Radially polarized beams are widely used in high-resolution imaging owing to their numerous advantages, such as the ability to provide significantly smaller spot sizes under tight focusing. The system comprises immersion medium and specimen with different refractive indices. The refractive index mismatch often results in aberrations that significantly affect the imaging performance, especially under large depths. The aberrations are prevalent even in well-corrected objectives. Correction of mismatch-induced aberrations using the traditional adaptive optics methods is limited in many ways. For instance, it requires complicated sensing methods and costly hardware, making it unsuitable for many practical applications. Therefore, the development of alternative methods for correcting the refractive index mismatch is highly desirable for high-resolution imaging.
Deep learning, a class of machine learning, has recently emerged as a useful technique for performing complex tasks on specific data using multilayered artificial neural networks. It has been successfully applied in image resolution enhancement, image processing, classification, among others. Lately, it has also been identified as a promising and useful tool for correcting aberrations. To this note, Professor Weibo wang’s team from the Harbin Institute of Technology presented an artificial neural networks-based computation strategy to correct the refractive mismatch-induced aberrations. The research was motivated by the hypothesis that microscopic images with refractive index mismatch-induced aberrations can reveal more useful information when the aberrations are compensated by capturing nonlinear relationships over large image areas. Their work is currently published in the journal, Optics Express.
In their approach, a laser scanning microscope consisting of two subsystems: focusing of incident light and imaging of fluorescent emission signal was used. Based on the established point spread function model, the refractive indices mismatched images were generated at different imaging depths. A deep neural network was trained to demonstrate the refractive index mismatch correction for radially polarized illuminations. The obtained results were compared with those obtained by image deconvolution methods using spatial frequency spectrum analysis and structural similarity index. Subsequently, the generalization of the trained network model was tested with new samples not initially included in the procedure to validate its feasibility.
Results showed that the proposed deep-learning-based method outperformed the widely used Richardson – Lucy deconvolution method at an imaging depth of 5 –50 µm. Consequently, the authors observed that the new network could accurately infer fine structures of new samples that were not part of the network’s training set through blind inference, a significant improvement compared to that achieved using the Richardson – Lucy deconvolution method. The cross-sections further revealed that the technique could correctly cover the information lost in the microscopy image due to refractive index mismatch-induced aberrations. Furthermore, the deep learning method exhibited several advantages in terms of structural simplicity, imaging speed, and cost. Additionally, it neither required additional hardware nor complicated wavefront sensing.
In summary, the study reported the use of deep learning based on deep convolutional neural networks to correct refractive index mismatch-induced aberrations. The method provided more reliable and accurate predictions of the aberration-free images due to the nonlinear nature of the neural network. Based on the results, the proposed strategy performed better than other methods, such as the widely used Richardson – Lucy deconvolution technique. In a statement to Advances in Engineering, Professor Weibo Wang noted that the study provided useful insights into the use of artificial neural networks to advance high-resolution imaging that would subsequently increase its practical application in various fields.
Wang, W., Wu, B., Zhang, B., Li, X., & Tan, J. (2020). Correction of refractive index mismatch-induced aberrations under radially polarized illumination by deep learning. Optics Express, 28(18), 26028.