Introduction

Temperature, a measure of molecules’ average translational kinetic energy, brings both life and force. It breathes warmth into life, drives the currents of oceans and winds, and fuels the engines of industry through its gradients, yet also mirrors the profound implications of global warming1 and shifts the states of matter, presenting challenges in harnessing its immense power2,3. As modern industrial materials and systems are pushed to their thermal limits, accurate high-temperature measurement becomes increasingly crucial. For instance, the ever-growing demand for higher thrust-to-weight ratio aircraft engines has driven turbine inlet temperatures to approach the hydrocarbon stoichiometric limit of 2400K4, which is expected to surpass the melting point of blade materials further. Despite advancements in high-temperature materials and sophisticated cooling methodology, precise temperature monitoring remains essential for operation safety assessment, thermal stress compatibility, and component lifespan forecast. In such a harsh environment, noninvasive radiation thermometry is more preferred than other techniques as it has a much higher measurable limit and no risk of ablation.

For an absolute temperature \(T\), the maximum thermal radiation per unit area and unit solid angle is emitted by an ideal blackbody based on Planck’s spectral distribution:

$${V}_{b}\left(\lambda,T\right)=\frac{{c}_{1}{\lambda }^{-5}}{{e}^{\frac{{c}_{2}}{\lambda T}}-1}$$
(1)

In this equation, \({c}_{1}=1.4388\times {10}^{3}\,{{\rm{\mu }}}{{\rm{m}}}\,{{\rm{K}}}\) and \({c}_{2}=3.7418\times {10}^{8}{{\rm{W}}}\,{{{\rm{m}}}}^{-2}\,{{\rm{\mu }}}{{{\rm{m}}}}^{4}\) is the first and second radiation constants. \(T\) is the thermal temperature. \({V}_{b}\) is the radiation of a blackbody at wavelength \(\lambda\) and temperature \(T\). However, a real surface emits only a portion of the blackbody radiation:

$$V(\lambda,T)=\varepsilon \,(\lambda,T){V}_{b}\left(\lambda,T\right)$$
(2)

where the spectral emissivity \(\varepsilon \left(\lambda,T\right){{\rm{\epsilon }}}\,[{\mathrm{0,1}}]\) depends on wavelength, temperature, and material properties (neglecting the influence of emitting direction).

The unknown emissivity poses a significant challenge for accurate temperature measurement; assumptions on emissivity (e.g., a given value or an empirical model) have to be made if only limited channels of thermal radiation are available. Single-wavelength and dual-wavelength pyrometers consider narrow-band incoming radiation as a discrete wavelength and calculate the temperature from a single channel or ratio of two channels of radiation5,6, which inevitably relies on the assumption of wavelength-independent emissivity and results in considerable measurement error7,8,9. Recent meta-lens applications for infrared-band10 and dual-wavelength11 thermometry follow a similar trend. Multi-spectral thermometry (with \(n\ge 3\) spectral channels) demonstrates a significant advantage in determining emissivity by utilizing a larger system of equations12. Temperature measurement accuracy can be further improved with sophisticated optimization algorithms and deep learning networks if a sufficient number of spectral radiance values is available. However, as the number of spectral channels increases, the spectrum splitting optics tends to become cumbersome and bulky, making it more suitable for ideal laboratory experiments than for practical applications in a space-limited and harsh environment. The inherent bulkiness of conventional lenses has posed significant obstacles to system miniaturization, compelling researchers to pursue alternatives like computational imaging to overcome these limitations. Most recent efforts have increasingly focused on computational imaging techniques to handle compressed snapshot imaging13,14. For instance, multi-spectral light-field thermometry (MSLF) combines an optical filter array with a microlens array to capture multi-spectral radiance with one snapshot15,16,17,18. Such a method could simplify the multispectral optics to some extent; nonetheless, the inherent thickness of conventional lenses remains a significant barrier to achieving compactness and miniaturization.

Rather than concentrating solely on well-established conventional lens techniques, it might be the right time to think outside the box and place hope on innovative flat optics. Recently, meta-lens has become an advanced application of metasurface, consisting of sub-wavelength nanoantenna arrays that allow precise control of phase19,20, amplitude21, polarization22, and spectrum23. By tailoring the arrangement and dimensions of these nanoantennas, a meta-lens can achieve novel electromagnetic properties. This technology significantly reduces the size of optical devices while providing enhanced functionalities for imaging24,25, sensing26, and functionalities of achromatic27 or aplanatic28. Due to their compact, planar structure and high integration potential, meta-lenses have rapidly progressed from principle exploration to function design.

Regarding spectrum manipulation, the meta-lens greatly contributes to hyperspectral and achromatic images. To eliminate chromatic aberration while avoiding suffering from bulky lens systems, transmissive and reflective achromatic meta-lenses have been developed in infrared and visible bands29,30. However, the spectral signals are stacked on the same focal plane, making it challenging to separate the information from individual channels. Therefore, chromatic meta-lenses have been designed for multi-foci across multiple channels28,31. It is inevitable that images from different focal planes have crosstalk from defocused spectral information. Therefore, a dispersive meta-lens is the most suitable device for high-temperature spectral sampling. The initial solution to this challenge is the development of a discrete dispersive meta-lens, achieved by arranging nanoantennas corresponding to specific discrete wavelengths32,33. Although achieving narrow-band transmission remains intricate, leading to occasional crosstalk from untailored spectral bands, our early theoretical study suggests meta-lens has great potential in radiation temperature measurement34. To avoid the crosstalk caused by untailored dispersion bands, a dispersive meta-lens with a nanoantenna array manipulated across the entire waveband is necessary.

While nanoantennas of infrared dispersive meta-lens are relatively easier to design and fabricate than their visible counterparts, and the infrared band is normally considered for temperature measurements, this work initiates the exploration of hyperspectral thermometry via meta-lens in the visible band for the following considerations. Firstly, accurate measurements for high temperatures are more challenging and demanding in engineering applications. According to Planck’s law, visible radiation at elevated temperatures becomes increasingly prominent and is likely to be detected by a regular visible CMOS sensor. The use of off-the-shelf visible CMOS sensors is more appealing than infrared ones in terms of resolution, cost and availability, making them particularly advantageous for precise high-temperature measurements. Secondly, high temperatures normally result from hydrocarbon combustion gases, which mainly contain H2O, CO2, and other substances. Such components pose a significant challenge for infrared thermometry due to their strong absorption in the infrared band. In contrast, these gases exhibit negligible absorption in the visible spectrum, substantially reducing background noise and enhancing the fidelity of the observed radiation signal35.

As a proof of theory, we propose and demonstrate DMT by utilizing a dispersive meta-lens array covering nearly the entire visible spectrum (450–650 nm) as conceptually shown in Fig. 1. We capture the high-temperature blackbody furnace using the DMT system. Spectrum compressive sensing (SCS) optimization and reverse dispersion network (RDN) are employed to decode the dispersive image into 21 wavelengths so as to improve the temperature measurement accuracy. To our knowledge, prior explorations have not ventured into radiation thermometry with a dispersive meta-lens. Our findings suggest that high-accuracy temperature measurements are possible with a dispersive meta-lens, which indicates a promising direction towards future miniaturization of multi-spectral/hyperspectral thermometers.

Fig. 1: Concept of the dispersive meta-lens thermometry.
Fig. 1: Concept of the dispersive meta-lens thermometry.
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Schematic of the DMT system, in which a dispersive meta-lens encodes broadband thermal radiation from a heat source into a spatially varying dispersion image. A single snapshot captured by a CMOS sensor is computationally decoded into hyperspectral data, enabling the temperature field reconstruction.

Results

Design and fabrication of a dispersive meta-lens array

To align with the sensitive wavelength of most visible CMOS sensors, we select the designed wavelength band ranging from 450 nm to 650 nm for high-temperature measurements. Regarding the number of radiation channels used for temperature calculation, systematic simulations suggest that 21 channels achieve a good balance between accuracy and efficiency. Increasing the number of channels yields diminishing returns in enhancing temperature-solving accuracy but places more computational burden on spectral decoding (Fig. S1 and Supplementary Material Section 1). With the working band range and spectral resolution established, a dispersive meta-lens is subsequently designed according to these parameters. The meta-lens array comprises 48 × 48 TiO2-based individual meta-lenses, each with a size of 30 µm. Each meta-lens contains over 25,000 TiO₂ nano-pillars and nanoholes, featuring a maximum aspect ratio of 40. A crucial step in achieving accurate temperature measurement involves obtaining hyperspectral data, which requires a transversely dispersive meta-lens. For a plane wave to focus at any point in the focal plane (x′, y′, f), the necessary phase profile is expressed as:

$$\varPhi \,\left(x,y,\lambda \right)=-\frac{2\pi }{\lambda }\left(\sqrt{{\left(x-{x}^{{\prime} }\right)}^{2}+{\left(y-{y}^{{\prime} }\right)}^{2}+{f}^{2}}-\sqrt{{\left({x}^{{\prime} }\right)}^{2}+{\left({y}^{{\prime} }\right)}^{2}+{f}^{2}}\right)$$
(3)

where f represents the focal length of the meta-lens. To achieve transverse dispersion, the broadband incident light must focus on a fixed focal plane while undergoing a significant lateral shift across different wavelengths. Typically, a meta-lens without specific aberration correction exhibits significant chromatic aberrations. These aberrations cause the focal points to shift along the optical axis at different wavelengths, resulting in what is commonly referred to as out-of-focus blur, making spectral information extraction difficult. In contrast, the transverse chromatic aberration utilized in this work disperses different wavelengths across the imaging plane, improving wavelength differentiation and significantly enhancing the extraction of spectral data.

A compensation phase is necessary to control the phase profile generated by the meta-lens across different wavelengths. Considering the working spectrum {λ1, λ2}, the compensation phase between start and end light is expressed as22:

$$\varDelta \varPhi \,\left(x,y,\lambda \right)=\varPhi \left({x}_{2},0,{\lambda }_{2}\right)-\varPhi \left({x}_{1},0,{\lambda }_{1}\right)$$
(4)

where x1 and x2 are the foci coordinates of the corresponding wavelength in the focal plane. Specifically, for different wavelengths, the focal point is intentionally set at\(\,(x{\prime},0,{f})\) here, and \(x{\prime}\) is a wavelength-dependent parameter. As a result, the focal points of different wavelengths will spread out in a line along the x-axis. This compensation phase is achieved through waveguide resonance in the specifically engineered nano-pillars and inverse structures. In this study, the working band is selected as {450 nm, 650 nm} with x1 = 43.9 μm, x2 = 67.0 μm, and f = 165 μm. Figure 2a, b illustrates the focusing behavior of the dispersive meta-lens at various incident wavelengths in the experiment and simulation, respectively. The white dotted line indicates the designed focal line. As shown in Fig. 2c, light beams of different wavelengths disperse along the x–z and x–y planes, maintaining a nearly constant focal length of 165 μm, and the foci shift laterally in the focal plane, which aligns well with theoretical predictions and is advantageous for spectral extraction. Figure 2d, e shows zoomed-in tilted-view scanning electron microscopy (SEM) images of inverse and solid nanostructures in a single meta-lens. The well-defined meta-atoms show the precise fabrication technique with hard mask transfer and etching processes. More information on meta-lens design and fabrication can be found in Supplementary Material Section 2, Table S1 and Figures S2–S4.

Fig. 2: Diagram of the dispersion in the meta-lens.
Fig. 2: Diagram of the dispersion in the meta-lens.
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a, b Intensity profiles along the x–z planes at various incident wavelengths (450 nm, 500 nm, 550 nm, 600 nm, and 650 nm) through simulation and experiment, respectively. The white dotted line indicates the designed focal line. c Intensity profiles along the x–z and x–y planes when five wavelengths incident simultaneously. d Zoomed-in top-view SEM image of the fabricated meta-lens’ inverse nanostructures. e Zoomed-in top-view SEM image of the fabricated meta-lens’ solid nanostructures.

Recording and decoding of hyperspectral thermal radiation

To experimentally validate the concept, a DMT prototype is constructed, and a series of radiation images is captured at temperatures ranging from 1673 K to 1873K in 10 K intervals, and a wide range from 1973K to 2973 K in 100 K intervals. The high-temperature radiation source is provided by two blackbody furnaces: one capable of reaching temperatures up to 1873 K with an emissivity of 0.95–1 (HT-H1600), and another providing temperatures up to 3273 K with an emissivity of 0.999–1 (BB-PyroG3000). As shown in Fig. 3, Figs. S5 and S12, thermal radiation is collected by a primary focusing lens (100 mm, f/2.0 − f/22, ZEISS Milvus 2/100 M), a linear polarizer and a quarter-wave plate are positioned after the main lens to modulate the polarization state of the incident radiation. The linear polarizer and quarter-wave plate are employed to generate circularly polarized light to match the geometric phase design and filter out other polarization states that cannot be properly controlled. One hundred dispersion images of the blackbody furnace are captured for every temperature measured, and Fig. 3c presents a portion of the dispersion image captured at 1873 K. Further experimental details, including the optical path alignment and calibration procedures, are discussed in Section 3 of the Supplementary Material.

Fig. 3: Experiment setup of the dispersive meta-lens thermometry.
Fig. 3: Experiment setup of the dispersive meta-lens thermometry.
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a 3D diagram of the DMT experimental setup. b Schematic illustration of the dispersion mode of the meta-lens. c Raw dispersion image of blackbody furnace at 1873 K.

The captured thermal radiation image includes spatial dimensions, along with the spectral dimension. Each dispersion image is formed by shifting the aligned three-dimensional data cube, under the assumption that the channels and dispersion correspond continuously. The projection of the data cube onto CMOS RGB channels can be expressed as the following equation:

$${{\bf{S}}}\left({{\bf{p}}},\left\{R,G,B\right\}\right)=\int {{{\mathbf{\Psi }}}}_{\lambda }\left(\left\{R,G,B\right\},\lambda \right)\cdot {{{\boldsymbol{{X}}}}}_{\lambda }\left({{\bf{V}}}\left({{\bf{p}}}\right),\lambda \right){{\rm{d}}}\lambda$$
(5)

In this equation, \({{\bf{S}}}\left({{\bf{p}}},\{R,G,B\}\right)\) denotes the radiative intensity obtained at pixel \({{\bf{p}}}\). The function \({{{\mathbf{\Psi }}}}_{\lambda }\) describes how the CMOS sensor responds to the spectrum. The term \({{{\boldsymbol{{X}}}}}_{\lambda }\) accounts for the wavelength-dependent dispersion shift of the thermal radiation.

To reconstruct the data cube, we implemented the traditional convex optimization technique SCS (Fig. S6), in which the inverse process of the aforementioned projection can be described as:

$${{{\rm{argmin}}}}_{{{\bf{V}}}}\parallel {{\mathbf{\Psi }}}{{\boldsymbol{{X}}}}{{\bf{V}}}-{{\bf{S}}}{\parallel }_{2}^{2}+{{{\rm{\alpha }}}}_{1}{\left\Vert {\nabla }_{{xy}}{{\bf{V}}}\right\Vert }_{1}+{{{\rm{\beta }}}}_{1}{\left\Vert {\nabla }_{\lambda }{{\bf{V}}}\right\Vert }_{1}$$
(6)

where \({{\mathbf{\Psi }}}\) and \({{\boldsymbol{{X}}}}\) are the response and dispersion matrix, respectively. The first term ensures the fidelity of data reconstruction. The second and third prior terms enforce the sparsity of gradients in the spatial and spectral dimensions. The feasibility of the SCS reconstruction algorithm is first verified with simulation images, and it is then applied to raw dispersion images. Figure 4a shows the reconstructed radiation image, and Fig. 4b shows 21 reconstructed hyperspectral images for the region in Fig. 4a (highlighted in the white box). As the thermal radiation is emitted from a blackbody furnace, its theoretical ground truth can be calculated from Planck’s equation. Figure 4e shows the comparison between 21 reconstructed channel images and the ground truth for four representative temperatures, 1673 K, 1753 K, 1813 K, and 1873 K, demonstrating a strong agreement with the theoretical estimation (correlation coefficient \(r > 0.97\)). Greater details on the SCS algorithm and results for each temperature measured can be found in Section 4 of the Supplementary Material.

Fig. 4: Results of hyperspectral decoding.
Fig. 4: Results of hyperspectral decoding.
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a, c Radiation image after spectral decoding by SCS and RDN at temperature 1873 K, respectively. b, d Zoomed-in 21 reconstructed hyperspectral images by SCS and RDN, respectively. e Average high-temperature radiative intensity calculated by SCS and RDN.

Furthermore, to augment the precision and efficiency of the spectral reconstruction, we developed RDN for real-time spectral decoding (Fig. S7). The RDN is built on transformer modules, which, compared to convolutional neural networks (CNNs), have superior capability in modeling long-range dependencies through the multi-head self-attention mechanism36. In decoding hyperspectral information from dispersed images, spectral components from different color channels are spatially multiplexed, leading to severe information loss. The faithful reconstruction of spectral information requires accurate modeling of the original spectral distribution and a deep understanding of the spatial-spectral relationship in the dispersive meta-lens. Initially, the observed image undergoes a shifting operation to account for the spatial displacement of different wavelengths. The network then processes the shifted image at three different scales in an end-to-end manner without iterative updates. The RDN can reconstruct a 3345 × 5129 pixel image in just 0.4 s on an RTX 3090 GPU. The reconstruction results, shown in Fig. 4c–e, demonstrate close alignment with those from convex optimization methods and theoretical ground truths (correlation coefficient \(r > 0.99\)). The principle of RDN and the results for each temperature measured are detailed in Section 4 of the Supplementary Material.

Temperature reconstruction and comparison with state-of-the-art

Planck’s law of multi-spectral hyperspectral radiometry gives the radiation intensity \({V}_{i}\) at each wavelength \({\lambda }_{i}\) as:

$${V}_{i} ={A}_{i}{c}_{1}\varepsilon \left({\lambda }_{i},T\right){\lambda }_{i}^{-5}\frac{1}{{e}^{{C}_{2}/{\lambda }_{i}T}-1}\\ ={A}_{i}{c}_{1}\varepsilon \left({\lambda }_{i},T\right){\lambda }_{i}^{-5}{e}^{-{C}_{2}/{\lambda }_{i}T},\,\left({e}^{{C}_{2}/{\lambda }_{i}T}\,\gg \,1\right)$$
(7)

where \({A}_{i}\) is a wavelength-dependent calibration factor, \(\varepsilon ({\lambda }_{i},{T})\) is the spectral emissivity, \({\lambda }_{i}\) is the \(i{{\rm{th}}}\) effective wavelength, and \({C}_{2}\) is the second radiation constant. Taking the natural logarithm of \({V}_{i}\) and\({V}_{{bi}}\) (radiation of blackbody):

$${{\mathrm{ln}}}\left(\frac{{V}_{i}}{{V}_{{bi}}}\right)-\frac{{C}_{2}}{{\lambda }_{i}{T}_{b}}=-\frac{{C}_{2}}{{\lambda }_{i}T}+{{\mathrm{ln}}}\,\varepsilon \left({\lambda }_{i},T\right)$$
(8)

Ideally, the temperature \(T\) from each channel should equal the true temperature. The expected deviation is minimized by:

$$\min f\left(x\right)={\sum }_{i=1}^{n}{[{T}_{i}-E\left(T\right)]}^{2}\to 0$$
(9)

where \(E\left(T\right)\) is the average temperature. The true temperature of each channel is found. This optimization problem can be well solved through the Chameleon swarm algorithm (CSA). More details about CSA can be found in Section 5 in the Supplementary Material.

Calculation results based on the aforementioned theory are provided in Fig. 5 for all measured temperatures and compared with the most recent MSLF technique. Due to the uniform surface temperature of the blackbody, the results indicate a consistent temperature distribution across an area of 3345 × 5129 pixels (40 mm × 60 mm). As can be readily seen from Fig. 5a, the average relative error of DMT (RDN) (\({\bar{u}}_{{\mathrm{RDT}}} < 0.32\%\)) and DMT (SCS) (\({\bar{u}}_{{\mathrm{SCS}}} < 0.7\%\)) is much lower than that of MSLF (\({\bar{u}}_{{\mathrm{MSLF}}} < 2\%\)) in most temperature conditions. This improvement is due to the hyperspectral radiation sampling, leading to a more accurate temperature and emissivity calculation. Additionally, deep learning demonstrates the highest accuracy in final temperature inversion, which reaches an absolute error as low as 6 K. Furthermore, Fig. 5b–d illustrates the error distributions for DMT (RDN), DMT (SCS), and MSLF at 1863 K, confirming the advantages of DMT over the conventional lens-based multispectral thermometry. Details on temperature and error distributions for all test cases are provided in Sections 5 and 6 of the Supplementary Material.

Fig. 5: Temperature measurement accuracy results of DMT and MSLF.
Fig. 5: Temperature measurement accuracy results of DMT and MSLF.
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a Comparison of three methods in relative error for 32 temperature test cases. b–d Relative error of 2D distribution at ground truth T = 1863K for DMT (RDN), DMT (SCS) and MSLF, respectively.

A series of flame impingement experiments were conducted to verify the capability of measuring different materials with temperature gradient distribution. Three high-temperature-resistant ceramics were chosen as impinging plates: alumina, zirconia, and silicon carbide, with reference emissivity vary from 0.2 to 0.937. A Hencken burner was employed to generate an approximately ideal adiabatic, steady-state hydrogen flame as heat source, as depicted in Fig. 6a. To fully assess DMT’s performance at lower temperatures, the silicon carbide impinging sample was positioned significantly farther from the flame outlet (H = 50 mm) compared to the other two materials (H = 20 mm) on purpose to reduce the heat input. Four B-type thermocouples were installed on the samples to provide reference temperatures (Fig. 6b). Figure 6c demonstrates relative errors and are mostly under 1.5%. Position ④, located farthest from the impingement point, corresponds to the lowest temperature among four positions. The lower temperature distribution on the silicon carbide plate is attributed to its greater distance from flame outlet, higher thermal conductivity38,39,40 and higher emissivity, which lead to the increased heat loss. The DMT system exhibits a 3% error at this point on SiC plate, which provides a comprehensive evaluation of DMT’s capability and indicates that current system’s lower temperature measurement limit reaches nearly 1230 K. The reconstructed results in Fig. 6d–f also exhibit the expected temperature gradient distribution. More information can be found in Section 7 of Supplementary Material.

Fig. 6: Flame impingement on plate.
Fig. 6: Flame impingement on plate.
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a Schematic of flame impingement on the plate. b Schematic of thermocouple installation locations. c Relative temperature difference between DMT and thermocouple. d–f Reconstructed surface temperature distribution with a temperature gradient for alumina, zirconia, and silicon carbide materials, respectively. The higher thermal conductivity, emissivity and greater \({{\boldsymbol{H}}}\) account for the lower temperature field in (f) comparing to the results in (d, e).

Discussion

In this study, we demonstrate a proof-of-concept for hyperspectral thermometry via dispersive meta-lens. High-temperature thermal radiations in the visible spectrum (450 nm to 650 nm) are dispersed and recorded with a single dispersive meta-lens array and a regular CMOS sensor. Up to 21 hyperspectral images are reconstructed from one snapshot using the traditional convex optimization technique and deep learning method. For the measured temperatures from 1673 K to 2973 K, the proposed DMT can achieve a measurement error lower than 0.32%, considerably more accurate than the most current MSLF technique17 (2%). These improvements indicate DMT’s key advantages: (1) higher spectral resolution via continuous dispersion control, (2) high accuracy powered by high spectral resolution and precise reconstruction, (3) protentionals for developing high accuracy, miniaturized, two-dimensional temperature sensors. To further validate, we also measured the temperature of flame-impingement plate, with a measurement error of mostly less than 1.5%. We have demonstrated that higher temperature favors DMT as it emits stronger radiation in the visible band. Indeed, a more sophisticated meta-lens design with higher focus efficiency and polarization independence would help improve measurement accuracy and broaden the measurable temperature range of DMT. Meanwhile, the DMT concept can equally be applied to infrared dispersive meta-lens to achieve similar performance for low-temperature measurements.

Methods

Metasurface fabrication

A high-quality TiO2 film is deposited onto an indium tin oxide (ITO)/glass substrate by an electro-beam evaporator (Syskey A-75). For the meta-lens patterning, a photoresistor layer, 120nm-thick PMMA A2, is spin-coated onto the TiO2 film and baked at 180 °C for 10 min. The prepared PMMA/TiO2/ITO/glass substrate is exposed to an electron-beam lithography system (Raith E-line Plus). After the development process, the designed meta-lens layout is transferred to the PMMA film. A 40 nm-thick chromium (Cr) is deposited on the top by the E-beam evaporator. Then, the pattern is transferred to the Cr layer via the lift-off process. The patterned Cr layer is the hard mask for the high aspect ratio etching process of TiO2. The TiO2 film is etched in an inductively coupled plasma etcher (Oxford ICP100), and the remaining Cr is removed by the chromium etchant. Finally, the final sample of the dispersive meta-lens array is obtained for high-temperature thermometry.

Optical characterization

The focusing behavior of the fabricated sample is characterized by the home-made optical experiment setup. The incident light with different wavelength is generated by a supercontinuum laser and acousto-optic tunable filters (AOTF). The laser beam with a circular polarization state is generated by using a linear polarizer and a quarter-wave plate. An objective (7.5×, NA = 0.21) is used to focus the incident circularly polarized light onto the achromatic meta-lens. The focused spot from the meta-lens in transmission is collected by the second objective (50×, NA = 0.55). The second set of a linear polarizer and a quarter-wave plate is used to select the modulated light. The second objective, the second set of a linear polarizer and a quarter-wave plate, and a camera are mounted on a motorized stage for scanning and obtaining the light intensity profile in the z-axis.