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Theoretical resolution enhancement of confocal laser-scanning microscopy (CLSM) is sacrificed for the best compromise between optical sectioning and the signal-to-noise ratio (SNR). The pixel reassignment reconstruction algorithm can improve the effective spatial resolution of CLSM to its theoretical limit. However, current implementations are not versatile and are time-consuming or technically complex. Here we present a parameter-free post-processing strategy for laser-scanning microscopy based on deep learning, which enables a spatial resolution enhancement by a factor of ∼ 1.3 , compared to conventional CLSM. To speed up the training process for experimental data, transfer learning, combined with a hybrid dataset consisting of simulated synthetic and experimental images, is employed. The overall resolution and SNR improvement, validated by quantitative evaluation metrics, allowed us to correctly infer the fine structures of real experimental images.

Supplement 1

Radially polarized field under strong focusing has emerged as a powerful manner for fluorescence microscopy. However, the refractive index (RI) mismatch-induced aberrations seriously degrade imaging performance, especially under high numerical aperture (NA). Traditional adaptive optics (AO) method is limited by its tedious procedure. Here, we present a computational strategy that uses artificial neural networks to correct the aberrations induced by RI mismatch. There are no requirements for expensive hardware and complicated wavefront sensing in our framework when the deep network training is completed. The structural similarity index (SSIM) criteria and spatial frequency spectrum analysis demonstrate that our deep-learning-based method has a better performance compared to the widely used Richardson-Lucy (RL) deconvolution method at different imaging depth on simulation data. Additionally, the generalization of our trained network model is tested on new types of samples that are not present in the training procedure to further evaluate the utility of the network, and the performance is also superior to RL deconvolution.

Second harmonic generation (SHG) microscopy is expected to be a powerful tool for observing the cellular-level functionality and morphology information of thick tissue owe to its unique imaging properties. However, the maximum attainable resolution obtainable by SHG microscopy is limited by the use of long-wavelength, near-infrared excitation. In this paper, we report the use of pixel reassignment to improve the spatial resolution of SHG microscopy. The SHG signal is imaged onto a position-sensitive camera, instead of a point detector typically used in conventional SHG microscope. The data processing is performed through pixel reassignment and subsequent deblurring operation. We present the basic principle and a rigorous theoretical model for SHG microscopy using pixel reassignment (SHG-PR). And for the first time, the optimal reassignment factor for SHG-PR is derived based on the coherent characteristics and the dependence of wavelength in SHG microscopy. To evaluate the spatial resolution improvement, images of nano-beads separated by different distances and of a microtubule array have been simulated. We gain about a 1.5-fold spatial resolution enhancement compared to conventional SHG microscopy. When a further deblurring operation is implemented, this method allows for a total spatial resolution enhancement of about 1.87. Additionally, we demonstrate the validity of SHG-PR for raw data with noise. LAY DESCRIPTION: Second harmonic generation (SHG) microscopy has emerged as a powerful imaging technique in clinical diagnostics and biological research. SHG microscopy is label-free and provides intrinsic optical sectioning for three-dimensional (3D) imaging. However, a near-infrared excitation wavelength results a restriction in the maximum attainable spatial resolution of SHG microscopy. In this paper, we present a simple resolution-enhanced SHG imaging method, SHG microscopy using pixel reassignment (SHG-PR). We demonstrate a rigorous theoretical model for SHG-PR and derive the optimal reassignment factor. The simulation result shows the clear improvement of the image resolution and contrast in the SHG-PR after deblurring operation. The FWHM value of single microtubule shows that SHG-PR enables a spatial resolution enhancement by a factor of 1.5, compared to conventional SHG microscopy. After a proper deblurring operation, this method allows for a total spatial resolution enhancement of about 1.87. The improvements of spatial resolution and contrast are still valid for raw data with noise. It is expected that this method can contribute towards new insights in unstained tissue morphology, interaction of cells, and diseases diagnosis.

For second harmonic generation (SHG) imaging, the specimen is often observed through an immersion medium and a cover glass whose refractive indices are usually different from that of the specimen. However, the currently used theoretical models are based on the assumption that the specimen is situated in a homogeneous medium. The limitation of these models is that they ignore the effects of the refractive index mismatches and the imaging depth. In this paper, we have demonstrated, for the first time to our knowledge, a rigorous model of SHG imaging through stratified media focused by radially polarized beams. Based on the proposed model, the detected SHG intensity patterns excited in a refractive index perfectly matched, aberration-free medium and in mismatched stratified media are compared. The effects of the imaging depth and effective numerical aperture (NA) on the performance of SHG imaging with oil immersion objectives are investigated by the stratified media model. It is found that the full width at half maximum (FWHM) in the axial direction at imaging depth of 80 µm is ~3.1 times as large as that of 10 µm imaging depth. While for the transverse FWHM, the increment is only about 23%. The quality of the SHG intensity distribution can be increased by reducing the NA appropriately at the expense of the detected signal strength. The proposed model is helpful to provide guidelines for the adaptive aberration correction in SHG imaging and can be used to optimize the experimental configuration.

Image scanning microscopy (ISM) is a promising tool for bioimaging owing to its integration of signal to noise ratio (SNR) and super resolution superior to that obtained in confocal scanning microscopy. In this paper, we introduce the annular radially polarized beam to the ISM, which yields an axially extended excitation focus and enhanced resolution, providing a new possibility to obtain the whole information of thick specimen with a single scan. We present the basic principle and a rigorous theoretical model for ISM with annular radially polarized beam (ISM-aRP). Results show that the resolution of ISM-aRP can be enhanced by 4% compared with that in conventional ISM, and the axial extent of the focus is longer than 6λ. The projected view of the simulated fluorescent beads suspension specimen demonstrates the validity of ISM-aRP to obtain the whole information of volume sample. Moreover, this simple method can be easily integrated into the commercial laser scanning microscopy systems.

A confocal configuration is added to the detection path in third harmonic generation (THG) microscopes for resolution improvement. The three-dimensional (3D) point-spread function (PSF) is a key indicator for the practical imaging ability of THG confocal microscopy. However, due to the coherent emission feature of THG, the 3D PSF for THG confocal microscopy is still pending and has not been investigated. In this paper, we have presented, for the first time to our knowledge, the 3D PSF model of THG confocal microscopy under circularly or radially polarized excitations. To make our study more realistic, based on the proposed model, the 3D PSF distributions of THG confocal microscopy with aberrations are analyzed further. The effects of the size of the confocal pinhole are also discussed. This work is important for the interpretation of THG confocal microscope images and for the adaptive aberration correction in THG confocal microscopy.

Second harmonic generation (SHG) polarization intensity distribution illuminated with radially polarized beams by lens focusing appears two peaks, when the nonlinear optical coefficients dominate that is relevant to the transverse electric field components. Such two peaks pattern may result in ghosting and the decrement of imaging resolution. In this paper, an elliptical mirror based system is proposed in the case of radially polarized beams illumination for SHG. The calculated predictions and numerical simulations demonstrate that for radially polarized beams, the proportion of transverse field components at the focal plane under the condition of elliptical mirror focusing is 2.6 times smaller than that with lens focusing when its numerical aperture (NA) is 1. Furthermore, the full width at half maximum (FWHM) of the total field intensity profile is approximately 81% of that in a lens focusing system. Due to the enhancement of longitudinal components of incident field, the distribution of SHG polarization presents a single-peak pattern, in which two peaks can be observed with lens focusing. The SHG polarizations in collagen fiber, KTiOPO4 , and LiNbO3 have been numerical simulated and discussed in detail to verify the validity of the proposed method. LAY DESCRIPTION: A novel focusing mode for second harmonic generation (SHG) microscopy is described in this paper. In the case of radially polarized excitations, the SHG polarization distributions of some specimens appear two peaks pattern with traditional lens focusing. Such two peaks pattern may result in ghosting and the decrement of imaging resolution. By introducing elliptical mirror, the modulation of electric field at the focal plane can be realized. Thus, the distribution of SHG polarization is converted into a single-peak pattern which eliminates the ghosting and improves the spatial resolution on SHG images. This proposed method can be used for SHG in various materials and the full width at half maximum (FWHM) of SHG polarization will compress in different degrees. Besides, there is a significant improvement on signal-to-noise ratio in SHG imaging when an annular aperture illumination is applied. The focusing mode with elliptical mirror can also be utilized in other nonlinear optics areas such as polarized third harmonic generation (THG) measurements and two-photon fluorescence (TPF) microscopy.

Absolute test is one of the most important and efficient techniques to saperate the reference surface which usually limits the accuracy of test results. For the position error correction in absolute interferometry tests based on rotational and translational shears, the estimation algorithm adopts least-squares technique to eliminate azimuthal errors caused by rotation inaccuracy and the errors of angular orders are compensated with the help of Zernike polynomials fitting by an additional rotation measurement with a suitable selection of rotation angles. Experimental results show that the corrected results with azimuthal errors are very close to those with no errors, compared to the results before correction. It can be seen clearly that the testing errors caused by rotation inaccuracy and alignment errors of the measurements can be consequently eliminated from the differences in measurement results by the proposed method.