1. Introduction

Measuring temperature at the nano and micro scales exhibits inherent limitations due to the non-propagative nature of heat, unlike light. Despite this, attempting to quantify thermally induced phenomena in this domain would greatly contribute to the development of innovative applications across various active research fields, such as drug release and transport [1,2], nanosurgery [3], optoacoustic imaging [4], photothermal cancer therapy [5–7], microfluidics [8,9] and storage of thermal information as memory [10]. Several methods of non-contact temperature measurement using optical detection from a distance have been developed so far. These techniques generally rely on either fluorescence intensity ratios [11,12] or the corresponding fluorescence lifetimes [13]. In recent times, researchers have also begun to investigate the potential of spectroscopic methods like Raman [14,15], infrared [16], and x-ray [17] for improving the precision and spatial detail of local temperature measurements. However, since all of these methods are fundamentally optical, there are a number of challenges that hold them back. The slow acquisition rate [14,16], lack of reliability [18], and low thermometric resolution are some of the major drawbacks. Out of these optical techniques, nanoscale temperature sensing based on fluorescence intensity assays (FIR techniques) has been recognised in the community since most of the fluorescent probes are either easy to synthesise or commercially available. These cover a large range of temperatures to be sensed with good sensitivities [11].

FIR techniques based on upconverting particles (UCPs) are particularly useful in this regard since these particles are abundant with thermally coupled energy levels [19–24]. Hence, one can employ multiple techniques with the same particle as probe by analysing either the FIR ratio, spectral shift, the polarimetry of spectra or by acquiring the spectral lifetime changes [19]. However, the most commonly used NaYF${_4}$, Yb$^{3+}$, Er$^{3+}$ upconversion particles are reported of poor thermometric sensitivities (in the orders of 10$^{-4}$ / K [25,26]).

These particles are identified as crucial probe particles in optical tweezers [27,28] because of their size [29], adequate refractive index [30,31], tuneable absorption by choice of wavelength [32,33], and low intra-cellular toxicity [34,35]. The size of the UCP has also been shown to impact its thermometric sensitivity, with larger sizes leading to reduced sensitivity, as reported in the study by Dong et al. [25].

When it comes to a single UCP in an optical trap at its resonance wavelength, Kumar et al. have shown that the particle follows hot-Brownian dynamics inside the trap [29], and recently with the same hot-Brownian UCP in optical tweezers, a microscopic Stirling engine has also been demonstrated by exploiting the anisotropic heating of the particle [36]. These works have exclusively shown the effects of optical heating of such particles on their dynamics. Thus, it is imperative to estimate the self-heating of such UCP in optical tweezers.

In this work, we first show that the luminescent thermometric technique fails to determine the degree of optical-heating of this particular, NaYF${_4}$, Yb$^{3+}$, Er$^{3+}$ UCP, pumped with the excitation wavelength sensitively. Subsequently, we present a thermo-optical phase microscopic method that relies on wavefront imaging of the emitted light from the particle. Previously, researchers have explored optical phase microscopy methods to achieve precise determination of optical path differences [37,38], enabling the extraction of refractive indices [39] with enhanced spatial resolution. However, these works failed to consider the convection currents formed due to the local heating. Here, we investigate how the phase change in the emission wavefront of a particle can account for the temperature change of the particle and its proximity, thus, the refractive index profile of its environment. An upconverting particle, illuminated by a 980 nm laser generally dissipates heat energy into the surrounding water [40], and a noticeable temperature gradient emerges within the water, especially near the particle. This gradient is particularly prominent along the path of the back-scattered emission. Such a local, heat-induced temperature profile of water, in turn, generates a gradient of the refractive index. We first show the temperature profile around the particle in such a configuration using COMSOL simulations where the conditions are matched with experiments. Experimentally, we capture the effects of optical-heating of an irradiated UCP in the emission wavefront of one of its thermally coupled emission spectral lines (550 nm). Furthermore, we standardize the relationship between the calculated temperature rise and phase values observed to establish a universal sensitivity parameter for the particular particle we used. There have been reports in the literature to estimate the temperature of a microscopic object using phase fronts [37] , [41] but the exact effect of heat generated by the upconverting particles have not been studied.

Here it may be mentioned that the proof of heating in upconverting particles is the formation of vapor bubbles shown in [29]. It was also shown that the UCPs can heat enough to kill cells within a minute [40] when placed inside it.

2. Theory and numerical modelling

We numerically study the changes in the flow behaviour in the water caused by heating in a 2D square enclosure having a height and width of 200 µm. Although a square domain has been chosen for the analysis, the results will be similar for domains having other shapes also. The enclosure is filled with water at ambient temperature ($T_0$ = 293K). Impermeable walls enclose the 2D domain on all sides. We assume that the temperature of the side walls remains fixed at $T_0$ during the heating process. We consider a square-shaped solid particle very close to the top wall. The particle acts as a hotspot causing the water to heat up [42]. We assume the particle temperature ($T_p$) remains constant during the study. Further, we assume the flow in the enclosure is laminar and the Boussinesq approximation is valid. The Boussinesq approximation is often used to study simple buoyant flows to avoid using the computationally expensive compressible form of the Navier-Stokes equations [43–45]. It considers that the changes in the fluid density due to changes in temperature give rise to buoyant forces but do not affect the flow field in any other way. In other words, the fluid density term in the Navier-Stokes equations is taken as constant except in the body force term. On the other hand, the body force term is considered as $\mathbf {F}=\left (\rho _0+\Delta \rho \right ) \mathbf {g} =\rho _0 \mathbf {g} -\frac {\rho _0\left (T-T_0\right )}{T_0} \mathbf {g}$ [45]. Here, $\mathbf {g}$ is the gravity vector, $\rho _0$ is the fluid density at ambient temperature $T_0$ and $\Delta \rho$ is the change in fluid density due to change in fluid temperature $\left (T-T_0\right )$. Therefore, the continuity, momentum, and energy equations take the following form [45,46],

Here, $\mathbf {u}$ is the fluid velocity, $p$ is fluid pressure, $\mu _0$ is the dynamic viscosity of water at temperature $T_0$. $T$ is the fluid temperature and $C_p$ is the constant pressure heat capacity. $K_0$ is the thermal conductivity of water at temperature $T_0$. $Q$ denotes the thermal dissipation term.

Here, only the case where $T_p=302.61K$ is discussed in detail for brevity (Fig. 1). The highest temperature is obtained in the immediate surrounding of the particle (Fig. 1(a)). We observe that the high-temperature region just below the particle spans a significant volume of water. Figure 1(b) shows the velocity magnitude inside the enclosure at a steady state. The warmer water immediately below the particle has a lower density than the surrounding cold water. This causes the surrounding cold water to replace the warmer water, which then moves up. Consequently, the highest fluid velocity is obtained below the particle. As the warm water moves up, it is reflected by the enclosure wall and the particle. This causes the warm water to move down along both sides of the particle. The motion of the fluid creates a few vortices in the enclosure. The arrows indicate the motion of the fluid inside the enclosure. The thermal conductivity of glass is about 1 W/(m.K.) while that of water is 0.5 W/(m.K.) which would be accentuated even further due to the convections.

 

Fig. 1. (a) Temperature T (K) contour and (b) velocity magnitude V (m/s) at steady state around the particle of 5 µm size. Here, the particle temperature is set at $T_p=302.61$K (resultant temperature with an irradiation of 975 nm laser at 3.3 MW/cm$^2$ intensity. (c) indicates the steady state temperature distribution along the mid-section (denoted by A-A in Fig. 1(a)) of the enclosure and the corresponding variation in the refractive index ($n$) of the water over layers. $x (\mu m)$ is the distance of the point under consideration below the particle. To compare the experimental geometry, we have only presented the temperature variation for $x=0-30$ $\mu m$.

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2.1 Strategy for estimation of temperature at various powers

It is instructive to visualize the temperature distribution (Fig. 1(c)) along the mid-section of the enclosure (denoted by A-A in Fig. 1(a)). $x (\mu m)$ is the distance of the point under consideration, below the particle. To match with the experimental geometry, here we present the temperature variation for $x=0-30$ $\mu m$ below the particle. It is seen that the water temperature below the particle reduces linearly with distance from the particle.

Here, the temperature ($T$) dependence of the refractive index of water ($n$) is generally obtained from the empirical formula [47],

We then take the temperature profile estimated from the previous simulation and try to match with experimentally obtained profile. In order to do that, we estimate the phase change in the water medium due to the temperature. Then, we assume that the total extra phase accrued by the light emanating from the particle is given as the excess phase change due to the higher temperature in water and match the two phase profiles to estimate temperature of the particle. This process is repeated for the various phase profiles due to the various powers.

The calculated values of the temperature-dependent refractive index are plotted in Fig. 1(c). The optical path ($\Lambda$) acquired by the light of emission inside the 30 µm sample chamber is given by,

The integral is performed along the line A-A. The corresponding phase ($\Phi$) acquired is $\frac {2\pi }{\lambda } \,\times \Lambda$. Here, we fix the wavelength ($\lambda$) at 550 nm both in simulations and experiments. We use 550 nm for the measurements because we have the 550 $\pm$ 10 nm interference filter with us.

Moreover, theoretically, the resulting change in temperature of the upconverting particle ($\Delta$T$_{calc}$) is generally calculated as [5,48],

3. Experimental details

3.1 Optical tweezers setup

The experiments are performed using an optical tweezers setup in an inverted microscope configuration, built from OTKB/M kit, Thorlabs (USA). We use a laser of wavelength 975 nm (butterfly type, 300 mW) to illuminate the sample particles. The schematic of the whole setup is depicted in Fig. 2(a). The laser is directed to the objective (oil immersion type, 100x. 1.3 NA) with a dichroic mirror (DM-1), after which it is tightly focused in the sample chamber. The sample chamber is illuminated from the top using a combination of white light LED, dichroic mirror (DM-2) and a condenser lens (air immersion type, 10x, 0.25 NA). It is then imaged using a CMOS camera (Thorlabs).

 

Fig. 2. a) The schematic of the experimental setup is shown. Inset shows the schematic of the sample chamber and the emission of an upconverting particle while illuminated with a 975 nm laser. The immediate water layers to the bottom side of the particle get heated up, giving rise to a temperature gradient ($\nabla$T) along the axial direction (z). DM - dichroic mirror, PBS - polarising beam splitter, BPF - bandpass filter (550 $\pm$ 10 nm), BS - beam splitter, SH - Shack- Hartmann wavefront analyser, BD - beam dump. b) FE-SEM image of a 5 µm sized UCP is shown to confirm its size and geometry.

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The sample specimen for the experiment is prepared by suspending upconversion particles (UCPs) in (De-Ionised) D.I. water, 20 µl of which is transferred to a glass slide (English glass, size 1) and is then mounted using a square coverslip (English glass). We look for a single particle that has adhered to the top surface of the sample chamber, oriented in a hexagonal face-on sense. The thickness of the sample chamber is measured to be 30 µm. The particle is illuminated with the laser at different intensities of illumination, and the emission from which is collected using a spectrometer and Shack-Hartmann wavefront sensor (see Fig. 2(a)). We use the 550 nm emission band for the purpose of wavefront construction.

There have been widely reported sensors and integrated optics for high upconversion efficiency, as reported in [49–57]. The Shack-Hartmann wavefront sensor (model FS1540-H300-F18-16.04, manufactured by OKO Technologies) is a prevalent variation of wavefront sensors. It operates by utilizing an arrangement of microlenses onto which the incoming light is collimated. The uniformly distributed light on the array is collected through a CCD camera, which is positioned precisely at the microlens array’s focal plane [58]. The employed sensor comprises a grid of 217 microlenses to constitute a hexagonal shape. In this configuration, each individual lens focuses the incoming radiation onto a designated point on the CCD sensor. The positioning of this focal point is then fine-tuned to account for the local distortions within the incident wavefront, which are averaged across the lenslet’s entire area.

3.2 Preparation of upconverting particles (UCPs)

Upconverting microparticles (NaYF${_4}$, Yb$^{3+}$, Er$^{3+}$ microparticles or UCPs) are prepared using the hydrothermal method [59]. Initially, about 1.23 g of sodium citrate (Na$_3$C$_6$H$_5$O$_7$) and 1.26 g of yttrium nitrate (Y(NO$_3$)$_3$, 63 at.% of Y) are dissolved and magnetically stirred on a hotplate for 10 minutes. A white solution is produced by combining the earlier solution with 0.38 g of ytterbium nitrate (Yb(NO$_3$)$_3$, 20 at.% of Yb) and 0.037 g of erbium nitrate (Er(NO$_3$)$_3$, 2 at.% of Er), which have been dissolved in 21 ml of the aqueous solution. Then, 1.411 g of sodium fluoride (NaF) is added to 67 ml of DI water to turn it into a transparent solution. We then stir it magnetically for one hour. The final mixture is then transferred to an autoclave lined with Teflon and carefully sealed. The autoclave reactor is heated for 12 hours at 200 $^{\circ }$C in a muffle furnace. The resultant white powder is cleaned five times with ethanol and water and then dried at 100 $^{\circ }$C to extract the sample in its purest form. The particle is observed to have a regular hexagonal geometry with a diagonal length of 5.1 $\pm$ 0.1 µm [60]. A microscope image of these particles is shown in Fig. 2(b). The lattice of these particular upconversion particles is comprised of NaYF$_4$, while the dopants Yb and Er replace the Y sites [33,61,62].

4. Results and discussions

Upconverting particles are known for their thermal response to the environment and are often used as luminescent thermometers on micro and nanoscale [11,19,26]. Generally, these particles have strong absorption of NIR radiation but with poor efficiency for upconversion (around $\sim$ 2 - 5 % for Yb$^3+$ and Er$^3+$ based pristine UCPs [63–66]. The rest of the absorbed energy is equivalently converted into heat by many non-radiative energy transfers [63,67]. The heat generated is enough to induce convection currents in water, which have been used to even form self -assembly [42,68]. Effectively, a temperature gradient that predominantly extends a few microns can be observed near the illuminated particle, along the back-scattered direction [29,40]. We show these effects of optical heating of the particle using a set of COMSOL simulation results, plotted in Fig. 1(a).

4.1 Temperature sensitivity from the spectral change analysis

To measure the local temperature in the case of optically heated UCPs, one can employ these particles that are abundant with thermally coupled energy levels. From diffusive reflectance spectroscopic characterisation of UCPs, $\sigma$ is obtained to be 9.68 $\times$ 10$^{-12}$ cm$^2$ at 975 nm (from the normalised absorption spectra, Fig. 3(a)), $\kappa$ for water is 0.598 W/m$\cdot$K at 25 $^{\circ }$C, and half the diagonal length (r) of the particle is 2.55 µm. It has been reported that NaYF${_4}$, Yb$^{3+}$, Er$^{3+}$ UCPs are characterised by thermally coupled energy levels at 520 nm and 550 nm to ground state [19,69,70], the intensity changes of which sense the temperature of the surroundings. The strong absorption of the 975 nm line by the particle, which is responsible for its optical-heating, is shown in Fig. 3(a). In Fig. 3(b), we show the corresponding emission spectra of a single UCP upon 975 nm laser illumination as a function of power density.

 

Fig. 3. a) shows the visible - NIR absorption spectra of the UCPs obtained from a diffusive reflectance spectrometer, taken in bulk. In Fig. (b), the emission spectra of a single UCP upon illumination with a 975 nm laser at different intensities are shown. In Fig. (c), the fluorescence intensity ratio (FIR) between the bands of 550 nm and 520 nm as a function of laser power density (I$_{ex}$) is shown, and in Fig. (d), the logarithmic plot between excitation ($I_{ex}$) and emission (of 550 nm line, $I_{em}$) intensities are plotted and the slope of which is found to be 2.03 $\pm$ 0.08, affirms the two-photon upconversion. A single upconverting particle can be either optically trapped or one placed on a glass surface isolated for the spectrum measurement. This was used for (b). All other measurements ((a), (c) and (d)) were in bulk.

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The conventional thermometry mechanism relies upon the fluorescence intensity ratio (FIR) between the thermally coupled levels at 550 nm and 520 nm. And in this case, the thermometric sensitivity (S) is defined as S $= \frac {\delta (FIR)}{\delta T}$ [21]. We plot FIR as a function of incident laser power density (I$_{ex}$) in Fig. 3(c) and show that FIR is unaffected by the increase in laser intensity, affirms the poor thermometric sensitivity of the single UCP we used.

In addition, we fit the logarithmic plot between incident laser intensity and emission intensity of 550 nm to a straight line with a slope of 2.03 $\pm$ 0.08, from which two-photon upconversion is evident(see Fig. 3(d). It implies that even at a power density of several MW/cm$^2$, the emission intensity of the thermally coupled 550 nm band does not show any sign of local heating, although the effects of optical-heating have been observed in several experiments earlier [29,71]. It makes these particles incompatible for the purpose of thermometry. Hence, we find that at a single particle level, though these particles are observed with high absorption and poor upconversion, the heat generated by them cannot be determined by their intrinsic luminescent thermometric mechanism, and one can infer that NaYF${_4}$, Yb$^{3+}$, Er$^{3+}$ UCPs are observed with very low thermometric sensitivity and poor photothermal conversion.

4.2 Thermo-optical phase microscopic technique for thermometry

We now investigate the wavefront imaging of the emission from the particle using a commercial Shack-Hartmann wavefront sensor. A single UCP in the face-on configuration is excited with a 975 nm laser at fixed intensities of illumination (see Fig. 4(a)). The emission from the particle is filtered at 550 nm and directed towards the Shack-Hartmann sensor, the illumination on the microlenses array of which is shown in Fig. 4(b). We standardise the offset of the experiment by finding the bare wavefront when there is very low emission from the particle, which is then taken as a reference throughout the experiment. Here, we find that, unless we use a power density value above 0.2 MW/cm$^2$ to excite the particle, the detector shows a completely flat wavefront, which is also found to be the threshold of the detector. We use slightly higher intensities of illumination above this threshold to ensure the proper illumination of the Shack-Hartmann sensor by the particle. In this manner, we obtain the baseline wavefront at a laser intensity of 0.33 MW/m$^2$, where the calculated rise in temperature is 0.23 K. The rise in temperature has been estimated from the straight line in the inset given in Fig. 4(f).

 

Fig. 4. In Fig. (a), the emission of a single UCP is imaged while the particle is illuminated with a 975 nm laser at 1.3 MW/cm$^{2}$ intensity. b) shows the illumination on the micro-lenslet array of the S-H sensor by the emission of the particle. In (c), the offset of the experiment is shown, obtained by not illuminating the particle with the laser. The wavefronts detected by the S-H sensor (with offset subtracted) when the power density is increased to (d) 0.33 MW/cm$^{2}$ (e) 3.26 MW/cm$^{2}$. Phase values are measured in radians. In (f), the peak phase detected ($\phi _{exp}$) in the experiment and the total phase acquired by the 550 nm line of the emission, obtained by simulations, are plotted against the calculated temperature from Eq. (6). Inset shows the plot between $\Delta$T$_{calc}$ and the illumination intensity. The slopes, $m_{sim}$ and $m_{exp}$ of the linearly fitted plots indicate the sensitivity parameters from simulations and experiments, respectively. Both the experimental and simulated data are correct to an additive arbitrary constant. Hence we adjust the constants to overlap the two sets of data.

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We establish this measure of phase change as the sensitivity of the sensor towards the thermo-optical phase microscopy. The Gaussian wavefronts (Fig. 4(d-e)) obtained at each power density are compared to each other in terms of the peak phase values($\phi _{exp}$). We observe that the peak phase values of the constructed wavefronts decrease as a function of illumination intensity on the particle, as shown in Fig. 4(f). We infer that this effect in phase is due to the local heating of the particle, which generates a temperature gradient across the water layers below the illuminated particle (see Sec. 4 for the experimental configuration). This local temperature rise may then introduce a refractive index gradient along the direction of the UCP’s emission, as shown by the simulations in Fig. 1(c).

The optically induced thermal gradient in water alters the optical path of the light being emitted by UCP and sensed by the S-H sensor. From the simulations, we calculate the refractive index change along the direction of emission at each calculated temperature value (using Eq. (6)). Also, the experimentally determined phase values are plotted as a function of the calculated change in temperature of the particle in Fig. 4(f). The same graph is overlaid with the calculated phase values as a function of $\Delta T_{calc}$. We observe a phase change of 0.088 radians in simulations. However, from the experiments, we find a value of 0.112 radians for a rise of 2.35 $^\circ$C in temperature (see Fig. 4(f). We define a sensitivity parameter ($m$) both from experimental and simulation results and make a comparison to each other to standardize the particle for temperature detection techniques. The sensitivity parameter is obtained from the slope of the graph between $\Delta T_{calc}$ and $\Phi$. And the sensitivity parameters of a single NaYF${_4}$, Yb$^{3+}$, Er$^{3+}$ particle, obtained from both simulations and experiments are given as, $m_{sim} = -0.0372\,\pm \,0.0002$ rad / $^{\circ }$C and $m_{exp} = -0.047\,\pm \,0.011\,$ rad / $^{\circ }$C respectively. This disparity may be inherently linked to the constraints imposed by the empirical formula that we use to determine the refractive index of water and subsequently derive the corresponding phase values. One could obtain more accurate values by expanding Eq. (4) further and thereby introducing the contribution of higher-order coefficients. In this manner, analyzing the phase change that occurred due to the localized heating of an upconverting particle, the particle can be standardized and further used as a very sensitive temperature sensor on the microscale.

Our technique is constrained to trying to extract the form of the absolute temperature gradient in proximity to the particle. Here, we emphasize that the heat-induced refractive index gradient of water is the main cause of the shift in the observed emission wavefront observed. The effect of this temperature gradient is observed to be significant in the range between a few nanometers to several micrometres below the illuminated particle, as simulated in Fig. 1(a,b).

4.3 Effects of self-heating of an optically trapped UCP

A single UCP optically confined at absorption wavelength (975 nm) has significant self-optical heating and observable in the axial dynamics of the particle (z-axis). The particle is generally trapped in a side-on sense [29,36], and a temperature gradient is observed across its hexagonal face. Due to this asymmetric temperature profile, the particle diffuses thermophoretically within the trap. This effect is observed as a super diffusion at its axial dynamics, as shown in Fig. 5(a). Figure 5(b) shows the corresponding power spectral density plot fitted with a Lorentzian. In earlier studies, such dynamics of the particle are referred to as hot Brownian motion [29,72] with a super-diffusive mean square displacement (see Fig. 5(c)), fitted with an expression that defines thermophoretic velocity and relaxation time (see Eq. (6) from our previous work [29]). Further, the histogram of the z positions of the particle, indicated in Fig. 5(a) deviates from a Gaussian and becomes a skewed Gaussian. Generally, the thermophoretic velocity ($v$) of the particle is defined as $v = -D_T\nabla T$ [36]. Where $D_T$ is the thermophoretic mobility defined by the Soret coefficient ($S_T$) and hydrodynamic diffusion constant ($D$) of the particle as $D_T = S_TD$. Here, the diffusivity, $D$ can be obtained from the amplitude of the Lorenzian fit at sufficiently large frequencies where trap forces dominate the activity of the particle. We assume that the top part has low temperature while the bottom part has 2.5 C higher temperature, such that the gradient of temperature is 0.5 C/($\mu$m)

 

Fig. 5. Fig. (a) shows the calibrated axial displacement time series (z-axial) of an optically trapped UCP. In Fig. (b), the corresponding power spectral density is plotted and calibrated with a fitted Lorentzian curve. In Fig. (c), the MSD v/s lag time is plotted for the time segment marked in Fig. (a). The velocity ($v$) and diffusion coefficient ($D$) obtained from the fit is 68.09 $\pm$ 4.5 nm/s and 42.8 $\pm$ 3.8 nm$^2$/s. The inset shows a schematic where the temperature gradient across trapped UCP due to its optical heating in our experiments is depicted (T$_h$ and T$_l$ denote the high and low temperatures at the edges of the particle, respectively). The laser power density at the trapping plane is measured to be 1.13 MW/cm$^2$.

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In this context, it should be noted that the confined UCP moves in a direction that takes it away from the centre of the trap. Consequently, the velocity ($v$) aligns with the direction of the temperature gradient ($\nabla T$), leading to a positive Soret coefficient exhibited by the particle. We calculate the velocity and diffusion constant values from the experiment at a trap laser intensity of 1.13 MW/cm$^2$. The Soret coefficient of a single UCP is then estimated to be 27 $\pm$ 4 /K, the magnitude of which is comparable to that of polystyrene spheres [73] but with the opposite sign. As wavefront microscopy contains information about the temperature gradient along the z-axis of the system, one can easily find the Soret coefficient of the particle in this manner. In this manner, the thermophoresis of any absorbing particles can be quantified.

5. Conclusions

To summarise and conclude, we have introduced a thermo-optical phase microscopic technique to image the wavefront of the emission from an upconverting particle in water. It is achieved by coupling a Shack-Hartmann wavefront sensor to a conventional inverted optical microscope. We perform simulations to quantify how the theoretically calculated heating of the particle affects its environment. We show that our technique is more sensitive than conventional FIR methods employed with upconverting particles. A thorough comparison between the upconverting particles for nano and micro thermometry that have recently been reported and our current work is systematically presented in Table 1. We have compared the degree of heating of the particle at different laser intensities and the numerically calculated particle temperature rise based on the intensities. The change in the refractive index of water in proximity to the UCP needs to be quantitatively and experimentally studied further. One can combine multiple thermometric techniques that work with UCPs with our wavefront imaging mechanism to measure temperature over a wide range of values with enhanced sensitivity and accuracy. We also emphasize that our method can be employed with other fluorescent particles with similar degrees of heating like rod shaped particles of dielectric materials, plasmonic structures like gold nanoparticles and other micro heat sources. In this line, critical applications may be developed in multiple disciplines, such as cellular biology, soft matter, and microfluidics. We do not know the exact upper bound for the estimation of temperature but believe it should be at least 20 degrees above the ambient temperature.

Table 1. The table illustrates the comparison of distinct lanthanide doped luminescent thermometers at 300 K. $\delta$T denotes the temperature uncertainty or temperature resolution of a particular system.

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