wide-field microscope, Pavani et al. realized super-resolution imaging of single-molecule fluorescence and high-resolution 3D positioning of fluorescence protein [37]. Bon et al. combined SELFI with conventional localization microscopy to visualize F-actin 3D filament networks and reveal the spatial distribution of the transcription factor OCT4 in human induced pluripotent stem cells at depths up to 50 mu m inside uncleared tissue spheroids [38]. Dupont et al. improved the original orbital tracking method, which can accurately trace the particles with a diameter of 5 nm; the capabilities of the system are demonstrated using single virus tracing to follow the infection pathway of Prototype Foamy Virus in living cells [39].

As described above, quantum-dot-based temperature measurement now has been examined extensively and deeply, but 3D temperature measurement on micro-nano scale has been poorly reported and still needs further investigation.

This study focused on CdTe quantum dot and analyzed the luminous mechanism of the fluorescence spectra; next, after the optimization, quantum dot temperature probe with favorable stability and reversibility was prepared. Moreover, a set of spectra detection system by integrating sample heating, temperature monitoring, and spectral signal detection was established for characterizing the spectral characteristics of CdTe quantum dot temperature probe. In addition, 3D positioning method based on dual-helix point spread function was proposed, and 3D temperature field measurement system based on quantum dot was designed for validating the effectiveness of the system.

2. Temperature characteristics of quantum-dot fluorescence spectra

2.1 Effect of temperature on the energy band of the quantum dot

The effect of temperature on the bandgap width of bulk materials heavily depends on the lattice’s thermal expansion and electro-acoustic interaction. For bulk semiconductor materials, the relationship between the bandgap width and energy band can be described by famous Varshni’s empirical formula. This empirical formula is also applicable to quantum dot and can be written as:

where E_g(0) denotes the forbidden bandwidth of the material at 0 K, with a unit of eV, α denotes the material’s thermal expansion coefficient, with a unit of eV·K⁻¹, T denotes the temperature, with a unit of K, and β denotes the material’s approximate Debye temperature, with a unit of K [40].

As described by Varshni’s empirical formula, the value of the last term $\frac{\alpha T^2}{\beta +T}$ increases with increasing temperature, accompanied by the reduction of the material’s forbidden bandwidth. For quantum dot, the optimal bandgap drops with increasing temperature.

The photoluminescent photon energy of quantum dot and the optimal bandgap ($E_g^{QD}$) obey the following relationship:

where h denotes the Planck constant, with a unit of J·s, c denotes the velocity of light, with a unit of m·s⁻¹, and λ denotes the wavelength of emitted photons, with a unit of m.

By taking the derivative of Eq. (2) relative to T, the energy is converted into electron volt, and the relationship of the wavelength of the emitted photons with bandgap and temperature can be derived as:

Equation (3) describes the relationship between the photoluminescent wavelength of the quantum dot with temperature and optimal bandgap. The effect of temperature on the quantum dot’s optimal bandgap is finally reflected by the change in peak fluorescence wavelength of the quantum dot. As the temperature of the quantum dot rises, the peak fluorescence wavelength increases. Based on this property, quantum dot can be used for temperature measuring probe.

2.2 Effect of temperature on fluorescence intensity of the quantum dot

All fluorescence molecules and materials exhibit the characteristics of temperature-related emission characteristics, which are induced by Boltzmann distribution. Temperature-relevant characteristics can be described by the function of the material’s electronic energy level structure. This study assumes a kind of materials in which radiation conversion can only occur at a low temperature T; then, at a higher temperature Ts, thermal energy can promote the electrons to move from the excited state to the ground state via overlapping vibration at different energy levels. Accordingly, the probability of non-radiative conversion at Ts increases. The non-radiative conversion probability related to the temperature T can be described by the following Arrhenius Equation [41]:

where $k_{\text{nrt}}$ denotes the probability of non-radiative conversion, $\Delta E$denotes the energy level between the lowest excited state and the possible coincident points in non-radiative conversion state, with a unit of eV, and k denotes the Boltzmann constant, with a unit of$J·K^{-1}$. According to Eq. (4), the probability of nonradiative recombination increases with increasing temperature.

The quantum fluorescence yield equals to the ratio of the number of emitted photons to the number of absorbed photons:

where Γ denotes the probability of radiation conversion. Obviously, Γ drops with increasing temperature.

Fluorescence intensity conforms to Parker’s rule [42]:

where I denotes the measured fluorescence intensity, I₀ denotes the intensity of the excited light, ϕ denotes the quantum yield of the luminous body, within a range 0–1, k denotes the geometric factor connected with the measuring device, ε denotes the absorptivity, d denotes the penetration length, and c denotes the concentration of the luminous body.

In ideal cases, I is only subjected to the variation of ϕ with temperature. However, in actual conditions, I is extremely easily affected by the change in other parameters in Parker’s rule induced by photo-bleaching and background radiation, and some experimental parameters including the geometric distance and uniform light can hardly be completely repeated. Therefore, the measurement of temperature based absolute fluorescence intensity is affected by many factors, thus exhibits larger error. In practical work, the ratio of the dual emission peaks is generally used for temperature measurement.

2.3 Effect of temperature on the half-peak width of the quantum dot

With varying temperature, the half-peak width of the fluorescence spectra of the quantum dot also varies. The variation is mainly determined by inhomogeneous broadening induced by the quantum dot size and shape distribution and homogeneous broadening induced by the scattering effect of laser by acoustic phonons and longitudinal optimal photons [43]. On account of the phonon effect, the half-peak widths of both bulk material and quantum dot increase with increasing temperature. The relationship between the half-peak width of the quantum dot and temperature can be fitted as [43,44]:

where ${\Gamma }_{inh}$ denotes the non-uniform item of half-peak width (eV); ${\gamma }_{AC}$ denotes the exciton-acoustic phonon scattering coefficient; ${\Gamma }_{LO}$ denotes the exciton-LO photon coupling intensity; ${\text{E}}_{LO}$ denotes the LO photon energy (J); and K_B denotes the Boltzmann constant, with a unit of $\text{J}·{\text{K}}^{-1}$.

3. Preparation of quantum dot temperature probe and optimization of temperature characteristics

The fluorescence spectra of the prepared CdTe quantum dot via aqueous-phase synthesis exhibit unstable temperature characteristics [45]. During the thermal cycling process at room temperature, the prepared quantum dot undergoes structural change and is no longer suitable for large-scale temperature detection. By combining the practical requirements in the measurement of cell temperature, the quantum dot temperature probe was first prepared by the means of layer-by-layer self-assembly, and then the temperature characteristics were optimized to develop quantum dot temperature probe with favorable stability and reversible thermal cycling.

3.1 Fabrication and optimization of quantum dot temperature probe

Layer-by-layer self-assembly is a simple and effective method of preparing organic polymers and nanoparticle composite films proposed by Decher and Hong [46]. Figure 1 illustrates the principle. Using this method, the self-assembled monolayers are realized via electrostatic attraction between nanoparticles with different charges or organic materials. In this study, the synthesized CdTe quantum dot and polymer electrolyte were deposited on the substrate layer by layer to form the composite film of CdTe quantum dot and polymer electrolyte. Accordingly, the agglomeration and oxidization of quantum dot can be effectively avoided, simultaneously satisfying the cell temperature monitoring conditions.

 

Fig. 1 Principle of layer-by-layer self-assembly process.

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Table 1 lists chemical reagents and materials used in the present experiment.

Table 1. Chemical reagents and materials used in the preparation of PDDA-CdTe quantum dot composite film

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CdTe quantum dot was synthesized following literature procedure [47]. After organic composite layer was prepared, quartz glass coated with mercaptosuccinic acid was placed in CdTe quantum dot solution for 10 min. Using this method, the synthesized quantum dot includes carboxyl groups on the surface and thus is negatively charged. After being taken out, the CdTe quantum dot was cleaned with ultrapure water for 2 min, dried, and placed the above PDDA solution for 10 min, taken out, cleaned, and dried again. This deposition process was then repeated until PDDA/CdTe composite layer with required number of layers was acquired. Figure 2 displays the prepared PDDA/CdTe composite layer after 15 layers of deposition under sunlight and ultraviolet (UV) light.

 

Fig. 2 Pictures of the prepared quantum dot film. (a) Under sunlight and (b) UV light.

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3.2 Fluorescence spectral characteristics of quantum dot temperature probe

In this study, green quantum dot with the emission peak at 550 nm was selected for analyzing the spectral temperature characteristics. At 550 nm, the quantum dot exhibits strong fluorescence intensity. For validating the temperature characteristics of the fluorescence spectra of the prepared PDDA/CdTe quantum dot composite film, the prepared composite film was annealed under nitrogen (N₂) atmosphere at 120 °C for 1 h and then the sample surface was spin-coated by a layer of PDMS to prevent the oxidation of quantum dot.

To examine the relationships between various parameters of the fluorescence spectra of the prepared quantum dot and temperature, this study established a set of spectral detection system, which possesses a series of functions of sample heating, temperature monitoring, and spectral signal measurement. Figure 3 displays the principle and structure of the established detection system. The whole system consists of a mercury lamp (100W), a light path module, a microscope thermostat, thermocouples, a spectrometer, and CCD for spectral detection. Figure 3(b) shows the picture of the detection system. UV light at 365 nm is first emitted from the mercury lamp, which illuminates the quantum dot sample after reflection by the dichroscope and focusing via the objective lens. The fluorescence is generated after the excitation of quantum dot, and then passes through the dichroscope; after reflection and focusing, the fluorescence enters into the slit of the spectrometer, split by the grating and falling onto the CCD surface, and finally, the electrical signal is transformed to output via photovoltaic conversion. The temperature of the quantum dot film is adjusted using a temperature controller and varies circularly from room temperature to 110 °C. Moreover, the exposure time and slit width of the spectrometer are adjusted to ensure that the detected fluorescence signal is within the appropriate range. Fluorescence spectra of the prepared PDDA/CdTe quantum dot composite film at different temperatures were also collected. Finally, the corresponding peak wavelength, peak intensity, and half-peak width of the spectral curve were acquired via data processing to analyze the relationship among various parameters and temperature.

 

Fig. 3 Principle and picture of the established fluorescence detection system. (a) Principle of the system. (b) Picture of the system.

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Figure 4 displays the variation curves of fluorescence spectra of the prepared CdTe quantum dot composite film with time in two thermal cycles. Apparently, with increasing temperature, fluorescence intensity drops gradually, peak wavelength gradually undergoes a red shift, and half-peak width becomes wider.

 

Fig. 4 Fluorescence spectra of the prepared CdTe quantum dot composite film in thermal cycles.

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Fig. 5 Variation curves of the peak wavelengths of the fluorescence spectra of the prepared quantum dot film with temperature. (a) In the first thermal cycling process and (b) The second thermal cycling process.

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As shown in Fig. 5, the prepared quantum dot film was investigated by electrostatic self-assembly possesses far more favorable thermal stability, and the sensitivity of the peak wavelength to temperature is 0.14–0.15nm/°C. As listed in Table 2, each variation curve has a good fitness degree of over 0.99. In spite of tiny difference, the fitted relationship curves between the peak and temperature in different processes are all in the allowable error range.

 

Fig. 6 Variation curves of the fluorescence intensity of the prepared quantum dot film with temperature. (a) In the first thermal cycling process and (b) The second thermal cycling process.

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Table 3 shows the linear relationship between the fluorescence intensity and temperature. After the first thermal cycling, the fluorescence intensity of the prepared quantum dot film can be recovered by 90% of that before heating; after the second thermal cycling, the fluorescence intensity increased to 94% of the initial value. The peak fluorescence intensity of the prepared quantum dot via aqueous-phase synthesis only reached up 33% of the initial value after one heating cycle. The prepared quantum dot in this study exhibits great improvements.

Table 3. Linear relationship between the fluorescence intensity of the prepared quantum dot film and temperature in each process

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Fig. 7 Variation curves of the half-peak widths of the fluorescence spectra of the prepared quantum dot film with temperature. (a) In the first thermal cycling process. (b) The second thermal cycling process.

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According to Eq. (7), the relationship between the half-peak width and temperature can be approximately fitted linearly in a broad temperature range, which also fit well with the experimental data. The reversibility of the half-peak width of the fluorescence spectrum to temperature change also confirms significantly enhanced thermal stability of the prepared quantum dot after thermal processing.

 

Fig. 8 Temperature characteristics of the peak wavelength of the fluorescence spectrum of the prepared quantum dot in multiple thermal cycles.

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4. Axial positioning method of the quantum dot

In this section, aiming at axial positioning, dual-helix point spread function was achieved by reasonably designing the related parameters, and the relevant experiments were validated.

4.1 Design of dual-helix point spread function

Dual-helix point spread function is a type of function for describing the optimal system’s interpretation ability of point light source. For the typical imaging system as shown in Fig. 9, the point spread function can be understood as the light field distribution of the corresponding image surface when a point light source exists on the object plane.

 

Fig. 9 Illustration of the defocusing in object space.

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Assuming that $h\left(x_o,y_o,x_i,y_i\right)$ denotes the point spread function and equals to the superposition of several Laguerre–Gaussian beams [48]:

where $x_o,y_o$ denotes the object coordinate, $x_i,y_i$ denotes the image coordinate, $c_j$denotes the weight coefficient, and $u_{m_j{n}_j}\left(r,\theta ,0\right)$ describes the distribution of Laguerre–Gaussian beams in the light field at $z=0$.

According to the properties of the vortex beam, the light field of the observation surface can rotate when the object plane keeps still and the observation plane deviates from the image plane. Based on the convolution exchange law, when the observation plane remains still and the point light source on the object plane is defocused, the image on the observation plane rotates with changing defocusing distance.

As shown in Fig. 9, according to the Fresnel diffraction formula, when the object moves along the optical axis and exhibits defocusing by $\Delta z$, the light distribution on the image plane can be described as:

where $\delta \left(x_o,y_o\right)$ denotes the impulse function and describes the light field distribution on the object plane, $\otimes$ is the convolution sign, and λ denotes the wavelength of the optimal wave.

In this study, Laguerre–Gaussian beams that satisfy $\left|\frac{\Delta n_{jp}}{\Delta m_{jp}}\right|=\frac{1}{2}$ are superimposed as the point spread function of the imaging system to achieve defocusing dual-helix.

4.2 Spectral validation of dual-helix point spread function

For the convenience of design, the group of (m, n) in Laguerre mode was set as (1, 0), (3, 1), (5, 2), (7, 3), and (9, 4) with the same weights. By compiling the program with MatLab language, the images corresponding to different defocusing distances of the point light source were created, as shown in Fig. 10, during which pure phase modulation function was used. The figure shows that using pure phase modulation function, the point light source was imaged to dual light spots, and the spots also rotated around the center as the defocusing distance changed.

 

Fig. 10 Defocusing images under pure phase modulation function.

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Two brightest points in two spots were found and connected. Using the anticlockwise direction as the positive direction and the clockwise direction as the negative direction, the rotating radians corresponding to different defocusing distances were calculated, as shown in Fig. 11.

 

Fig. 11 Variation the rotating radian with defocusing distance when pure phase modulation function is used.

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The defocusing data were then fitted by the arc-tangent function, and the fitted equation can be written as:

where θ denotes the rotating arc (rad), and $\Delta d$ denotes the defocusing distance (m).

The axial position of the quantum dot temperature probe in the cell can be calculated according to Eq. (10). In addition, the radial position is measured by CCD in order to achieve 3D positioning of the quantum dot in the cell.

5. Design of 3D temperature field measurement system

After the fabrication of quantum dot temperature probe and the acquisition of spatial coordinates of the temperature probe, a temperature measurement system was designed to detect the temperature in the cell so as to achieve 3D temperature field measurement.

5.1 Design of 3D temperature measurement system based on quantum dot temperature probe

Figure 12 displays the design scheme of the measurement system. First, the space to be measured is pre-amplified by the micro-imaging system (①), and then the micro-imaging light path is split into two parts, which enter the quantum dot fluorescence temperature measurement system (②) and quantum-dot 3D positioning system (③).

 

Fig. 12 Illustration of the design scheme of the 3D temperature measurement system① Micro-imaging system ② Quantum dot fluorescence temperature measurement system ③ Quantum-dot 3D positioning system.

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The quantum dot first undergoes fluorescence excitation and amplifies images using the micro-imaging system; the imaging light path is split into two paths, and then enters the quantum dot fluorescence temperature measurement system and quantum dot 3D positioning system. The former temperature measurement system mainly consists of the grating spectrometer and the spectral-detection CCD, which is used for measuring the fluorescence spectra of quantum dot and thus achieving temperature measurement. In the quantum dot positioning system, dual-helix point spread function is used as the core, and the quantum dot is imaged into dual light spots, and 3D positions of the quantum dot can be calculated at the spot center and the rotating radian.

5.2 Design of quantum dot fluorescence temperature measurement system

The image spectrometer (Andor Shamrock 303i) and the spectral detector (Andor iDus DU420A-BV) in our laboratory were selected for the design of quantum dot fluorescence temperature measurement system. The image spectrometer is a full-automatic planar-imaging grating spectrometer, which can achieve the spectral measurement with different resolutions by selecting different gratings. The spectrometer operates under the following two modes—imaging mode and spectral measurement mode. Figures 13(a) and 13(b) display the imaging of the quantum dot and the corresponding spectra, respectively.

 

Fig. 13 Illustration of the measurement process of the grating spectrometer.

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The temperature resolution of the temperature measurement system, the grating resolution of the spectrometer, and the sensitivity of peak wavelength of the used probe can be expressed by the following relationship:

where $\Delta T$ denotes the temperature resolution, with a unit of K, $\Delta \lambda$denotes the grating resolution, with a unit of m, and S_wave denotes the sensitivity of peak wavelength, with a unit of m·K-1.

In this study, the grating resolution was as set as 0.1 nm, and the temperature sensitivity of the peak wavelength of the prepared quantum dot temperature probe is approximately 0.16nm/°C; after calculation, the temperature resolution of the developed measurement system was found as 0.625 °C.

5.3 Calibration of the quantum dot temperature probe

The calibration of quantum dot temperature measurement system mainly refers to the calibration of the temperature characteristics. The relationship between the temperature and fluorescence peak wavelength is first experimentally calibrated for further temperature measurement. Using the above-described method, CdTe quantum dot was prepared, and green fluorescence quantum dot was obtained when the reaction lasted for 2.5 h, as shown in Fig. 14.

 

Fig. 14 Prepared quantum dot in the present experiment.

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Next, the spectral temperature measurement was used for calibration. Figure 15(a) displays the fluorescence spectra of the prepared quantum dot at different temperatures. Through Gaussian fitting, the corresponding peak wavelength was calculated. The relationship between the fluorescence peak wavelength and temperature was also fitted for subsequent temperature measurement. Figure 15(b) shows the fitted line. Through linear fitting, the relationship between the peak wavelength and temperature can be written as:

 

Fig. 15 Relation between the quantum dot fluorescence spectra and temperature. (a) Fluorescence spectra of the prepared quantum dot at different temperatures. (b) Relationship between the fluorescence peak wavelength and temperature.

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where λ denotes the fluorescence peak wavelength of the prepared quantum dot, with a unit of nm, and T denotes the temperature of the prepared quantum dot (°C).

6. Experiment and analysis of the results

In this section, experiment was designed for achieving the positioning of quantum dot temperature probe and measuring the temperature change of the prepared quantum dot during the heating process to evaluate 3D temperature measurement ability of the developed measurement system. Figure 16 illustrates the installation of the quantum dot temperature probe and the heating sheet. The heating sheet of the temperature controller (③) is in direct contact with the fixed support of the movable object slide (②), and the object slide with the quantum dot (①) is placed above the fixed support (②).

 

Fig. 16 Picture of the quantum dot temperature probe and the installation of the heating sheet ① Quantum dot temperature probe ② the fixed support of movable object slide ③ heating sheet of the temperature controller.

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During the experiments, the image was observed via the eye lens, and the position of the object slide was adjusted so that insufficient quantum dots with high fluorescence intensity can be included in the field of view; meanwhile, the operating distance of the objective lens was also adjusted to acquire clear images. Next, the images of the quantum dots were acquired by the camera. For distinguishing the prepared quantum dots and background, the overall contrast of the images was enhanced via histogram equalization, and the effect of background noise was also reduced with the use of mean filtering algorithm. After the above processing, a few number of quantum dots were found and marked in green, as shown in Fig. 17.

 

Fig. 17 Image of the quantum dots after processing. (a) In high-concentration region and (b) In low-concentration region.

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As shown in Fig. 17(b), three quantum dots were then selected as the measurement objects. Using the image center as the origin, the image of three quantum dots was processed. The extremely bright points in dual-spots were extracted and connected, and the midpoint was selected; the horizontal position was then calculated according to the CCD measurement results while the axial position was calculated in accordance with the inclination angle of the connecting line and Eq. (10). Finally, 3D positions of three quantum dots in the space were acquired, as listed in Table 5.

Table 5. Spatial positions of the quantum dots

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The temperature of the temperature controller was set as 65 °C, and the temperature controlled was switched on for heating the quantum dots. Meanwhile, the spectral measurement program started for automatically measuring the fluorescence spectra of the quantum dots. The measured spectra were then Gaussian fitted, and the temperatures of the three probes were solved according to Eq. (12). Since the three quantum dot temperature probes were located at different positions in the space, they exhibited different heating processes, as shown in Fig. 18.

 

Fig. 18 Temperature variations of the quantum dot temperature probes in heating process.

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Accordingly, 3D positioning and temperature measurement of the prepared quantum dot temperature probes were realized and also validated for 3D temperature measurement ability of the designed system. The peak wavelengths of quantum dots can be measured by the experiment as 543.66, 543.59 and 543.92 nm, respectively. By substituting the peak wavelength values into Eq. (12), the corresponding initial temperatures of the three quantum dot probes can be calculated as 23.85, 23.47 and 25.40 °C. Then they gradually increased to the maximum at 300 s, and the temperature of QD2 was the highest at 38.25°C. The color of quantum dots represents its temperature value. The color changes from dark blue to dark yellow, and the corresponding temperature range ranges from 22 °C to 40 °C.

If we can break through the effect of cell toxicity on the temperature probe of quantum dots, the above experiments can be used to measure the three-dimensional temperature distribution of the internal temperature field of the cell. The hypothesis is shown in the upper left of Fig. 18. As the heating process continues, it can be observed from Fig. 18 that the color of quantum dots changes slowly and yellow shifts, which indicates that the temperature of quantum dots increases. It also means that the temperature of cells corresponding to quantum dots increases gradually. The proposed method that can accurately monitor three-dimensional (3D) temperature gradient distribution in cells and tissues or even on subcellular level and detecting subtle change in local temperature can greatly enhance the detectability of tumors and local inflammation and provide a more precise monitoring tool for hyperthermia.

7. Conclusions

In this study, the temperature characteristics of peak wavelength, peak intensity, and half-peak width of the fluorescence spectra of the prepared quantum dot were investigated, and the fitting relationship between the florescence peak wavelength of the quantum dot and temperature was established. First, CdTe quantum dot temperature probe was prepared by the means of layer-by-layer electrostatic self-assembly technique. In addition, some optimization methods for temperature characteristics were proposed. In addition, the probe’s spectral characteristics were effectively characterized. According to the experimental results, the sensitivity of the prepared CdTe quantum dot probe is 0.16 nm/°C. Moreover, the prepared CdTe quantum dot temperature probe exhibits strong stability and excellent reversibility in thermal cycles, favorable light resistance as well as less susceptibility to environment, which can thus be capable of continuous measurement for a long time. In addition, 3D positioning method based on dual-helix point spread function was proposed. Based on grating spectrometer, 3D temperature field measurement system with a temperature resolution of 0.625 °C was designed to achieve spatial positioning and temperature measurement of the prepared quantum dot. The present study successfully overcomes the problem that 3D temperature can hardly be measured on micro-nano scale and used for the measurement of 3D temperature distribution in the cell, providing a novel research tool for further revealing the cell metabolism.