Digital holography with advanced autofocusing and reconstruction algorithms

Abstract

Digital holography (DH) is a rapidly developing field that has drawn tremendous attention from both research and commercial points of view. It can optically record a three-dimensional (3D) scene as a 2D digital hologram, and reconstruct the object with numerical back-propagation. Due to the dynamic, label-free and phase-contrast imaging, DH has been widely used in 4D biological microscopy and surface topography. Yet, autofocusing and Fresnel propagation-based algorithms are essential steps for reconstruction. The purpose of this dissertation is to handle the autofocusing in DH, and to harness the recent emerging learning-based algorithm to cope with the challenges arising with digital holographic reconstruction. First, although DH allows post-processing on holograms to reconstruct multi-focus images, it suffers from defocus noise in numerical reconstruction. A method that can achieve extended focused imaging (EFI), in which all sections are in-focus and sharp, and can reconstruct a depth map (DM) which presents true depths of the individual sections, of a 3D scene is demonstrated. A depth-from-focus algorithm is first used to create the DM for each pixel based on entropy minimization. Then, computationally, the EFI of the whole 3D object is obtained with the help of DM. Second, since in DH a 3D object that consists of multiple discrete sections may have overlapping regions with each other, this situation brings more challenging to autofocusing. To deal with the overlapping, a focus metric based on the Lp norm of the eigenvalues of structure tensor matrix is proposed. The efficacy of the proposed autofocusing method on non-overlapping and overlapping cases is verified by holographically recording a multi-sectional object. Furthermore, conventional autofocusing, which is tackled by evaluating the sharpness of sequential reconstructed images within an estimated range using a focus metric, while effective, is computationally demanding and time-consuming. To cope with this problem, the autofocusing is cast as a regression, in which the focal distance is regarded as the response of a raw hologram. Therefore, estimating the object’s distance turns into predicting the hologram, which is solved by training a deep convolutional neural network with substantial holograms and true responses acquired a priori. It is shown that, by doing so, even in the absence of knowing the physical parameters, reconstructing an image stack for autofocusing is avoided, leading to fast prediction. Fourth, although conventional reconstruction algorithms are effective, filtering operation, autofocusing and prior knowledge such as the pixel pitch and the source wavelength are inevitable and consume more time. While for phase-contrast imaging, the phase aberration has to be compensated with additional hardware or algorithm, and subsequently an unwrapping step, which is sensitive to noise and distortion, follows to recover the true phase. Besides, for a multi-sectional object, the EFI and DM are desired for many applications, but current approaches tend to be computationally demanding. Thus, an end-to-end deep learning framework is proposed to tackle these holographic reconstruction problems. Through this data-driven approach, it is demonstrated that it is possible to reconstruct a noise-free image that does not require any prior knowledge directly from a raw hologram.