We present a fast and precise deep-learning architecture, which we term O-Net, for obtaining super-resolved images from conventional phase-modulated optical microscopical techniques, such as phase-contrast microscopy and differential interference contrast microscopy. O-Net represents a novel deep convolutional neural network that can be trained on both simulated and experimental data, the latter of which is being demonstrated in the present context. The present study demonstrates the ability of the proposed method to achieve super-resolved images even under poor signal-to-noise ratios and does not require prior information on the point spread function or optical character of the system. Moreover, unlike previous state-of-the-art deep neural networks (such as U-Nets), the O-Net architecture seemingly demonstrates an immunity to network hallucination, a commonly cited issue caused by network overfitting when U-Nets are employed. Models derived from the proposed O-Net architecture are validated through empirical comparison with a similar sample imaged via scanning electron microscopy (SEM) and are found to generate ultra-resolved images which came close to that of the actual SEM micrograph.

The field of optical nanoscopy, a paradigm referring to the recent cutting-edge developments aimed at surpassing the widely acknowledged 200nm-diffraction limit in traditional optical microscopy, has gained recent prominence & traction in the 21 st century. Numerous optical implementations allowing for a new frontier in traditional confocal laser scanning fluorescence microscopy to be explored (termed super-resolution fluorescence microscopy) have been realized through the development of techniques such as stimulated emission and depletion (STED) microscopy, photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), amongst others. Nonetheless, it would be apt to mention at this juncture that optical nanoscopy has been explored since the mid-late 20 th century, through several computational techniques such as deblurring and deconvolution algorithms. In this review, we take a step back in the field, evaluating the various in silico methods used to achieve optical nanoscopy today, ranging from traditional deconvolution algorithms (such as the Nearest Neighbors algorithm) to the latest developments in the field of computational nanoscopy, founded on artificial intelligence (AI). An insight is provided into some of the commercial applications of AI-based super-resolution imaging, prior to delving into the potentially promising future implications of computational nanoscopy. This is facilitated by recent advancements in the field of AI, deep learning (DL) and convolutional neural network (CNN) architectures, coupled with the growing size of data sources and rapid improvements in computing hardware, such as multi-core CPUs & GPUs, low-latency RAM and hard-drive capacities.

We present herein a triplet string of concatenated O-Net ('bead') architectures (formulated as discussed in our previous study) which we term 'Θ-Net' as a means of improving the viability of generated super-resolved (SR) images in silico. In the present study, we assess the quality of the afore-mentioned SR images with that obtained via other popular frameworks (such as ANNA-PALM, BSRGAN and 3D RCAN). Models developed from our proposed framework result in images which more closely approach the gold standard of the SEM-verified test sample as a means of resolution enhancement for optical microscopical imaging, unlike previous DNNs. In addition, cross-domain (transfer) learning was also utilized to enhance the capabilities of models trained on DIC datasets, where phasic variations are not as prominently manifested as amplitude/intensity differences in the individual pixels [unlike phase contrast microscopy (PCM)]. The present study thus demonstrates the viability of our current multi-paradigm architecture in attaining ultra-resolved images under poor signal-to-noise ratios, while eliminating the need for a priori PSF & OTF information. Due to the wide-scale use of optical microscopy for inspection & quality analysis in various industry sectors, the findings of this study would be anticipated to exhibit a far-ranging impact on several engineering fronts.