Shortwave infrared single-pixel spectral imaging based on a GSST phase-change metasurface

Chenning Tao; Huanzheng Zhu; Yusheng Zhang; Si Luo; Qiang Ling; Bin Zhang; Zhangwei Yu; Xiao Tao; Daru Chen; Qiang Li; Zhenrong Zheng; Zhenrong Zheng

doi:10.1364/OE.467994

1. Introduction

Shortwave infrared (SWIR) imaging with approximate spectral range from 1 µm to 2.5 µm obtains reflective information invisible to human eyes or silicon-based detectors. Facilitated by low scattering effects inversely proportional to the fourth power of wavelength, spectral fingerprints corresponding to overtones of molecular vibrations, and possibility of intense illumination without obstructing human views, SWIR imaging is now extensively used in various fields such as biomedical imaging [1,2], agriculture [3–5], night-time surveillance [6], pharmaceuticals and cosmetics quality control [7,8], etc. However, for conventional SWIR detectors (e.g. Ge, InP, or MCT), due to the intrinsic massive dark noise, a detector cooling system with temperature stabilization by liquid nitrogen or Stirling cryocooler is demanded, which excessively increases the cost, volume, and weight of the imaging system [9]. Though detectors made of InGaAs alleviate these issues with low dark current at room temperature, the focal plane array (FPA) detector for SWIR imaging is still unaffordable for most applications [10].

The development of the compressive sensing theory and the derived single-pixel imaging create new opportunities for SWIR imaging [11]. In single-pixel imaging, incoming light is firstly modulated by a series of spatially resolved patterns and then sequentially captured by a single-pixel detector. Finally, pixelated images are reconstructed based on sparse representation of compressive sensing. Under the single-pixel imaging scheme, SWIR imaging can be achieved without the usage of the expensive exotic FPA detector [12–16].

On the other hand, to make full use of SWIR spectral fingerprints, information in grayscale SWIR imaging is insufficient; it is indispensable to acquire the spectrum for each spatial pixel, i.e., SWIR spectral imaging. An elaborate combination of single-pixel imaging and spectral imaging in the SWIR regime can maintain the advantages of both parts and promote applications. However, SWIR spectral imaging via single-pixel detector remains a challenge due to the difficulty on spatial and spectral modulation, which are essential for single-pixel imaging and spectral imaging, respectively. Although FPA-based SWIR spectral imaging have been demonstrated with dispersive elements (e.g. prism or grating) [17–19], electronically tunable filters (e.g. liquid crystal tunable filter or acousto-optical tunable filter) [20–22] and Fourier transform interferometers (Fourier transform infrared, FTIR) [23,24], there is no existing SWIR spectral imaging system based on compressive sensing that simultaneously achieves the spatial-spectral modulation. Consequently, advanced technology for high-efficient spatial-spectral modulations needs to be explored for effectiveness and functionality of the SWIR single-pixel spectral imaging system.

Recently, reconfigurable dynamic metasurfaces based on phase-change materials capacitate multidimensional manipulation of light propagation, facilitating the tunable response of a single device [25,26]. Typically for the chalcogenide alloy phase-change materials (e.g. Ge₂Sb₂Te₅, Ge₂Sb₂Se₄Te₁, and Ge₃Sb₂Te₆) [27–30], the large contrast of dielectric constants between the amorphous and crystalline phases can dramatically vary the spectral reflectance or transmittance of phase-change metasurface via elaborate design on the structure, which could potentially enable the crucial spectral modulation for compressive spectral imaging.

In this paper, SWIR single-pixel spectral imaging with phase-change metasurface spectral modulator based on Ge₂Sb₂Se₄Te₁ (GSST) is proposed. By varying the crystallinity of the GSST pillar in the phase-change metasurface, the transmittance spectrum can be tuned by the wavelength shift of multipole resonances, validated by the multipole decompositions and electromagnetic field distributions. Based on the spectral modulations via transmittance tuning, the SWIR hyperspectral image can be compressively sensed through single-pixel imaging and then reconstructed with high fidelity in both spectral and spatial dimensions. The reconstructed SWIR hyperspectral images can facilitate potential applications demanding object classification via identification of spectral fingerprints. Furthermore, the feasibility of metasurface optimization under the coherence minimization principle is demonstrated by the design of pillar height.

2. Results

2.1 System schematic

The schematic of the SWIR single-pixel spectral imaging system is shown in Fig. 1(a). The SWIR hyperspectral image is discretized into a 3D datacube ${\textbf f} \in {\mathrm{\mathbb{R}}^{M \times N \times N}}$ according to the resolutions, with two spatial dimensions and one spectral dimension of size N and M, respectively. The 3D hyperspectral datacube is sequentially filtered by L spectral modulations, which are performed by the transmission spectrum variation of a single metasurface constituted by phase-change material GSST pillars on a silica substrate (Fig. 1(b)). The matrix form of the spectral modulation is ${{\textbf H}_r} \in {\mathrm{\mathbb{R}}^{L \times M}}$. From the amorphous phase to the crystalline phase, the refractive index of GSST increases within the full SWIR range (from 3.63 to 5.34 at the wavelength of 1 µm, see Supplement 1, note 1). As a non-volatile phase-change material, the intermediate phase of GSST is stable and can be realized by partial crystallization [29,31–33]. The permittivity of partially crystallized GSST is estimated by the effective medium theory [34,35]:

(1)$$\frac{{\varepsilon ({\lambda ,C} )- 1}}{{\varepsilon ({\lambda ,C} )+ 2}} = C \times \frac{{{\varepsilon _c}(\lambda )- 1}}{{{\varepsilon _c}(\lambda )+ 2}} + ({1 - C} )\times \frac{{{\varepsilon _a}(\lambda )- 1}}{{{\varepsilon _a}(\lambda )+ 2}}$$

where λ is the wavelength, C is the crystallinity, and ${\varepsilon _a}$ and ${\varepsilon _c}$ are the permittivity of amorphous and crystalline GSST. The spectral transmittance of the phase-change metasurface is tuned by different phases of GSST, with L spectral modulations including the fully amorphous/crystalline phases and L - 2 intermediate phases. The spectrally modulated hyperspectral image is then modulated in the spatial dimension by K binary (block-unblock) patterns, as is conventional single-pixel imaging [11,36], and the corresponding matrix form is ${{\textbf H}_c} \in {\mathrm{\mathbb{R}}^{K \times {N^2}}}$. The spatially modulated hyperspectral image can be either projected to a 2D surface by summation in the spectral dimension corresponding to the detection by FPA, or projected to a 0D point by summations in all dimensions corresponding to single-pixel detection (here 0D means the single-pixel detection obtains a scalar without spatial or spectral resolution). For single-pixel detection, the system can be described by ${\textbf g} = ({{{\textbf H}_r} \otimes {{\textbf H}_c}} ){{\textbf f}_v}$, where ${\textbf g} \in {\mathrm{\mathbb{R}}^{LK}}$ is the row vector of the compressively sensed detection, ⊗ is the Kronecker product, and ${{\textbf f}_v} \in {\mathrm{\mathbb{R}}^{M{N^2}}}$ is the vectorized form of f.

Fig. 1. Principle and schematic of the SWIR single-pixel spectral imaging system. (a) Simplified schematic. The spatial-spectral modulation is independent. The input SWIR hyperspectral datacube f is sequentially modulated by L spectral modulations implementing the transmission spectrum variation of a phase-change metasurface. Within each spectral modulation, K spatial modulations utilizing a spatial light modulator are performed on the datacube f before it projected to the single pixel detector. (b) Phase-change metasurface spectral modulator based on GSST.

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To be specific, the spectral modulation based on the phase-change metasurface can be realized by multi-state tuning with thermal annealing [37,38] or electrical/optical switching [35,39–42]. The crystallization from amorphous phase to crystalline phase (blue arrow in Fig. 1(b)) is achieved by local temperature close to or slightly higher than the crystallization temperature. The amorphization from crystalline phase to amorphous phase (red arrow in Fig. 1(b)) is achieved by local temperature higher than the melting point. For the partial crystallization to the intermediate phases, the crystallinities can be controlled by the thermal annealing temperature or time [34], electrical pulse intensity or width [39], and pulsed laser intensity or repetition numbers [41,42]. While for the spatial modulation based on the binary patterns, the spatial light modulator (SLM) e.g. digital mirror devices, can be operated at a higher frequency than the spectrally switch. Therefore, the spatial-spectral modulation is conducted independently: for each crystallinity of the phase-change metasurface, all the spatial patterns are sequentially loaded on the SLM; and after the spatial modulations are accomplished, the crystallinity is tuned for the next spectral modulation. A possible configuration of SWIR single-pixel spectral imaging system is shown in Supplement 1, note 2.

2.2 Phase-change metasurface spectral modulation principle

To achieve high-efficient spectral modulation and improve the reconstructed SWIR spectral images, the phase-change metasurface is designed according to the coherence minimization principle in the compressive sensing theory, which will be described in details in the later section. The optimized phase-change metasurface formed by GSST pillars is shown in Fig. 2(a), with the periodicity p of 950 nm, the pillar height h of 600 nm, and the pillar diameter d of 570 nm. To clarify the principle of spectral modulation by the phase-change metasurface, the multipole analysis [43,44] is applied on the transmittance spectra for phases at different crystallinities, as shown in Fig. 2(b). The transmittance in blue solid lines are directly obtained by finite element method; while the transmittance in red dashed lines are represented by the multipole decomposition with electric dipole (ED), magnetic dipole (MD), electric quadrupole (EQ), and magnetic quadrupole (MQ), whose contributions are indicated by the absolute values in reflection coefficients (R) before interference (Fig. 2(c), see Supplement 1, note 3). The slight difference between direct simulation and multipole decomposition is mainly related to the silica substrate with refractive index inequal to 1 (see Supplement 1, note 4, for multipole decomposition without substrate).

Fig. 2. Phase-change metasurface configuration and multipole decomposition analysis. (a) Schematic of the GSST-based metasurface spectral modulator. (b) Transmittance spectra obtained by finite element method (blue solid lines) and multipole decomposition (red dashed lines) of the metasurface spectral modulator at different phases (C = 0%, 50%, and 100%). (c) Absolute values of the multipole contributions in the reflection coefficients before interference. (d) Normalized magnetic field strength |H|/|H_max| and vectors of electric displacement field D inside the GSST pillar in the x-z plane, at the magnetic dipole (MD) peak wavelengths for different phases. Normalized electric displacement field |D|/|D_max| and vectors of magnetic field strength H inside the GSST pillar in the y-z plane, at the (e) electric dipole (ED) and (f) electric quadrupole (EQ) peak wavelengths for different phases.

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In SWIR range, the peak wavelengths of the MD resonances for phase-change metasurface at 0%, 50%, and 100% crystallinities are 2.01 µm, 2.40 µm, and 2.50 µm, respectively (I, I′, and I′′ in Fig. 2(b), respectively). The corresponding normalized magnetic field strength |H|/|H_max| and vectors of electric displacement field D are shown on the cross section of pillar in the x-z plane (Fig. 2(d)). At the MD resonance wavelengths, the magnetic field is enhanced at the center of the oscillating loop formed with electric displacement field. For the ED resonances, the peak wavelengths are 1.71 µm, 2.01 µm, and 2.49 µm, respectively for 0%, 50%, and 100% crystallinities (II, II′, and II′′ in Fig. 2(b), respectively). The corresponding normalized electric displacement field |D|/|D_max| and vectors of magnetic field strength H are shown on the cross section of pillar in the y-z plane (Fig. 2(e)). The collective polarization within the metasurface unit is formed at the ED resonance wavelengths, which can also be characterized by the oscillating loop of magnetic field strength around the largest enhancement of electric displacement field. For EQ resonances (Fig. 2(f)), the peak wavelengths are 1.44 µm, 1.62 µm, and 1.39 µm, respectively for 0%, 50%, and 100% crystallinities (III, III′, and III′′ in Fig. 2(b), respectively). Different from ED, there are two enhancements for normalized electric displacement field, and two corresponding oscillating loops of magnetic field strength for EQ resonances. Apart from the mode III′′ of EQ for crystalline GSST, the distributions of electric displacement field and magnetic field strength for the same resonance are similar among different phases/wavelengths, which validates the multipole decomposition of transmittance spectra and illustrates the physical mechanism of low transmittance dips. Therefore, the spectral modulation can be realized by phase-change metasurface, via transmittance spectrum tuning with significant red-shift of multipole resonances through the crystallization of GSST.

2.3 SWIR hyperspectral reconstruction

The reconstruction of the SWIR hyperspectral image is an under-determined problem [45–47]:

(2)$$ \hat{\mathbf{f}}_{v}=\boldsymbol{\Psi} \underset{\boldsymbol{\mathrm{\theta}}}{\arg \min }\left(\left\|\left(\mathbf{H}_{r} \otimes \mathbf{H}_{c}\right) \boldsymbol{\Psi} \boldsymbol{\mathrm{\theta}}-\mathbf{g}\right\|_{2}^{2}+\tau\|\boldsymbol{\mathrm{\theta}}\|_{0}\right) $$

where $\boldsymbol{\Psi}$ is the sparse prior, $\boldsymbol \mathrm{\theta}$ is the sparse representation of the datacube f_v under $\boldsymbol{\Psi}$, ${||\cdot || _2}$ is the $\ell_2$-norm, ${||\cdot || _0}$ is the $\ell_0$-norm constraining the sparsity of $\boldsymbol \mathrm{\theta}$, and τ is the regularization parameter. The sparse prior $\boldsymbol{\Psi}$ is trained with patches of size 8 × 8 × 151 (N = 8, M = 151 representing the spectral bands ranging from 1 µm to 2.5 µm at an interval of 0.01 µm) extracted from the hyperspectral images in the dataset acquired by airborne visible/infrared imaging spectrometer (AVIRIS data) [48] via dictionary learning (see details of dictionary learning in Supplement 1, note 5). We implement 64 binary patterns (K = 64) and 11 spectral modulations (L = 11) with different crystallinities of GSST between the amorphous phase and the crystalline phase. Therefore, the compression ratio for the spatial dimension is K / (N × N) = 1, while the compression ratio for the spectral dimension is M / L = 7.28%, which is equal to the total compression ratio for the system. The transmittance spectra for all spectral modulations are shown in Fig. 3(a). To demonstrate the feasibility of the proposed SWIR single-pixel spectral imaging system, the reconstructed hyperspectral images are shown in false color (Fig. 3(c) and 3(f), with spectral bands around wavelength of 2.25 µm, 1.75 µm, and 1.25 µm mapped to RGB, respectively), compared to the SWIR ground truths (Fig. 3(b) and 3(e), test images from AVIRIS data different from the training set for dictionary learning) and shown with the corresponding visible images in actual color (Fig. 3(d) and 3(g)). Image quality metrics including the peak signal-to-noise ratio (PSNR), the structure similarity index measure (SSIM) and the spectral angle mapping (SAM) [49] for the reconstructed hyperspectral images are shown in Fig. 3(c) and 3(f).

Fig. 3. Hyperspectral reconstruction in the SWIR single-pixel spectral imaging system. (a) The transmittance spectra for phase-change metasurface at different crystallinities of GSST. (b) The ground truth and (c) the reconstructed SWIR hyperspectral image, shown in false color, and (d) the visible image of a city. (e) The ground truth and (f) the reconstructed SWIR hyperspectral image, shown in false color, and (g) the visible image of a village. (h) - (m) The spectral signatures denoted by squares in (b) and (e), with the ground truths and the reconstructed results represented by black dashed lines and colored solid lines, respectively. The PSNR and SAM values for the reconstructed spectral signatures are also shown.

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For SWIR hyperspectral images of the city (Fig. 3(c)) and the village (Fig. 3(f)), the reconstructions restore the spatial morphology from the compressively sensed detection, which enable recognition of characteristics e.g. roads and districts in the city or croplands and ponds in the village. For the spectral dimension, the reconstructions faithfully recover the spectrum for most spatial pixels, indicated by the images in false color and the point spectra of pixels shown in Fig. 3(h)-(m). PSNR and SAM are calculated to evaluate the reconstruction quality of the point spectra. The reconstructed spectra at these pixels (colored solid lines) are close to the ground truths (black dashed lines), in terms of both absolute intensity and spectral signatures. Based on the reconstructed SWIR spectra, the spectral signatures potentiate the classification of objects in different scenes, e.g. soil in Fig. 3(h) and 3(k), vegetation in Fig. 3(i) and 3(l), and rock in Fig. 3(j) and 3(m). In addition, the robustness of the SWIR hyperspectral reconstruction at different noise levels is analyzed in Supplement 1, note 6.

2.4 Phase-change metasurface optimization

According to the compressive sensing theory [50], the possibility of finding the exact solution of the under-determined problem (2) depends on the coherence µ between the system matrix ${{\textbf H}_r} \otimes {{\textbf H}_c}$ and the sparse prior $\boldsymbol{\Psi}$ [36,51]:

(3)$$\mu = ||{{{\boldsymbol {\Psi} }^T}{{({{{\textbf H}_r} \otimes {{\textbf H}_c}} )}^T}({{{\textbf H}_r} \otimes {{\textbf H}_c}} ){\boldsymbol {\Psi} } - {\textbf I}} ||_F^2$$

where I is the identity matrix with dimensions identical to the number of columns in $\boldsymbol{\Psi}$ and $||\cdot || _F^2$ is the square of the Frobenius norm of the matrix. For lower value of coherence, the possibility to solve the under-determined problem is generally larger, indicating better reconstruction performance as well as fewer demanded compressive samplings. Therefore, the phase-change metasurface is designed to minimize the coherence, based on a pre-trained sparse prior $\boldsymbol{\Psi}$ for the SWIR hyperspectral image dataset and a fixed set of randomly-generated spatial modulation patterns ${{\textbf H}_c}$.

Taking the optimization of the pillar height h as an example, the transmittance spectra versus varying pillar height from 200 nm to 900 nm, are shown in Fig. 4(a), 4(b) and 4(c), respectively for 0%, 50%, and 100% crystallinities. Still, the spectral modulations ${{\textbf H}_r}$ are composed of transmittance spectra for the fully amorphous and crystallized phases together with 9 intermediate phases (L = 11). The corresponding coherence for spectral modulations of transmittance spectra combinations reaches the minimum value 0.9874 at the pillar height of 600 nm, as shown in Fig. 4(d). For the coherence-optimized pillar height, the average PSNR and structure similarity index measure (SSIM) for five testing SWIR hyperspectral images reach their maximum values, while the average SAM reaches its minimum value, as shown in Fig. 4(e)–(g). Large PSNR value represents low reconstruction error, indicated by low mean square error compared to the peak intensity in the hyperspectral image; large SSIM value corresponds to the high similarity of luminance, intensity contrast, and spatial structure between reconstruction and ground truth; and small SAM value illustrates high parallelity between the point spectra of reconstruction and ground truth, by regarding the point spectrum as a vector in higher dimensional space, manifesting high spectral fidelity of reconstruction. Therefore, best performance in terms of overall error, spatial similarity and spectral fidelity, is obtained in the reconstructed SWIR hyperspectral images based on the optimized pillar height, which validates the optimization of phase-change metasurface based on coherence minimization.

Fig. 4. The optimization of the pillar height h in the phase-change metasurface and the reconstruction quality comparison. (a) - (c) The transmittance spectra versus pillar height h at different phases (C = 0%, 50%, and 100%). (d) Coherence, and average (e) PSNR, (f) SSIM and (g) SAM versus pillar height h for five testing SWIR hyperspectral images.

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3. Discussion

Spectral modulators based on tunable transmittance of phase-change metasurface is proposed for SWIR single-pixel spectral imaging. First, the physical mechanism of the transmittance spectra tuning by different crystallinity of GSST pillar in phase-change metasurface is clarified by multipole analysis and electromagnetic field distributions. The red-shift of main multipole resonances through GSST crystallization contributes to the large-scale regulation of transmittance spectra in terms of amplitude and peak/dip wavelengths. Second, the spectral modulation constituted by transmittance spectra corresponding to amorphous, crystalline, and partially crystallized GSST can sense the SWIR hyperspectral image in a high-efficient and sufficiently compressive manner, indicated by the similar false color and point spectra in reconstruction. Third, the spectra in accurately reconstructed SWIR hyperspectral image exhibit the potential of object classification. Last, minimization of coherence in compressive sensing is applied on the spectral modulations to optimize the configuration of the phase-change metasurface. The phase-change metasurface with optimal pillar height functions best as the spectral modulator, corresponding to the optimal quality metrics of reconstructions. Ultimately, the phase-change metasurface based spectral modulators and the single-pixel imaging scheme potentiate miniaturized and dynamic SWIR spectral imaging system, enabling applications in remote sensing, military, biomedical imaging, etc. This work may open the opportunities for tunable and reconfigurable modulations essential for compressive sampling, thus paving the way towards high-efficient computational imaging based on dynamic nanophotonics.

Funding

Natural Science Foundation of Zhejiang Province (2022C03066, 2022C03084, LQ22F050007).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Shortwave infrared single-pixel spectral imaging based on a GSST phase-change metasurface

Abstract

1. Introduction

2. Results

2.1 System schematic

2.2 Phase-change metasurface spectral modulation principle

2.3 SWIR hyperspectral reconstruction

2.4 Phase-change metasurface optimization

3. Discussion

Funding

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (4)

Equations (3)

Optics Express