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• An ultra-compact add-on module (about 30 mm in total) based on two polarization gratings is built for single shot DIC type quantitative phase imaging. • A fast sythethis aperture (line-scanning) method is proposed. • The zdirectional sectional ability of 3D phase imaging is discuused in the supplementary material and several important conlusions are made. Differential interference contrast (DIC) microscopy is an important member of quantitative phase imaging (QPI) family owing to its simple optical implementation and high compatibility regarding to different coherence degree of illumination field. Such compactivity means that the DIC-based phase imaging can be conveniently converted between 2D-integrational and 3D-sectional modes by switching the spatial coherence degree of illumination field between low degree and high. However, there is a potential trade-off compromise in the existed experimental implementations for DIC imaging regarding to the optical simplicity, space-bandwidth utilization and temporal resolution. In this manuscript, we proposed a polarization gratings pair (PGs) based off-axis DIC system to realize integrational and sectional QPI. Building on a bright field microscope and getting rid of the additional 4f lens system, the proposed PGs-DIC system can realize single-shot QPI with an ultra-compact optical configuration. In order to improve the imaging resolution and optical sectional ability, a fast synthetic aperture technology is introduced, in which multiple interferograms with different line-filtered illumination are captured. Both high resolution 2D-integrational and 3D-sectional phase imaging results indicate that the proposed PGs-DIC system is a good candidate for QPI. Specially, a theoretical model is proposed to quantitatively estimate z-direction resolution for z -scanning 3D phase imaging technology and future application in the PGs-DIC system. [ABSTRACT FROM AUTHOR]

• Non-blind algorithms, such as the Wiener filter and the Lucy-Richardson algorithm, are always used to restore images of the optical synthetic aperture imaging (OSAI) system, but can't apply in practice easily due to the unknown prior information of system. Deep learning is a new technology rising nowadays, and has many successful application cases in different fields. An improved U-shaped network named RestoreNet is designed to remove the blur and recover the image from OSAI system. • After enough training, RestoreNet has advantages as below: • Restoring ability : After enough training, RestoreNet can remove the blur definitely and easily in OSAI system; • Fast for applying : In testing period, the recovering time for one image is just ~30ms , but the restoration effect is better than the Lucy-Richardson algorithm, which takes 470ms for one image; • Prior information unknown : RestoreNet can restore images without the prior information of system , for example, the point spread function or the optical transfer function, which is not provided by the non-blind algorithms; • Generalization ability : RestoreNet has strong ability in generalization ability whether facing different types of images or imaging systems with different sub-aperture arrangements. Imaging blur is an inevitable problem in optical synthetic aperture imaging system because of the low response of frequency. Non-blind deconvolution algorithms are usually used for image restoration to obtain clear and high-resolution images. However, accurate prior information on the optical transfer function of system is required in the non-blind methods. As a data-driven approach, recent developments in deep learning have shown great potential in image processing. In this paper, a U-shaped deep learning framework named RestoreNet is proposed for image restoration, especially for removing the blur of optical synthetic aperture imaging system in a blind way. Numerical simulation and experiment results show that RestoreNet is an effective alternative with great restoration ability, stability and generalization in the image restoration of optical synthetic aperture imaging system. [ABSTRACT FROM AUTHOR]