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npj Nanophotonics

Coincidence imaging for Jones matrix with a deep-learning approach

Jiawei Xi, Tsz Kit Yung, Hong Liang, Tan Li, Wing Yim Tam, Jensen Li

Published Mar 6, 2024• 11 citations
Publisher

Abstract

Abstract Coincidence measurement has become an emerging technique for optical imaging. Based on measuring the second-order coherence g2, sample features such as reflection/transmission amplitude and phase delay can be extracted with developed algorithms pixel-by-pixel. However, an accurate measurement of g2 requires a substantial number of collected photons which becomes difficult under low-light conditions. Here, we propose a deep-learning approach for Jones matrix imaging using photon arrival data directly. A variational autoencoder (β-VAE) is trained using numerical data in an unsupervised manner to obtain a minimal data representation, which can be transformed into an image with little effort. We demonstrate as few as 88 photons collected per pixel on average to extract a Jones matrix image, with accuracy surpassing previous semi-analytic algorithms derived from g2. Our approach not only automates formulating imaging algorithms but can also assess the sufficiency of information from a designed experimental procedure, which can be useful in equipment or algorithm designs for a wide range of imaging applications.

DOI
10.1038/s44310-024-00002-z

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Abstract Coincidence measurement has become an emerging technique for optical imaging. Based on measuring the second-order coherence g2, sample features such as reflection/transmission amplitude and phase delay can be extracted with developed algorithms pixel-by-pixel. However, an accurate measurement of g2 requires a substantial number of collected photons which becomes difficult under low-light conditions. Here, we propose a deep-learning approach for Jones matrix imaging using photon arrival data directly. A variational autoencoder (β-VAE) is trained using numerical data in an unsupervised manner to obtain a minimal data representation, which can be transformed into an image with little effort. We demonstrate as few as 88 photons collected per pixel on average to extract a Jones matrix image, with accuracy surpassing previous semi-analytic algorithms derived from g2. Our approach not only automates formulating imaging algorithms but can also assess the sufficiency of information from a designed experimental procedure, which can be useful in equipment or algorithm designs for a wide range of imaging applications.
Two-photon interference is an important effect that is tightly related to the quantum nature of light. Recently, it has been shown that the photon bunching from the Hong-Ou-Mandel (HOM) effect can be used for quantum imaging in which sample properties (reflection/transmission amplitude, phase delay, or polarization) can be characterized at the pixel-by-pixel level. In this work, we perform Jones matrix imaging for an unknown object based on two-photon interference. By using a reference metasurface with panels of known polarization responses in pairwise coincidence measurements, the object's polarization responses at each pixel can be retrieved from the dependence of the coincidence visibility as a function of the reference polarization. The post-selection of coincidence images with specific reference polarization in our approach eliminates the need in switching the incident polarization and thus parallelized optical measurements for Jones matrix characterization. The parallelization in preparing input states, prevalent in any quantum algorithms, is an advantage of adopting two-photon interference in Jones matrix imaging. We believe our work points to the usage of metasurfaces in biological and medical imaging in the quantum optical regime.
Quantum imaging using photon pairs with strong quantum correlations has been harnessed to bring quantum advantages to various fields from biological imaging to range finding. Such inherent non-classical properties support the extraction of more valid signals to build photon-limited images, even in low-light conditions where the shot noise becomes dominant as light decreases to a single-photon level. Numerical optimization algorithms are possible but require thousands of photon-sparse frames, and they are thus unavailable in real time. We demonstrate fast correlated-photon imaging enhanced by deep learning as an intelligent computational strategy to discover a deeper structure in big data. Our work verifies that a convolutional neural network can efficiently solve inverse imaging problems associated with strong shot noise and background noise (electronic noise, scattered light). Our results show that we can overcome limitations due to the trade-off between imaging speed and image quality by pushing the low-light imaging technique to the single-photon level in real time, which enables deep-learning-enhanced quantum imaging for real-life applications.
Abstract The phase sensitivity of photonic NOON states scales O(1/N), which reaches the Heisenberg limit and indicates a great potential in high-quality optical phase sensing. However, the NOON states with large photon number N are experimentally difficult both to prepare and to operate. Such a fact severely limits their practical use. In this article, we soften the requirements for high-quality imaging based on NOON states with large N by introducing deep-learning methods. Specifically, we show that, with the help of deep-learning network, the fluctuation of the images obtained by the NOON states when N = 2 can be reduced to that of the currently infeasible imaging by the NOON states when N = 8. We numerically investigate our results obtained by two types of deep-learning models—deep neural network and convolutional denoising autoencoders, and characterize the imaging quality using the root mean square error. By comparison, we find that small-N NOON state imaging data is sufficient for training the deep-learning models of our schemes, which supports its direct application to the imaging processes.
Quantum correlation, as an intrinsic property of quantum mechanics, has been widely employed to test the fundamental physical principles and explore the quantum-enhanced technologies. However, such correlation would be drowned and even destroyed in the conditions of high levels of loss and noise, which drops into the classical realm and renders quantum advantage ineffective. Especially in low light conditions, conventional linear classifiers are unable to extract and distinguish quantum and classical correlations with high accuracy. Here we experimentally demonstrate the classification of quantum correlation using deep learning to meet the challenge in the quantum imaging scheme. We design the convolutional neural network to learn and classify the correlated photons efficiently with only 0.1 signal photons per pixel. We show that decreasing signal intensity further weakens the correlation and makes an accurate linear classification impossible, while the deep learning method has a strong robustness of such task with the accuracy of 99.99%. These results open up a new perspective to optimize the quantum correlation in low light conditions, representing a step towards diverse applications in quantum-enhanced measurement scenarios, such as super-resolution microscope, quantum illumination, etc.
The sensitivity of optical measurement is ultimately constrained by the shot noise to the standard quantum limit.It has become a common concept that beating this limit requires quantum resources.A deep-learning neural network free of quantum principle has the capability of removing classical noise from images, but it is unclear in reducing quantum noise.In a coincidence-imaging experiment, we show that quantum-resource-free deep learning can be exploited to surpass the standard quantum limit via the photon-number-dependent nonlinear feedback during training.Using an effective classical light with photon flux of about 9 × 10 4 photons per second, our deep-learning-based scheme achieves a 14 dB improvement in signal-to-noise ratio with respect to the standard quantum limit.
Three-dimensional (3D) imaging in low-light environments has broad application prospects. High-quality 3D imaging requires obtaining both the depth and reflectivity information of the target. With the rapid development of Quantum Information Technology (QIT), Quantum Imaging (QI) provides a new approach to achieve high-quality 3D imaging. However, traditional QI methods are limited to Two-dimensional (2D) imaging and cannot accurately extract the depth information from the target. These methods also suffer from insufficient precision in reflectivity calculations. Therefore, we introduce a novel quantum 3D imaging and reflectivity estimation method based on entangled photons. Specifically, we first utilize the spatiotemporal correlation characteristics of entangled photon pairs combined with coincidence measurement technology to accurately determine target depth. Second, we analyze the distribution of entangled photon numbers during free-space transmission to construct a photon-based detection probability model. Third, we use this model to derive the probability density function of coincidence counts. Finally, we estimate the surface reflectivity information through statistical analysis of coincidence counting. Experimental results demonstrate that the proposed method can accurately reconstruct both depth and reflectivity profiles of the target in low-light environments. These findings validate the effectiveness of our method and highlight the potential of quantum 3D imaging for target detection in low-light environments.