This article introduces PtychoPINN: an unsupervised physical information deep learning method for fast high-resolution scanning coherent diffraction reconstruction

Coherent diffraction imaging (CDI) is a promising technique that uses the diffraction of light beams or electrons to reconstruct an image of a sample without the need for optical components. The method has a variety of applications, from nanoscale imaging to X-ray stack photography and astronomical wavefront setups. However, one of the main problems of CDI is the phase retrieval problem, and the detector cannot record the phase of the diffracted wave, resulting in information loss.

A large amount of research has been conducted to solve this problem, mainly focusing on the use of artificial neural networks. Although these methods are much more efficient than traditional iterative methods, they require large amounts of labeled data for training, which is experimentally onerous. In addition, these methods also lead to degradation of reconstructed image quality, so better methods are needed. Therefore, the authors of this research paper from the SLAC National Accelerator Laboratory in the United States introduce PtychoPINN. This unsupervised neural network reconstruction method retains the significant speedup of previous deep learning-based methods while improving quality.

Traditional physics-based CDI methods are accurate, but computationally expensive and are iterative in nature. In contrast, neural network-based methods rely on large training data sets to capture specific data regularities well and have better reconstruction speed. Therefore, the researchers tried to combine the advantages of both methods to create PtychoPINN. The researchers defined the model’s loss function on the forward-mapped neural network output, which forces the network to learn the physics of diffraction.

PtychoPINN utilizes an autoencoder architecture consisting of convolution, average pooling, upsampling, and custom layers to scale the input and output. The researchers used the Poisson model output and the corresponding negative log-likelihood target to model the Poisson noise inherent in the experimental data. Three different types of data sets are used to train and evaluate models: “Line” for randomly oriented lines, Gaussian Random Fields (GRF), and “Large Features” for experimentally derived data. Each data set is based on sharpness, isotropy and characteristic length in real spatial structures. For each data set, the researchers simulated a set of diffraction patterns that corresponded to a rectangular grid of scanned points on the sample and the known detection function.

The researchers compared the performance of PtychoPINN to the supervised learning baseline PytchoNN. The former shows minimal true spatial amplitude and phase degradation, while the latter experiences significant blurring. In addition, PytchoPINN also exhibits better peak signal-to-noise ratio (PSNR). Although both perform well, PytchoPINN has better Fourier ring correlation at the 50% threshold (FRC50) than the other when evaluated against reconstructions of “large feature” amplitudes.

In summary, PytchoPINN is an autoencoder framework for coherent diffraction imaging into which researchers incorporate physical principles to improve accuracy, resolution, and generalization while requiring less training material. This framework significantly outperforms the supervised learning baseline PytchoNN on metrics such as PSNR and FCR50. While this is a promising tool, it’s far from perfect, and researchers are working to further improve its capabilities. Nonetheless, the framework is a promising tool with the potential for instantaneous, high-resolution imaging exceeding that of lens-based systems without compromising imaging throughput.

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