• Chinese Optics Letters
  • Vol. 23, Issue 7, 071104 (2025)
Jun Wan1, Bin Zhang1,3, Xianzhe Li1, Tao Li1..., Qirong Huang1,2, Xinyu Yang1,2, Kaiqing Zhang1, Wei Huang2 and Haixiao Deng1,*|Show fewer author(s)
Author Affiliations
  • 1Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
  • 2Laboratory of Quantum Engineering and Quantum Materials, School of Physics, South China Normal University, Guangzhou 510631, China
  • 3ShanghaiTech University, Shanghai 201210, China
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    DOI: 10.3788/COL202523.071104 Cite this Article Set citation alerts
    Jun Wan, Bin Zhang, Xianzhe Li, Tao Li, Qirong Huang, Xinyu Yang, Kaiqing Zhang, Wei Huang, Haixiao Deng, "Enhancing terahertz imaging with Rydberg atom-based sensors using untrained neural networks," Chin. Opt. Lett. 23, 071104 (2025) Copy Citation Text show less

    Abstract

    Terahertz (THz) imaging based on the Rydberg atom achieves high sensitivity and frame rates but faces challenges in spatial resolution due to diffraction, interference, and background noise. This study introduces a polarization filter and a deep learning-based method using a physically informed convolutional neural network to enhance resolution without pre-trained datasets. The technique reduces diffraction artifacts and achieves lens-free imaging with a resolution exceeding 1.25 lp/mm over a wide field of view. This advancement significantly improves the imaging quality of the Rydberg atom-based sensor, expanding its potential applications in THz imaging.

    1. Introduction

    THz radiation (0.1–10 THz) is widely used in industrial applications like medical imaging, security screening, and communication[1] due to its non-ionizing, low-energy properties. Additionally, it serves as a unique tool in scientific research, enabling the study of fundamental modes, such as electron motion, molecular rotations, lattice vibrations, and superconducting oscillations[2].

    Recent advancements in THz imaging technologies have demonstrated significant progress. Frequency-domain THz imaging now operates through three primary sensor types[3]: thermal sensors[4,5], field sensors[6,7], and photon sensors[8,9]. Thermal sensors typically achieve millimeter-scale spatial resolution but suffer from sub-Hz frame rates and limited sensitivity at room temperature[10]. Photon sensors, though offering high sensitivity and faster imaging speeds as tens of frames per second (fps), require cryogenic cooling and complicated practical deployment[11]. Field sensors bring sub-millimeter spatial resolution and frame rates of 10–100 fps, yet their sensitivity remains insufficient for high-precision applications[12]. Notably, none of these conventional approaches simultaneously deliver high speed, high sensitivity, and room temperature operation[13]. Building on the breakthrough performance in microwave detection[1416], Rydberg atom-based sensors now demonstrate revolutionary capabilities in THz regimes[1720]. Resulting from the large electric dipole moment, the Rydberg atom has nearly single-photon sensitivity to THz radiation, which surpasses thermal sensors and field sensors by orders of magnitude and is similar to photon sensors. In addition, it potentially enables imaging with a speed on the order of the megahertz.

    A method for real-time full-field imaging[21] has recently been developed, leveraging cesium Rydberg atoms to up-convert THz frequencies into the optical range. This innovation allows conventional optical cameras to rapidly capture full-field images, enabling real-time imaging in the THz spectrum. Furthermore, an improved THz imaging system has been introduced[22], achieving remarkable sensitivity and an impressive imaging speed of 6000 fps.

    Rydberg atom-based THz imaging, while promising, encounters significant challenges such as diffraction, interference fringes, and background noise, which degrade spatial resolution. Although studies[21,22] have shown that Rydberg-based detection systems can theoretically achieve diffraction-limited spatial resolution, these findings are largely based on experimental evaluations conducted under single pinhole imaging. The actual performance of these detectors in large-area imaging scenarios remains unverified. This study tackles these issues by reducing THz wave interference within the atomic vapor cell physically and employing image preprocessing techniques. Additionally, an untrained neural network is utilized to process images captured by the camera, effectively minimizing noise and diffraction effects, thereby improving the quality of fluorescence imaging.

    2. Experimental Setup

    The system depicted in Fig. 1 utilizes cesium atoms in a Rydberg state to convert THz waves into detectable visible fluorescence, which is subsequently captured by a charge-coupled device (CCD). The cesium atoms within the atomic vapor cell are excited into the Rydberg state through a three-step excitation process[23] involving three infrared laser beams, as outlined in prior research[21]. These infrared beams form an elliptical spot measuring 100 µm in width and 20 mm in height and are shaped by a cylindrical lens. A dove prism is also employed to correct for angular misalignment, ensuring proper beam overlap.

    Layout of the terahertz imaging experiment. SAS, saturated absorption spectroscopy; EIT, electromagnetically induced transparency; HR mirror, high reflective mirror.

    Figure 1.Layout of the terahertz imaging experiment. SAS, saturated absorption spectroscopy; EIT, electromagnetically induced transparency; HR mirror, high reflective mirror.

    The detection laser (wavelength: 852 nm, power: 35 mW) is initially stabilized to the 6S1/2F=46P3/2F=5 hyperfine transition using polarization spectroscopy. The coupling laser (wavelength: 1470 nm, power: 20 mW) is stabilized to the 6P3/2F=57S1/2F=4 transition. Following this, the Rydberg laser (wavelength: 843 nm, power: 300 mW) is tuned to the 7S1/214P3/2 transition, although it is not actively frequency stabilized.

    The detection and coupling beams travel in the same direction along the x-axis within the atomic vapor cell, which measures 10mm×10mm×20mm (x-axis: length, y-axis: width, z-axis: height, respectively) and is 1 mm thick and is constructed from quartz glass. In contrast, the Rydberg beam travels in the opposite direction. Recently, a larger atomic vapor cell made of quartz glass, measuring 60mm×5mm×60mm and is 2 mm thick, has been developed to provide a larger imaging plane. These beams intersect inside the atomic vapor cell, forming a thin two-dimensional sheet. THz waves (approximately 0.55 THz, with a maximum power of 1.85 mW), are generated by a 36-fold frequency doubling chain and a 26 dB terahertz horn, propagating along the optical axis (y-axis) to transmit the image of an object before entering the atomic vapor cell. The THz waves excite the cesium atoms from the 14P3/2 state to the 13D5/2 state, which has a relatively long lifetime, typically on the order of microseconds before decaying back to the 6P3/2 state through spontaneous emission and producing detectable fluorescence at 535 nm.

    The emitted fluorescence is focused on an optical camera, generating a single-shot image of the incident THz field. To enhance the conversion efficiency from THz to optical, the cesium vapor is heated by encasing two-thirds of the vapor cell in a Teflon shell, with ceramic heaters (HT24S) maintaining the temperature at 65°C to maximize fluorescence output. By scanning the frequency of the THz source from 548.58 to 548.64 GHz, we observe that the fluorescence intensity peaks at a frequency of 548.613 GHz[22], confirming that this imaging system operates as a single-frequency THz imaging setup at this precise frequency.

    3. Principle and Method

    3.1. Interference fringe suppression

    The Rydberg atom-based sensor employs cesium atoms in a Rydberg state within a quartz-encased atomic vapor cell to detect THz waves at 548.613 GHz, which carry object information. However, THz waves reflecting off the inner surface of the vapor cell generate standing waves, resulting in interference fringes on the detection plane. In the experiment, as shown in Fig. 2(a), 29 bright fringes are observed on a vapor cell measuring 10mm×10mm×20mm with an internal width of 8 mm. According to Fresnel’s equations[24], THz waves polarized parallel to the x-axis exhibit stronger reflection compared to those polarized parallel to the z-axis. By positioning a THz polarizer at the source antenna and aligning it with the z-axis, the brightness of the standing wave fringes is significantly reduced, as shown in Fig. 2(b).

    Fluorescence images acquired pre- and post-installation of a terahertz polarizer. (a) The fluorescence image before positioning a terahertz polarizer. (b) The fluorescence image after positioning a terahertz polarizer.

    Figure 2.Fluorescence images acquired pre- and post-installation of a terahertz polarizer. (a) The fluorescence image before positioning a terahertz polarizer. (b) The fluorescence image after positioning a terahertz polarizer.

    3.2. Diffraction pattern suppression

    The object modulates the transmitted THz waves, encoding information within the complex function of the wavefront, as shown in Eq. (1), where I(x,y) represents the intensity. The evolution of the wavefront from the object to the detection planes is described by Eq. (2), where H denotes the system transfer function, and Uo and Ui denote wavefront functions at the object and detection planes, respectively. In an aberration-free system, Eq. (3) simplifies to Eq. (4)[25], with * indicating the convolution. The imaging process is described by Eq. (5), where T accounts for the free-space propagation in Eq. (6), and L describes the optical element transformations, Uo(x,y)=I(x,y)eiφ(x,y),Ui(x,y)=H(Uo),Ui(x,y)=Uo(x,y)H[δ(x,y)]dxdy,Ui(x,y)=Uo(x,y)*PSF,Ui(x,y)=Uo(x,y)*T(x,y,d1)·L1Ln1*T(x,y,dn),T(x,y,d)=++ei2πd1λ2fx2fy2ei2π(fxx+fyy)dfxdfy.

    In coherent imaging, directly determining H is challenging, but the relationship between Uo and Ui can be calculated or measured. After THz waves pass through the object, phase information is lost in the intensity image. Drawing inspiration from prior studies[26,27], we enhance a deep neural network by incorporating the physical prior to determining H, thereby eliminating the need for pre-existing datasets. This approach processes fluorescence images to minimize diffraction speckles.

    The neural network architecture used in this study, depicted in Fig. 3(a), is the U-Net convolutional neural network[28], widely applied in computational imaging. It comprises four main components: a 3×3 convolutional kernel activated by the leaky ReLU function, a 2×2 max pooling layer, a 2×2 up-convolution layer, and skip connections. The algorithm shown in Fig. 3(b) takes the square root of the normalized fluorescence intensity I(x,y) as input and outputs a 2-channel tensor containing the real and imaginary components of the reconstructed object image Uo, as in Eq. (7). The network, represented by f with weights θ, solves the problem in Eq. (8). For n=1, phase loss leads to unstable predictions. For n>1, additional data constraints improve the accuracy of the object recovery, Uo(x,y)=fθ[I(x,y)],fθ*=argminθϵΘ{i=1nHi[fθ(Ii)]Ii}.

    Schematic illustration of the pipeline of the untrained neural network. (a) Details for the U-shaped network structure. (b) Schematic diagram of the physics-enhanced deep neural network.

    Figure 3.Schematic illustration of the pipeline of the untrained neural network. (a) Details for the U-shaped network structure. (b) Schematic diagram of the physics-enhanced deep neural network.

    3.3. Background noise suppression

    Raw fluorescence images are typically unsuitable for direct enhancement due to their high noise levels, requiring preprocessing for effective recovery. The fluorescence resulting from incident THz waves contains emissions around 535 nm, which correspond to the de-excitation of the 13D5/2 state. However, cesium atoms transitioning from the 14P3/2 state also emit other visible wavelengths[29]. These photon wavelengths are closely spaced, making optical filtering challenging. The total fluorescence detected by the camera can be decomposed into three components: fluorescence induced by THz waves, fluorescence independent of THz waves, and background noise from the camera.

    Initially, cesium atoms in the vapor cell are in the ground state, and a grayscale image Ibase is captured. Subsequently, three laser beams excite the cesium atoms to the Rydberg state 14P3/2, and another image ITHzoff is taken. After introducing THz waves, a final image ITHzon is captured. The difference ITHzonITHzoff corresponds to the fluorescence emitted during the interaction of the THz waves with the Rydberg atoms. As established in previous studies, the fluorescence intensity is proportional not only to the incident THz wave intensity but also to the quantity of the atoms in the 14P3/2 state, which itself is proportional to the fluorescence intensity recorded as ITHzoff. Therefore, the renormalized intensity image associated with the THz waves I can be determined by the first part of Eq. (9). However, it is essential to account for fluctuations in the central frequency and linewidth of the lasers, which can cause instability in the fluorescence intensity. Notably, the fluorescence intensity caused by THz waves that were detected by the camera after passing through an optical filter is significantly higher than that produced by non-THz radiation. Consequently, to reflect the experimental conditions, the data preprocessing is described using the second part of Eq. (9). To further reduce random noise, a 5×5 Gaussian blur using OpenCV is followed by scaling the image down from 2048 pixel × 2048 pixel to 512 pixel × 512 pixel. After preprocessing, the intensity image I loses its absolute intensity information, but the relative intensity distribution remains intact and provides sufficient information for analysis, I=ITHzonITHzoffITHzoffIbaseITHzonIbaseITHzoffIbase,ITHzonITHzoff.

    4. Simulation and Experimental Results

    As indicated by Eq. (4), in an aberration-free imaging system or in regions where aberrations can be neglected, the amplitude and phase of the system’s impulse response can be experimentally measured, yielding the complex point spread function. This enables high-resolution reconstruction of diffraction patterns, as shown by the iterative process in Eq. (10), fθ*=argminθϵΘ(i=1nfθ(Ii)*PSFiIi).

    However, in THz imaging, the development of aberration-correcting lens systems is prohibitively expensive due to the limited range of suitable materials and the high fabrication cost. Fortunately, free space inherently functions as an aberration-free imaging system[30], with its system transfer function H clearly defined by Eq. (5) without the need of for any lens elements L, as shown in Eq. (6). By modulating the THz wavefront solely through free space, the requirement for complex optical lenses is eliminated.

    To validate this approach, we simulated THz imaging using a resolution test card (Type 18D). The incident THz wavefront’s amplitude was modulated by the card, as shown in Fig. 4(a), while the phase remained constant. After propagating 9 mm in free space, the pattern in Fig. 4(b1) appeared on the detection plane, and after 13 mm, the pattern in Fig. 4(b2) emerged. Applying a neural network to these patterns allowed for reconstruction. With n=1, the amplitude and phase predictions as Figs. 5(a1) and 5(b1) were suboptimal. Increasing n to 2 and using both patterns, improved accuracy, as shown in Figs. 5(a2) and 5(b2), showing n=2, suffices for reconstruction. Higher n values enhance stability and reduce noise but must be balanced with the imaging system’s frame rates. A potential solution involves using a beamsplitter and multiple Rydberg atom-based sensors to capture images at different distances simultaneously.

    Simulation for the resolution test card imaging. (a) Binarization diagram of the resolution test card. (b1) Intensity image of the resolution test card at 9 mm distance. (b2) Intensity image of the resolution test card at 13 mm distance.

    Figure 4.Simulation for the resolution test card imaging. (a) Binarization diagram of the resolution test card. (b1) Intensity image of the resolution test card at 9 mm distance. (b2) Intensity image of the resolution test card at 13 mm distance.

    Simulation for fluorescence image processing using untrained neural networks. (a1), (b1) represent the amplitude image and the phase image predicted by the neural network with n = 1, respectively. (a2), (b2) represent the amplitude image and the phase image predicted by the neural network with n = 2, respectively.

    Figure 5.Simulation for fluorescence image processing using untrained neural networks. (a1), (b1) represent the amplitude image and the phase image predicted by the neural network with n = 1, respectively. (a2), (b2) represent the amplitude image and the phase image predicted by the neural network with n = 2, respectively.

    We conducted experiments with the setup depicted in Fig. 1, replacing the imaging light path assembly with free space filled with air, as illustrated in Fig. 6. In practice, the lasers used for the Rydberg atom excitation are sensitive to environmental factors, such as vibration, temperature, and humidity, leading to up to 20% fluctuations in fluorescence intensity. Nevertheless, the method requires capturing at least two images at different distances along the optical axis, which may experience fluorescence intensity variations between captures. To address the issue, we employed a solution outlined in Eq. (11), which normalizes the fluorescence signal based on the optimization of Eq. (8), fθ*=argminθϵΘ{i=1nHi[fθ(Ii)]mean{Hi[fθ(Ii)]}Iimean(Ii)}.

    Schematic diagram of the imaging experiment.

    Figure 6.Schematic diagram of the imaging experiment.

    In our imaging experiment, we acquired fluorescence images of the resolution test card at varying distances from the light sheet ranging from 2.5 to 12.5 mm in 2 mm increments, as illustrated in Fig. 7. Due to diffraction effects, the line-pair patterns on the detection plane appeared blurred and indistinct.

    Resolution test card fluorescence imaging experiment. (a)–(f) denote the imaging distances of 2.5, 4.5, 6.5, 8.5, 10.5, and 12.5 mm, respectively.

    Figure 7.Resolution test card fluorescence imaging experiment. (a)–(f) denote the imaging distances of 2.5, 4.5, 6.5, 8.5, 10.5, and 12.5 mm, respectively.

    Applying our methods, we reconstruct the amplitude image shown in Fig. 8(a) with n=2 by processing fluorescence images captured at distances of 2.5 and 4.5 mm. Next, We produced the amplitude image in Fig. 8(b) using data from fluorescence images at distances of 2.5, 4.5, 6.5, and 8.5 mm. Finally, Fig. 8(c) presents the amplitude image reconstructed using all six sets of fluorescence images with n=6. As expected, increasing the value of n enhanced the quality of the reconstructed image. Analysis of Fig. 8(c) reveals that the finest resolvable line pairs, marked by the yellow arrows within the white box, correspond to a resolution of 1.25 lp/mm. Based on the Abbe limit, the diffraction limit at this location is determined to be λ2NA0.28mm, where NA denotes the numerical aperture. Equivalently, the resolution of the diffraction limit indicated by the red arrow is calculated to be 3.55 lp/mm.

    Resolution test card fluorescence image processing results. (a)–(c) represent the amplitude images reconstructed from n = 2, n = 4, and n = 6 pictures by our algorithm, respectively.

    Figure 8.Resolution test card fluorescence image processing results. (a)–(c) represent the amplitude images reconstructed from n = 2, n = 4, and n = 6 pictures by our algorithm, respectively.

    In this experiment, the atomic vapor cell is made of quartz, a material that reflects THz radiation. This reflection results in multiple internal interactions with cesium atoms, generating scattering noise that compromises signal quality. As shown in Fig. 9, a circular metallic disc is positioned adjacent to the cell wall to block THz waves from entering the atomic vapor. Despite this measure, fluorescence signals remain affected by speckle patterns and additional interference caused by quartz reflections, which degrade imaging resolution and prevent the system from reaching the diffraction limit. To address this, replacing quartz with a material that exhibits better THz transmission properties could reduce reflection-based noise. Furthermore, the excitation laser’s light sheet suffers from non-uniform energy distribution, operating effectively over a 60mm×30mm area instead of the intended 60mm×60mm area. This limitation also impacts imaging quality, underscoring the importance of optimizing the light sheet’s uniformity to enhance overall performance.

    Phenomenon of THz waves reflecting within the atom vapor cell. (a) Fluorescence image of the metallic disc. (b) Fluorescence image without THz irradiation.

    Figure 9.Phenomenon of THz waves reflecting within the atom vapor cell. (a) Fluorescence image of the metallic disc. (b) Fluorescence image without THz irradiation.

    The neural network was developed utilizing the PyTorch framework and Python version 3.10.0. We employed the Adam optimizer with a learning rate set at 0.001 to optimize the weights and biases. To improve convergence, uniformly distributed noise within the range of 0 to 0.01 is introduced to the fixed input I at every 200 optimization steps. In this study, the input I dimensions are 512 pixel × 512 pixel. On average, the network requires approximately 10,000 epochs to achieve a highly accurate estimate, a process that takes around 5 min on a system equipped with an Intel i9-14900 K CPU, 32 GB of RAM, and an NVIDIA A100 GPU. To demonstrate the applicability of our imaging techniques, we applied them to a range of objects, followed by algorithmic processing, and yielding comparable outcomes. The data and code that support the finding of this study are available on GitHub at https://github.com/ssrfwanjun/PhysenNet_mat.git.

    5. Conclusion

    This study tackles the issue of high noise levels in single-frequency THz imaging systems leveraging Rydberg atoms, presenting an innovative method for processing raw images and optimizing the illumination system. By employing an untrained deep neural network, the approach effectively reduces diffraction noise in preprocessed fluorescence images, eliminating the need for specialized THz datasets. Experimental outcomes demonstrate notable enhancements in imaging quality, achieving a resolution exceeding 1.25 lp/mm at an imaging distance of 2.5 mm, all without relying on lens-based systems. Furthermore, with anticipated advancements in the materials used for atomic vapor cells and the stability of excitation lasers, the resolution is projected to approach the diffraction limit of 3.55 lp/mm. These breakthroughs pave the way for high-resolution high-speed THz imaging, representing a significant leap forward in the field.

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    Jun Wan, Bin Zhang, Xianzhe Li, Tao Li, Qirong Huang, Xinyu Yang, Kaiqing Zhang, Wei Huang, Haixiao Deng, "Enhancing terahertz imaging with Rydberg atom-based sensors using untrained neural networks," Chin. Opt. Lett. 23, 071104 (2025)
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