Theory and algorithm of the homeomorphic Fourier transform for optical simulations

Numerical analysis of micro-optics based single photon sources via a combined physical optics and rigorous simulations approach

The use of 3D printed micro-optical components has enabled the miniaturization of various optical systems, including those based on single photon sources. However, in order to enhance their usability and performance, it is crucial to gain insights into the physical effects influencing these systems via computational approaches. As there is no universal numerical method which can be efficiently applied in all cases, combining different techniques becomes essential to reduce modeling and simulation effort. In this work, we investigate the integration of diverse numerical techniques to simulate and analyze optical systems consisting of single photon sources and 3D printed micro-optical components. By leveraging these tools, we primarily focus in evaluating the impact of different far-field spatial distributions and the underlying physical phenomena on the overall performance of a compound micro-optical system via the direct evaluation of a fiber in-coupling efficiency integral expression.

Dual convolutional neural network for aberration pre-correction and image quality enhancement in integral imaging display

This paper proposes a method that utilizes a dual neural network model to address the challenges posed by aberration in the integral imaging microlens array (MLA) and the degradation of 3D image quality. The approach involves a cascaded dual convolutional neural network (CNN) model designed to handle aberration pre-correction and image quality restoration tasks. By training these models end-to-end, the MLA aberration is corrected effectively and the image quality of integral imaging is enhanced. The feasibility of the proposed method is validated through simulations and optical experiments, using an optimized, high-quality pre-corrected element image array (EIA) as the image source for 3D display. The proposed method achieves high-quality integral imaging 3D display by alleviating the contradiction between MLA aberration and 3D image resolution reduction caused by system noise without introducing additional complexity to the display system.

Spiral-phase-objective for a compact spiral-phase-contrast microscopy

Spiral-phase-contrast imaging, which utilizes a spiral phase optical element, has proven to be effective in enhancing various aspects of imaging, such as edge contrast and shadow imaging. Typically, the implementation of spiral-phase-contrast imaging requires the formation of a Fourier plane through a 4f optical configuration in addition to an existing optical microscope. In this study, we present what we believe to be a novel single spiral-phase-objective, integrating a spiral phase plate, which can be easily and simply applied to a standard microscope, such as a conventional objective. Using a new hybrid design approach that combines ray-tracing and field-tracing simulations, we theoretically realized a well-defined and high-quality vortex beam through the spiral-phase-objective. The spiral-phase-objective was designed to have conditions that are practically manufacturable while providing predictable performance. To evaluate its capabilities, we utilized the designed spiral-phase-objective to investigate isotropic spiral phase contrast and anisotropic shadow imaging through field-tracing simulations, and explored the variation of edge contrast caused by changes in the thickness of the imaging object.

Wavelength-tunable spiral-phase-contrast imaging

Wavelength-tunable spiral-phase-contrast (SPC) imaging was experimentally accomplished in the visible wavelengths spanning a broad bandwidth of ∼200 nm based on a single off-axis spiral phase mirror (OSPM). By the rotation of an OSPM, which was designed with an integer orbital angular momentum (OAM) of l = 1 at a wavelength of 561 nm and incidence angle of 45°, high-quality SPC imaging was obtained at different wavelengths. For the comparison with wavelength-tunable SPC imaging using an OSPM, SPC imaging using a spiral phase plate (manufactured to generate an OAM of l = 1 at 561 nm) was performed at three wavelengths (473, 561, and 660 nm), resulting in clear differences. Theoretically, based on field tracing simulations, high-quality wavelength-tunable SPC imaging could be demonstrated in a very broad bandwidth of ∼400 nm, which is beyond the bandwidth of ∼200 nm obtained experimentally. This technique contribute to developing high-performance wavelength-tunable SPC imaging by simply integrating an OSPM into the current optical imaging technologies.

Generation of wavelength-tunable optical vortices using an off-axis spiral phase mirror

Wavelength-tunable optical vortices with a topological charge equal to l=1 of orbital angular momentum (OAM) were experimentally realized using a single off-axis spiral phase mirror (OSPM) with lasers of various visible-light wavelengths. Using an OSPM designed for 561 nm and an incidence angle of 45°, circular doughnut-shaped l=1 optical vortices were obtained at 561, 473, and 660 nm by rotating the OSPM to modify the laser incidence angle. Wavelength-tunable l=1 optical vortices were obtained at the respective incidence angles of 45°, 53.4°, and 33.7°, because the effective geometrical thickness of the OSPM, which determines the order of OAM, was identical at each wavelength. This flexible OSPM which operates over a wide wavelength range will provide continuously wavelength-tunable optical vortices for applications in the fields of advanced optics and photonics in which optical vortices with wide wavelength tunability are in demand.

Wavefront phase representation by Zernike and spline models: a comparison

A comparative analysis of spline and Zernike models is presented for wavefront phase construction. The techniques are analyzed on the basis of representation accuracy, computational costs, and the number of samples used for representation. The strengths and weaknesses of each model over a set of various wavefront phases with different domain shapes are analyzed. The findings show that both models efficiently represent a simple wavefront phase at irregular domain shapes. On the other hand, when complex wavefront phases at irregular domain shapes are represented, the spline model performs much better than the Zernike model. Further, results show that the spline model evaluation speed is significantly faster than the Zernike model.

Light-shaping design by a fourier pair synthesis: the homeomorphic case

From a physical-optics point of view, the far-field light-shaping problem mainly requires a Fourier pair synthesis. The Iterative Fourier Transform Algorithm (IFTA) is one of the algorithms capable of realizing this synthesis, however, it may lead to stagnation problems when the fields of the Fourier pair exhibit a homeomorphic behavior. To overcome this problem, we use a mapping-type relation for the Fourier pair synthesis. This approach results in a smooth phase response function in a single step, without requiring an iterative procedure. The algorithm is demonstrated with examples and the results are investigated via physical-optics modeling techniques.

Generalized far-field integral

The propagation of light in homogeneous media is a crucial technology in optical modeling and design as it constitutes a part of the vast majority of optical systems. Any improvements in accuracy and speed are therefore helpful. The far-field integral is one of the most widely used tools to calculate diffraction patterns. As a general rule, this approximate method requires the observation plane located in the far-field region, i.e., a very considerable propagation distance. Only in the well-designed (namely aberration-free) optical system does the far-field integral not suffer from the limitation of the large distance. Otherwise, the far-field integral cannot provide accurate results. In the present work, we generalize the far-field integral to a more general concept with a much more flexible application scope, which allows for the inclusion of aberrations as well. Finally, as an essential part of this generalization, the propagation to arbitrarily oriented planes is also taken into account.

Numerical analysis of tiny-focal-spot generation by focusing linearly, circularly, and radially polarized beams through a micro/nanoparticle

Obtaining a tiny focal spot is desired for super resolution. We do a vectorial numerical analysis of the linearly, circularly, and radidally polarized electromagnetic fields being focused through a dielectric micro/nanoparticle of size comparable to the wavelength. We find tiny focal spots (up to ∼0.05 λ²) can be obtained behind micro/nanoparticles of various shapes, e.g. spherical, disk-shaped, and cuboid micro/nanoparticles. Furthermore, we also investigate the influence of the misalignment of a real lens system on the tiny focal spots. We find that tiny focal spots can still be generated even though they are distorted due to the misalignment.

Frequency sampling strategy for numerical diffraction calculations

Diffraction calculations play an essential role in Fourier optics and computational imaging. Conventional methods only consider the calculation from the perspective of discrete computation which would either cause error or sacrifice efficiency. In this work, we provide a unified frequency response analysis from the joint physics-mathematics perspective and propose corresponding adaptive frequency sampling strategies for five popular diffraction calculation methods. With the proposed strategies, the calculation correctness is guaranteed and the calculation efficiency is improved. Such an idea of unified frequency response study would help researchers make a do-it-yourself analysis for various diffraction calculation tasks and choose or develop a method for accurate and efficient computations of the diffraction fields.

Generalized Debye integral

The Debye integral is an essential technique in physical optics, commonly used to efficiently tackle the problem of focusing light in lens design. However, this approximate method is only valid for systems that are well designed and with high enough Fresnel numbers. Beyond this assumption, the integral formula fails to provide accurate results. In this work, we generalize the Debye integral to overcome some of its limitations. The theory explicitly includes aberrations and extends the integral to fields on tilted planes in the focal region. We show, using examples, that the new formulas almost reach the accuracy of a rigorous modeling technique while being significantly faster.

Light shaping by freeform surface from a physical-optics point of view

Modeling techniques for light-shaping systems with freeform surface are presented from a physical-optics point of view. We apply the modeling techniques to different light-shaping systems with freeform surfaces designed by "ray mapping method". The simulation results show that the design is not always valid. Diffraction effects occur, especially in paraxial situations. We discuss the accuracy of the design via physical-optics simulation, and find an explanation in the geometric-optics assumption of the design algorithm being sufficient only if the optical system results in homeomorphic behavior for the electric field between the input and target.

Light shaping from a physical-optics point of view

In the design of optical element for light shaping, a geometric-optics assumption is usually used, where the validity of the assumption is rarely discussed in literature. In this work, the field tracing techniques for modeling light-shaping systems are presented, which reveals the optical element resulted from those geometric-base algorithm is not always accurate enough for the design task. An example is demonstrated with the functional embodiment of the element. The simulation result shows that diffraction effect may occur, especially in paraxial situation. However, the designed result start with the assumption is well-introduced initial guess for further optimization with the iterative Fourier transform algorithm (IFTA).