A Topological Approach to Shrinking Higher Dimensions of Space to Observable Space-Time: Can the Dimensional Anisotropy of Space Satisfy Mach’s Principle?

We create a model universe by equipping a topological surface (system) with compact dimensions insulated by an information blocking horizon. The insulated compact WF can produce entanglement independent of distance. Interaction between the system and the WF changes the curvature of the first and the quantum state (frequency) of the second in an interconnected relationship. Thus, the field curvature measures the evolution of the particle WF as time. Positive field curvature creates pressure, whereas negative field curvature generates a vacuum, satisfying the Borsuk-Ulam Theorem and the Page and Wootters mechanism of static time. The accumulation of pressure or vacuum generates poles with contrasting dimensionalities, two-dimensional black hole horizons (time infinite), and four-dimensional cosmic voids (time zero). The orthogonality of the field and the compact WF give rise to global self-regulation that fine-tunes the cosmic parameters and can promote fractal topology. The four-dimensional vacuum in cosmic voids can produce an accelerating expansion without dark energy. When gravity effects are eliminated, we find a new, so far unexplored, order-increasing side of entropy. The verifiable and elegant hypothesis satisfies Mach's principle.

Field curvature correction in video endoscope lenses through the parameters of air meniscus

The research presents a method to synthesize lens data of an air meniscus built into the optical layout and acting as a correction element that fixes the field curvature of the entire optical system. The practical application of the proposed method is relevant when creating miniature lenses for medical video endoscopes when a small number of lenses and a flat image field for a CCD/CMOS sensor are important. Analytical dependencies for the lens data of the air meniscus are obtained and significant conditions for the field curvature correction are formed. A numerical example of a front stop lens design is demonstrated and confirms the correctness of the formulated conditions. A comparison of the aberration values of the original lens and an upgraded system is carried out. It is shown that, the values of the field curvature and astigmatism have been compensated as a result of introducing the synthesized parameters of the air meniscus into the optical layout. The correction is achieved while keeping the values of coma, distortion, focal length, and optical system total length at the level of the initial values.

Design of Refractive/Diffractive Hybrid Projection Lens for DMD-Based Maskless Lithography

The projection lens is the core component of DMD-based maskless lithography and its imaging quality directly affects the transferal of exposure pattern. Based on the traditional projection lens system, we have designed diffractive optical element (DOE) and aspheric surfaces to optimize the refractive/diffractive hybrid projection lens system to improve its imaging quality. We found that the best effect is obtained when DOE is very close to the front lens group before the diaphragm of the hybrid system. Compared with the traditional projection lens system, this hybrid projection lens system has lower wave aberration with the help of DOE, and higher image quality owing to the modulation transfer function (MTF) value being improved. Finally, a hybrid projection lens system with working distance of 29.07 mm, image Space NA of 0.45, and total length of 196.97 mm is designed. We found that the maximum distortion and field curvature are 1.36 × 10−5% and 0.91 μm, respectively.

Calibration Techniques For Low-Cost Star Trackers

This study presents a series of cost-effect strategies for calibrating star trackers for microsatellite missions. We examine three such strategies that focus on the calibration of the image detector, geometric calibration of the lab setup used for ground testing, and an optical calibration due to lens aberrations. Procedures are developed for each of these strategies that emphasize speed of implementation and accuracy, while trying to minimize manual labour. For the detector calibration, an existing calibration technique was adapted and implemented to reduce fixed pattern noise and dark current. Preliminary results show reduced variations in pixel sensitivity by approximately 21%, averaged across each pixel color given the use of a color imager. Although not substantial, this reduction in pixel variation will help preserve the Gaussian illumination pattern of imaged stars, aiding in correct centroid location. Results pertaining to the lab calibration show accurate star placement, in angular terms to 0.0073º across most of the field of view. This provides an accurate low-cost, variable solution for characterizing sensor performance; specifically pattern matching techniques. Finally, we present some initial results for lens aberration characterization. Using a Gaussian model of star image shape gives trends consistence with astigmatism and field curvature aberrations. Together, these calibrations represent tools that aim to improve both development and manufacture of modern microsatellite star trackers.

Calibration Techniques For Low-Cost Star Trackers

This study presents a series of cost-effect strategies for calibrating star trackers for microsatellite missions. We examine three such strategies that focus on the calibration of the image detector, geometric calibration of the lab setup used for ground testing, and an optical calibration due to lens aberrations. Procedures are developed for each of these strategies that emphasize speed of implementation and accuracy, while trying to minimize manual labour. For the detector calibration, an existing calibration technique was adapted and implemented to reduce fixed pattern noise and dark current. Preliminary results show reduced variations in pixel sensitivity by approximately 21%, averaged across each pixel color given the use of a color imager. Although not substantial, this reduction in pixel variation will help preserve the Gaussian illumination pattern of imaged stars, aiding in correct centroid location. Results pertaining to the lab calibration show accurate star placement, in angular terms to 0.0073º across most of the field of view. This provides an accurate low-cost, variable solution for characterizing sensor performance; specifically pattern matching techniques. Finally, we present some initial results for lens aberration characterization. Using a Gaussian model of star image shape gives trends consistence with astigmatism and field curvature aberrations. Together, these calibrations represent tools that aim to improve both development and manufacture of modern microsatellite star trackers.

Optical Design of a Novel Collimator System with a Variable Virtual-Object Distance for an Inspection Instrument of Mobile Phone Camera Optics

The resolution performance of mobile phone camera optics was previously checked only near an infinite point. However, near-field performance is required because of reduced camera pixel sizes. Traditional optics are measured using a resolution chart located at a hyperfocal distance, which can only measure the resolution at a specific distance but not at close distances. We designed a new collimator system that can change the virtual image of the resolution chart from infinity to a short distance. Hence, some lenses inside the collimator systems must be moved. Currently, if the focusing lens is moved, chromatic aberration and field curvature occur. Additional lenses are required to correct this problem. However, the added lens must not change the characteristics of the proposed collimator. Therefore, an equivalent-lens conversion method was designed to maintain the first-order and Seidel aberrations. The collimator system proposed in this study does not move or change the resolution chart.

A 2D Membrane MEMS Device Model with Fringing Field: Curvature-Dependent Electrostatic Field and Optimal Control

An important problem in membrane micro-electric-mechanical-system (MEMS) modeling is the fringing-field phenomenon, of which the main effect consists of force-line deformation of electrostatic field E near the edges of the plates, producing the anomalous deformation of the membrane when external voltage V is applied. In the framework of a 2D circular membrane MEMS, representing the fringing-field effect depending on |∇u|2 with the u profile of the membrane, and since strong E produces strong deformation of the membrane, we consider |E| proportional to the mean curvature of the membrane, obtaining a new nonlinear second-order differential model without explicit singularities. In this paper, the main purpose was the analytical study of this model, obtaining an algebraic condition ensuring the existence of at least one solution for it that depends on both the electromechanical properties of the material constituting the membrane and the positive parameter δ that weighs the terms |∇u|2. However, even if the the study of the model did not ensure the uniqueness of the solution, it made it possible to achieve the goal of finding a stable equilibrium position. Moreover, a range of admissible values of V were obtained in order, on the one hand, to win the mechanical inertia of the membrane and, on the other hand, to ensure that the membrane did not touch the upper disk of the device. Lastly, some optimal control conditions based on the variation of potential energy are presented and discussed.