In digital holography, it is crucial to extract the object distance from a hologram in order to reconstruct its amplitude and phase. This is known as autofocusing, which is conventionally solved by first reconstructing a stack of images, and then the sharpness of each reconstructed image is computed using a focus metric such as entropy or variance. The distance corresponding to the sharpest image is considered the focal position. This approach, while effective, is computationally demanding and time-consuming. To cope with this problem, we turn to machine learning, where we cast the autofocusing as a regression problem, with the focal distance being a continuous response corresponding to each hologram. Therefore, distance estimation is converted to hologram prediction, which we solve by designing a powerful convolutional neural network trained by a set of holograms acquired a priori. Experimental results show that this allows fast autofocusing without reconstructing an image stack, even when the physical parameters of the optical setup are unknown.

Since its invention in 1948, holographic imaging has been a powerful technique in recording the diffracted wavefront of a three-dimensional (3-D) scene.¹ A significant step forward from analog holography is to record digitally the interference pattern with an electronic sensor and to reconstruct the object numerically, including the amplitude and phase information, with a computer.² Due to its noninvasive and label-free properties, digital holography (DH) has been applied to biological imaging,^3,4 air quality monitoring,⁵ and surface characterization,^6,7 to name just a few application areas.

Digital holographic imaging is a powerful technique that can provide wavefront information of a three-dimensional object for biological and industrial applications. However, due to the constraint and cost of imaging sensors, the acquired digital hologram is limited in terms of pixel count, thus affecting the resolution in holographic reconstruction. To overcome this constraint, we propose a deep learning-based method to super- resolve holograms and to improve the quality of low-resolution holograms by training a convolutional neural network with large- scale data for resolution enhancement. Moreover, this algorithm can be broadly adapted to enhance the space-bandwidth product of a holographic imaging system without the need of any advanced hardware. We experimentally validate its capability using a lens-free off-axis holographic system, and compare the performance of various loss functions and interpolation methods in training such a network.

In digital holographic microscopy, phase aberrations, which are usually caused by the imperfections of components and nontelecentric configuration of the optical system, severely affect the visualization and quantitative measurement for phase-contrast imaging. Here, we propose a purely numerical and automatic method to compensate for phase aberrations. Without any manual involvement of selecting a sample-free background, the compensation is cast as a surface fitting problem, in which the aberration surface is approximated by formulating an inverse problem. By adopting the ℓ₁-norm as the loss function and by minimizing an objective function, aberrations can be accurately fitted and thus removed numerically. Synthetic and experimental results are demonstrated to verify the efficacy of this method over the least squares method.

The veiling effect caused by the scattering and absorption of suspending particles is a critical challenge of underwater imaging. It is possible to combine the image formation model (IFM) with the optical polarization characteristics underwater to effectively remove the veiling effect and recover a clear image. The performance of such methods, to a great extent, depends on the settings of the global parameters in the application scenarios. Meanwhile, learning-based methods can fit the underwater image information degradation process nonlinearly to restore the images from scattering. Here, we propose for the first time a method for full scene underwater imaging that synergistically makes use of an untrained network and polarization imaging. By mounting a Stokes mask polarizer on the CMOS camera, we can simultaneously obtain images with different polarization states for IFM calculation and optimize the imaging automatically by an untrained network without requiring extra training data. This method makes full use of the nonlinear fitting ability of a neural network and corrects the undesirable imaging effect caused by imperfect parameter settings of the classical IFM in different scenes . It shows good performance in removing the impact of water scattering and preserving the object information, making it possible to achieve clear full scene underwater imaging.

Determining the optimal focal plane amongst a stack of blurred images in a short response time is a non-trivial task in optical imaging like microscopy and photography. An autofocusing algorithm, or in other words, a focus metric, is key to effectively dealing with such problem. In previous work, we proposed a structure tensor-based autofocusing algorithm for coherent imaging, i.e., digital holography. In this paper, we further extend the realm of this method in more imaging modalities. With an optimized computation scheme of structure tensor, a significant acceleration of about fivefold in computation speed without sacrificing the autofocusing accuracy is achieved by using the Schatten matrix norm instead of the vector norm. Besides, we also demonstrate its edge extraction capability by retrieving the intermediate tensor image. Synthesized and experimental data acquired in various imaging scenarios such as incoherent microscopy and photography are demonstrated to verify the efficacy of this method.