Coherent diffractive imaging (CDI) is a promising technique that leverages diffraction from a beam of light or electron for reconstructing the image of a specimen by eliminating the need for optics. The method has numerous applications ranging from nanoscale imaging to X-ray ptychography and astronomical wavefront settings. One of the major issues with CDI, though, is the phase retrieval problem, where the detectors fail to record the phase of the diffracted wave, leading to information loss.
A considerable amount of research has been done to address this problem, focusing mainly on using artificial neural networks. Although these methods are much more efficient than conventional iterative methods, they require a large volume of labeled data for training, which is experimentally burdensome. Additionally, these methods also lead to a degraded reconstructed image quality, necessitating a need for a better approach. Therefore, the authors of this research paper from SLAC National Accelerator Laboratory, USA have introduced PtychoPINN. This unsupervised neural network reconstruction method retains a significant speedup of previous deep learning-based methods while improving the quality simultaneously.
Conventional physics-based CDI methods are accurate but are computationally expensive, being iterative in nature. On the contrary, neural-network-based methods rely on a large training dataset to capture particular data regularities well and have better reconstruction speed. The researchers have thus tried to incorporate the pros of both these methods to create PtychoPINN. The researchers defined the loss function of the model over the forward-mapped neural network output, which forces the network to learn diffraction physics.
PtychoPINN leverages an autoencoder architecture incorporating convolutional, average pooling, upsampling, and custom layers to scale the input and output. The researchers used a Poisson model output and corresponding negative log-likelihood objective, which modeled the Poisson noise intrinsic in the experimental data. Three distinct types of datasets were used for training and evaluating the model – ‘Lines’ for randomly oriented lines, Gaussian Random Field (GRF), and ‘Large Features’ for experimentally derived data. Each dataset is based on sharpness, isotropy, and characteristic length in real-space structure, and for each of them, the researchers simulated a collection of diffraction patterns that correspond to a rectangular grid of scan points on the sample and a known probe function.
The researchers compared the performance of PtychoPINN with the supervised learning baseline PytchoNN. The former shows minimal real-space amplitude and phase degradation, while the latter experiences significant blurring. Moreover, PytchoPINN also demonstrated a better peak signal-to-noise ratio (PSNR). Though both performed well, when evaluated against the reconstruction of the ‘Large Features’ amplitude, PytchoPINN outperformed the other with a better Fourier ring correlation at the 50% threshold (FRC50).
In conclusion, PytchoPINN is an autoencoder framework for coherent diffractive imaging, into which the researchers have incorporated physical principles to improve the accuracy, resolution, and generalization while requiring less training data. The framework significantly outperforms the supervised learning baseline PytchoNN on metrics like PSNR and FCR50. Although a promising tool, it is still far from perfect, and the researchers are working on further improving its capabilities. Nonetheless, the framework is a promising tool and has the potential to be used in real-time, high-resolution imaging that exceeds the resolution of lens-based systems without compromising imaging throughput.
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