Data-driven computational methods in optical imaging and characterization

Abstract

Data-driven methods have advanced rapidly in the recent decades. They offer an approach to model complex systems without prior information, which may be too difficult to be modelled manually. This approach has shown great achievements in many different domains and it is a great opportunity to leverage it to solve challenges in photonics. A few problems in photonic areas are selected in this thesis to demonstrate its potentials in a wide range of tasks. Two-photon microscopy (2PM) has been an important tool for bioimaging thanks to its high lateral and axial resolution, high specificity and contrast, and deep penetration depth. However, it has a slower imaging speed due to its laser-scanning requirement. In functional brain imaging, a high volumetric imaging speed is required because the neuronal activities are short-lived and span across a large volume. One technique to increase the volumetric imaging speed is to use extended depth of field to project the volume onto 2-dimesional image instead of scanning a z-stack. However, one major drawback is that the depth information is lost during the projection which limits its applications. With regard to optical characterization, design of photonic devices usually require the understanding of the light propagation. However, these propagation dynamics are highly nonlinear and their simulations require computationally intensive numerical simulations. This greatly limits the possibilities of optimization techniques applicable to these tasks because of the infeasible time cost. Thus, an accurate yet fast method to simulate these dynamics is invaluable for photonic designs as it can create a lot of opportunities for optimization. My contributions aim to solve the above challenges in imaging and photonics using data- driven approaches and they can be grouped into three sections: (1) By leveraging the bending of Airy beam, 3D volume can be reconstructed from 2D projected images using Airy beam. The limitation due to the symmetric property of Airy beam is solved by capturing images from multiple focal planes. High axial and lateral reconstruction accuracy has been achieved. The field of view is also expanded due to the lateral shift introduced by the Airy beam. A data-driven approach using deep neural network (transformer) is demonstrated without prior knowledge about the imaging system and sample. (2) A deep learning method based on conditional generative adversarial network has been trained to enhance the image quality of undersampled 2PM images. By conditioning the generator and discriminator on the input image, the model produces very few artefacts. Enhancement in resolution and contrast, and noise suppression are demonstrated. With a 2x2 downsampling ratio, a 4 times increase in imaging speed has been achieved. (3) A transformer model is proposed to predict the nonlinear dynamics in fiber. It has achieved an order of magnitude lower in loss, and an order of magnitude faster than a recurrent neural network. It has significant better prediction accuracy in long and complex sequence. Furthermore, an adaptive sampling method is proposed to improve long-range prediction without introducing overhead. Lastly, the generalizability of the model is improved by providing additional input regarding the environment. (An abstract of exactly 500 words)