In this review paper, we first provide comprehensive tutorials on two classical methods of polygon-based computer-generated holography: the traditional method (also called the fast-Fourier-transform-based method) and the analytical method. Indeed, other modern polygon-based methods build on the idea of the two methods. We will then present some selective methods with recent developments and progress and compare their computational reconstructions in terms of calculation speed and image quality, among other things. Finally, we discuss and propose a fast analytical method called the fast 3D affine transformation method, and based on the method, we present a numerical reconstruction of a computer-generated hologram (CGH) of a 3D surface consisting of 49,272 processed polygons of the face of a real person without the use of graphic processing units; to the best of our knowledge, this represents a state-of-the-art numerical result in polygon-based computed-generated holography. Finally, we also show optical reconstructions of such a CGH and another CGH of the Stanford bunny of 59,996 polygons with 31,724 processed polygons after back-face culling. We hope that this paper will bring out some of the essence of polygon-based computer-generated holography and provide some insights for future research.

In this study, we first analyze the fully analytical frequency spectrum solving method based on three-dimensional affine transform. Thus, we establish a new method for combining look-up tables (LUTs) with polygon holography. The proposed method was implemented and proved to be accelerated about twice compared to the existing methods. In addition, principal component analysis was used to compress the LUTs, effectively reducing the required memory without artifacts. Finally, we calculated very complex objects on a graphics processing unit using the proposed method, and the calculation speed was higher than that of existing polygon-based methods.

Microlens arrays (MLAs) are widely used in optical imaging, dense wavelength division multiplexing, optical switching, and microstructure patterning, etc. However, the light modulation capability for both the conventional refractive-type MLA and planar diffractive-type MLA is still staying at the diffraction-limited scale. Here we propose and experimentally demonstrate a high numerical aperture (NA) supercritical lens (SCL) array which could achieve a sub-diffraction-limited focal spot lattice in the far field. The intensity distribution for all the focal spots has good uniformity with the lateral size around 0.45 λ / N A (0.75X Airy unit). The elementary unit in the SCL array composes a series of concentric belts with a feature size in micrometer scale. By utilizing an ultrafast ultraviolet lithography technique, a centimeter scale SCL array could be successfully patterned within 10 mins. Our results may provide possibilities for the applications in optical nanofabrication, super-resolution imaging, and ultrafine optical manipulation.

The advancement of digital holography in the past 2 decades has enabled precise capturing of three-dimensional (3-D) images of physical objects. This important technology has been widely applied in numerous industrial sectors such as, but not limited to remote sensing, metrology, bio-medical imaging, advertising, and entertainment. Most of the hologram acquisition techniques developed to date are employing digital cameras for recording the hologram, hence imposing rigid restrictions on the size and resolution of the captured 3-D image. This limitation, however, is not found in optical scanning holography (OSH). Based on a scanning mechanism and a single pixel sensor, OSH is capable of capturing digital holograms of both macroscopic and microscopic, as well as fluorescent objects with high precision. Since its invention in the late 70s, numerous research works have been conducted to enhance this technology, optimizing important factors such as acquisition speed, precision, data size, and security. The objective of this review paper is to provide a walkthrough of the state-of-the-art of the OSH technology, from its original principle, to different variants that have been developed over the years with emphasis on their feature extraction capabilities under the incoherent mode of operation. Whenever possible, we shall provide the key formulations of each approach, and experimental outcomes for demonstrating the pros and cons of the method.

Optical scanning holography (OSH) involves the principles of optical scanning and heterodyning. The use of heterodyning leads to phase-preserving, which is the basic idea of holography. While heterodyning has numerous advantages, it requires complicated and expensive electronic processing. We investigate an off-axis approach to OSH, thereby eliminating the use of heterodyning for phase retrieval. We develop optical scanning theory for holographic imaging and show that by properly designing the scanning beam, we can perform coherent and incoherent holographic recording. Simulation results are provided to verify the proposed idea.