Optimal Focal Length Research Articles

Measurement method of virtual image distance for a head-mounted display based on a variable-focus liquid lens

The distance from the virtual image to the human eye is an important factor in measuring the comfort of a head-mounted display (HMD). However, accurately measuring their distance is challenging due to the dynamic changes in virtual presence and distance. In this paper, we proposed a virtual image distance measurement prototype based on a variable-focus liquid lens and derived a virtual image distance calculation model. We built a variable-focus liquid lens experimental platform to verify the method’s correctness. In addition, we proposed an improved optimization algorithm that can efficiently and accurately search for the optimal focal length corresponding to the maximum sharpness moment of the virtual image within the focal length value space. Verified in an experimental scene of 0.5 m to 3.5 m, we observed that the error between the object image distance and the virtual image distance at the same focal length is about 5 cm. The proposed virtual image distance measurement method can accurately measure the distance value of the virtual image in the HMD. This method can be widely used in virtual and augmented reality, especially in the task of constructing realistic scenes.

Vehicular Visible Light Positioning System Based on a PSD Detector.

In this paper, we explore the use of visible light positioning (VLP) technology in vehicles in intelligent transportation systems (ITS), highlighting its potential for maintaining effective line of sight (LOS) and providing high-accuracy positioning between vehicles. The proposed system (V2V-VLP) is based on a position-sensitive detector (PSD) and exploiting car taillights to determine the position and inter-vehicular distance by angle of arrival (AoA) measurements. The integration of the PSD sensor in vehicles promises exceptional positioning accuracy, opening new prospects for navigation and driving safety. The results revealed that the proposed system enables precise measurement of position and distance between vehicles, including lateral distance. We evaluated the impact of different focal lengths on the system performance, achieving cm-level accuracy for distances up to 35 m, with an optimum focal length of 25 mm, and under low signal-to-noise conditions, which meets the standards required for safe and reliable V2V applications. Several experimental tests were carried out to validate the results of the simulations.

Optimal camera focal length detection method for GPS-supported bundle adjustment in UAV photogrammetry

The global positioning system (GPS) supported bundle adjustment (BA) method of unmanned aerial vehicle (UAV) photogrammetry significantly minimises the number of ground control points (GCPs); however, there are often systematic errors in the vertical axis direction of the 3D reconstruction results. In this study, a method that relies only on a small number of GCPs for detecting and estimating the optimal focal length of the camera is proposed. First, the scene structure information is obtained based on the conventional GPS-supported BA optimisation method, and the camera focal length is redefined based on a single GCP. Second, a second-order polynomial is used to fit the redefined camera focal lengths of multiple GCPs and the corresponding positioning accuracy. The highest accuracy position is selected as the optimal focal length of the camera. Finally, the optimal focal length of the camera is taken as a constant, and the conventional GPS-supported BA method is used to complete the optimisation again. The experimental results show that under the same number and distribution of GCPs, the camera detection method’s total positioning accuracy proposed in this paper is improved by an average of 37.64%. The optimal camera focal length obtained by the method can correct the systematic error in the vertical direction while keeping the vertical accuracy consistent with the horizontal accuracy.

Satellite-to-ground optical downlink model using mode mismatching multi-mode photonic lanterns.

Photonics lanterns (PLs) provide an effective mode diversity solution to mitigate atmospheric turbulence interference in free-space optical communications (FSOC). This paper presents mode-mismatching multimode photonic lanterns (MM-PLs) for diversity receiver in satellite-to-ground downlink scenarios. Our study evaluates the coupling characteristics of the mode-selective PLs (MSPLs) and non-mode-selective PLs (NSPLs) for the influence of strong-to-weak turbulence and confirms that MSPLs outperform NSPLs under weak turbulence conditions. The research further explores the impact of fiber position error (FPE) on the spatial light-to-fiber coupling, including the optimal focal length deviation and lateral offset of receiving fiber devices. We have calculated and compared the coupling power and signal-to-noise ratio (SNR) of few-mode PLs (FM-PLs) and MM-PLs for various turbulence intensities. The results indicate that the optimal focal length tolerance, which corresponds to a decrease of approximately 1 dB in the average coupling power, is 2-3 m and 5-6 m for FM-PLs and MM-PLs, respectively. Furthermore, regardless of whether it is strong or weak turbulence, MM-PL exhibits a lateral offset tolerance exceeding 12 µm for a 0.5 dB drop in the mean coupled power, whereas the lateral offset tolerance of FM-PL is only 3 µm under weak turbulence. Additionally, the decrease in the average SNR of MM-PLs is gentle, only 0.67-1.16 dB at a 12 µm offset under weak turbulence, whereas there is a significant reduction of 6.50-8.49 dB in the average SNR of FM-PLs. These findings demonstrate the superiority of MM-PLs over FM-PLs in turbulence resistance and fiber position tolerance in the satellite-ground downlink.

Three-dimensional density measurements of a heated jet using laser-speckle tomographic background-oriented schlieren

Tomographic background-oriented schlieren (TBOS) is a promising optical technique for 3D density field measurement in turbulent flows. Path-integrated information on refractive index gradients is captured by cameras looking through the flow at textured background patterns in the form of apparent displacements of the patterns. A tomographic reconstruction of the three-dimensional refractive index gradients is performed, from which the instantaneous three-dimensional density field is obtained. Most TBOS measurements to date have been limited by large temporal blurring and/or large defocus blurring. Our 15-camera experimental set-up uses a pulsed laser for both illumination and creation of a laser-speckle background pattern. The high-power laser ensures adequate exposures in nanoseconds, so temporal integration is minimised in each measurement. The beam is spread to illuminate a surface that is observed by fifteen cameras that are evenly spaced circumferentially around the flow. Laser speckle patterns are observed by the cameras due to the diffuse reflection and interference of coherent light from roughness on the surface. We develop a methodology for selecting the optimal focal length, focus distance, and lens aperture by considering the compromise between displacement sensitivity, defocus blurring and speckle size. Low temporal- and spatial-blurring 3D temperature field measurements with excellent resolution of turbulent flow features are obtained and good agreement with thermocouple. Classical behaviours of the potential core instability such as vortex rollup and radial ejections are identified. The behaviour of the potential core is examined further, which reveals that the potential core undergoes considerable deformation and fragmentation during the transition to turbulence.

Non-Invasive Heat-Induced Numerous Tissue Ablation Simulation in a Medical Environment Using Different Focal Length High Intensity Focused Ultrasound Apparatus

In the field of biomedical, HIFU is a non-invasive therapeutic method that employs non-ionizing acoustic waves to increase the temperature. According to its high efficiency and cheap cost, it has been the main focus of this research. The key stages of this tumor ablation include mechanical and thermal effects. Simulations on tissue ablation with HIFU were implemented in this research to investigate how multiple tissue ablation works and how to enhance tumor ablation while avoiding injury to surrounding healthy tissue by altering the optimal intensity, power, focal length and lens radius of curvature. In order to find the optimal features of the proposed model, this analysis employs clinical applications. Numerous soft and hard tissues from the human body were chosen for this analysis. At a specified acoustic power and exposure period, each tissues optimal frequency (1.6 MHz to 3.5 MHz) and power (120 W to 140 W) were obtained for effective tissue ablation. This research performed all computations by changing the focal length from 55 mm to 65 mm. The outcomes of this therapy might require several weeks to comfortably remove tumor. This optimum result indicates that HIFU tumor ablation procedure has a high probability of success.

Optimal focal length search and design of a compact zoom lens based on a telecentric intermediate image.

The design of a compact zoom lens requires a designer's most abundant and professional skills and experience, which increases the difficulty of zoom lens miniaturization. In this paper, an automatic optimal focal length search method for a catadioptric zoom lens is proposed. After 7 h of searching for the initial structure and further optimization, a 3× compact zoom lens based on a telecentric intermediate image is obtained, which is applicable for 1/4 inch (6.35 mm) CMOS, with a focal length range of -4.8∼-14mm and a F-number range of 2.7-8.0. The depth and total length are within 6 mm and 30 mm, separately. The proposed method helps to reduce researchers' difficulty in designing compact zoom lenses and can provide some reference for the development of the mobile zoom lens industry.

Highly efficient diode-pumped alkali-vapor amplification with near-extreme-limit gain.

We report high-efficiency optical amplification with near-extreme-limit gain from a diode-pumped Cs vapor cell. We used wavelength-division multiplexing to couple 852 nm pump and 895 nm seed lasers to achieve nearly overlapping spatial modes in the Cs vapor cell. We investigated the amplification factor as a function of the focal length of the lens focusing on the combined pump and seed signals and determined the optimal focal length under our experimental conditions. The small-signal amplification factor from the Cs vapor cell reached >30 dB at 240 mW pump power, and the optimal optical amplification factor per pump power was 4171/W.

Hard-aperture effect on self-focusing of high-power laser beams propagating in the atmosphere.

The hard-aperture effect on self-focusing of high-power laser beams propagating from the ground through the atmosphere to space orbits is studied. It is shown that the spot size on the target increases as the truncation parameter decreases and the beam power increases. However, as the truncation parameter decreases, the apertured laser beam is less affected by self-focusing. On the other hand, two effective design rules are presented to optimize the intensity on the target, i.e., the optimal power and the optimal focal length. It is proven that the self-focusing effect and the hard-aperture effect both can be compensated by applying the optimal initial beam defocusing. It is also found that the higher maximum intensity on the target will occur by applying the optimal focal length rather than the optimal power.

Investigation of factors affecting on the efficiency of second harmonic ‎generation of the continuous-wave focused Gaussian beam of 1064 nm inside the ‎periodically poled nonlinear crystals

In this research, the nonlinear propagation equations of the fundamental and second harmonic waves coupled to the heat equation are solved for a focused Guassian beam inside two quasi-phase matched periodically poled MgO: PPLN and MgO: PPLT crystals, and the optimum focal length and radius of the continuous-wave laser beam with the wavelength of 1064 nm and with Gaussian profile, and also, the optimal phase-mismached parameter are calculated and the dependence of the second harmonic efficiency on these parameters is shown. Also, the effects of the thermal distribution inside the crystal on the second harmonic generation efficiency are investigated and it is shown how the thermal distribution reduces the second harmonic efficiency and, accordingly, the optimal crystal length for different incident powers is determined and shown that the lower crystal lengths should be selected for higher incident powers. Finally, a comparison between the second harmonic efficiencies in two crystals of MgO: PPLN and MgO: PPLT is performed considering the thermal distribution for different insident powers and it is shown that for the lower/ higher incident power than 21 watts, the crystal of MgO: PPLN / MgO: PPLT is more suitable and more efficient for second harmonic generation.

Characteristics of high-power partially coherent laser beams propagating upwards in the turbulent atmosphere.

The characteristics of high-power partially coherent laser beams propagating upwards in the turbulent atmosphere are studied, where the principal features of diffraction, nonlinear self-focusing and turbulence are considered. Based on the "thin window" model, the analytical propagation formulae are derived by using the quadratic approximation of the nonlinear phase shift. It is found that the turbulence effect plays an important role in beam propagation characteristics. But the turbulence and self-focusing effects can be suppressed by increasing the laser elevation. Furthermore, the influence of laser elevation on the turbulence effect is stronger than that on the self-focusing effect, and influence of laser elevation on the self-focusing effect is stronger than that on the diffraction effect. In particular, the optimal focal length and wavelength are proposed to decrease the beam spot size on the target.

Preliminary geometric parameters optimization of lobster-eye-type wide field of view soft x-ray imager

The lobster-eye optical system is widely used in the wide field of view (FOV) soft x-ray imaging device. The payload soft x-ray imager (SXI) onboard the solar wind magnetosphere ionosphere link explorer satellite will apply this technology to achieve panoramic imaging of the dayside magnetosphere. In order to optimize the imaging performance of SXI, we focus on geometric parameters optimization of a lobster-eye lens. The results show an appropriate microchannel ratio of length to width of lobster-eye optics with radius of curvature of 600 mm could be 30:1 (microchannel width of 40 μm and length of 1.2 mm). For a monochromatic parallel light source with energy of 1 keV, this combination of parameters can theoretically provide relatively large total effective area of about 15.52 cm2 and focusing efficiency of about 0.2887 along with spatial angular resolution of about 6 arc min at the center of FOV. Combined with the actual lobster-eye optics, the aberrations from deformation of the microchannel, the deviation of radius of curvature and planar detector are analyzed. For SXI with planar CCD detector, an optimum focal length could be 304.2 mm to ensure better resolution in full FOV.

Coupling efficiency of a partially coherent collimating laser from turbulent biological tissue to fiber

Abstract We propose a model of the fiber coupling efficiency for a partially coherent collimating laser beam propagating through turbulent biological tissue to fiber. By studying the influence of link parameters on fiber coupling efficiency, we find that there are optimal focal length and transmitting beam radius for specific turbulent tissue. We also find that a larger characteristic length and small length-scale factor, or smaller fractal dimension and strength coefficient of refractive-index fluctuation will lead to larger fiber coupling efficiency. In order to improve the fiber coupling efficiency, we recommend select the optimum focal length, moderate transmitting beam radius, lower aperture diameter of the coupling lens, longer wavelength and higher coherent degree of light source.

Coupling efficiency of a partially coherent laser beam from the anisotropy and non-Kolmogorov marine-atmosphere turbulence to fiber

We evaluate the parameter effects of the laser source, coupling lens and turbulence on the fiber coupling efficiency. Our results indicate that there are optimal radius of the wave-front curvature and transmitting radius of laser beam and optimal focal length of a coupling lens for specific turbulence strength and propagation distance. By utilizing the optimal wave-front curvature, optimal focal length and optimal transmitting beam radius, one can maximize the coupling efficiency.

New model of the fiber coupling efficiency of a partially coherent Gaussian beam in an ocean to fiber link

The fiber coupling efficiency between the turbulent ocean to fiber of a partially coherent Gaussian beam propagating through the weak to strong anisotropic oceanic turbulence is studied. We derive the expression of new model of the fiber coupling efficiency for the partially coherent Gaussian beam. The numerical analyses reveal that larger inner scale and anisotropic factor, weaker oceanic turbulence strength, and smaller temperature-salinity contribution ratio will lead to a higher coupling efficiency; a longer wavelength, an suitable aperture diameter of the coupling lens, an optimum focal length and beam size, and a higher coherent degree will improve the fiber coupling efficiency. Our fiber coupling efficiency is higher than the previous fiber coupling efficiency.

Analytical beam propagation model of micro-lensed fibers for wavelength selective switch

Micro-lensed fibers require some features such as low coupling loss and wide tolerance to function in wavelength selective switch (WSS). In this paper, Fourier optics and scalar diffraction theory are used to analyze the major beam propagation and transformation by switching different focus length micro-lens in WSS. A hemispheric micro-lens array is then etched with designed optimum focal length. In experiment, a method is proposed for measuring the insertion loss (IL) and coupling efficiency of a fiber coupling micro-lens in WSS. The theoretical calculations of the spot size at any distance from micro-lens agree well with experimental results. The experimental coupling efficiency can reach up to 70%.

Research and Design of Compound Fresnel Concentrator

An efficient and compact concentrator Fresnel concentrator is discussed and designed,The central region is a conventional Fresnel lens designed according to Snell's law of refraction,The edge region is designed to be TIR (internal total reflection) prism.According to the Fresnel formula,the best segmentation position and the optimum focal length of two kinds of lens are calculated,and use SolidWorks to build 3D model,The ray tracing simulation of the designed lens is carried out by using TracePro software.The results show that the efficiency is 89.6% and the F/# is 0.5 at high concentration. The efficiency of the traditional Fresnel concentrator is only 66% when the F/# is the same. The design goal of compact structure and high light performance is achieved.

Optimal focal length of primary mirrors in Fresnel linear collectors

In a linear Fresnel plant adopting slightly curved primary mirrors (cylindrical or parabolic), a significant gain in the collected radiation can be achieved using primary mirrors with different focal lengths, dependent on the position of the mirror with respect to the receiver. This work introduces a universal function that provides the optimal focal length of a mirror, given only the mirror’s position relative to the receiver and the latitude, for a NS-oriented collector with a flat horizontal effective target. In a solar plant with the focal lengths defined by this function, the efficiency gain with respect to a solar field adopting identical mirrors is estimated in the range 1.5–6%, with the gain increasing if mirror imperfections or tracking errors are present: this means that the regulation of the focal lengths is especially useful in containing the loss of efficiency due to defects. The given rule is tolerant to errors in the focal length regulation (up to 10%). The function can be used as a reference for future projects, or as a starting point for more refined optimizations.

Simulation-based optimisation of a linear Fresnel collector mirror field and receiver for optical, thermal and economic performance

Increasing the efficiency of concentrating solar power (CSP) technologies by means of optimisation tools is one of the current topics of solar thermal researchers. Of these technologies, Linear Fresnel collectors (LFCs) are the least developed. Therefore, there is plenty of room for the optimisation of this technology. One of the goals of this paper, in addition to the optimisation of an LFC plant, is introducing an applicable optimisation procedure that can be applied for any type of CSP plant. This paper focuses on harvesting maximum solar energy (maximising plant optical efficiency), as well as minimising plant thermal heat loss (maximising plant thermal efficiency), and plant cost (the economic optimisation of the plant), which leads to the generation of cheaper solar electricity from an LFC plant with a fixed power plant cycle (The performance optimisation of this study is based on the plant performance throughout an imaginary summer day). A multi-tube cavity receiver is considered in this study since there is plenty of room for its optimization. For the receiver, optimal cavity shape, tube bundle arrangement, tube numbers, cavity mounting height and insulation thickness are considered, while for the mirror field, the number of mirrors, mirror width, mirror gaps and mirror focal length are considered to achieve the optimisation goals. A multi-stage optimisation process is followed. Firstly, optical (using SolTrace), thermal (using a view area approach) and economic performance are combined in a multi-objective genetic algorithm as incorporated in ANSYS DesignXplorer (DX). This leads to an optimal LFC with a variable focal length for each mirror. After determining a fixed optimal focal length for all the mirrors, a Computational Fluid Dynamics (CFD) approach is used to optimise the thermal insulation of the cavity receiver for minimal heat loss and minimal insulation material. The process is automated through the use of ANSYS Workbench and Excel (coding with Visual Basic for Application (VBA) and LK Scripting in SolTrace). The view area approach provides an inexpensive way of calculating radiation heat loss from the receiver that is shown in the subsequent CFD analysis to be dominating the heat transfer loss mechanisms. The optimised receiver is evaluated at different LFC plant tube temperatures to assess its performance.

Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens.

To assess the morphologic, biochemical, and optical properties of bovine lenses treated with hyperbaric oxygen. Lenses were exposed to hyperbaric nitrogen (HBN) or hyperbaric oxygen (HBO) for 5 or 15 hours, lens transparency was assessed using bright field microscopy and lens morphology was visualized using confocal microscopy. Lenses were dissected into the outer cortex, inner cortex, and core, and glutathione (GSH) and malondialdehyde (MDA) measured. Gel electrophoresis and Western blotting were used to detect high molecular weight aggregates (HMW) and glutathione mixed protein disulfides (PSSG). T2-weighted MRI was used to measure lens geometry and map the water/protein ratio to allow gradient refractive index (GRIN) profiles to be calculated. Optical modeling software calculated the change in lens optical power, and an anatomically correct model of the light pathway of the bovine eye was used to determine the effects of HBN and HBO on focal length and overall image quality. Lenses were transparent and lens morphology similar between HBN- and HBO-treated lenses. At 5- and 15-hour HBO exposure, GSH and GSSG were depleted and MDA increased in the core. Glutathione mixed protein disulfides were detected in the outer and inner cortex only with no appearance of HMW. Optical changes were detectable only with 15-hour HBO treatment with a decrease in the refractive index of the core, slightly reduced lens thickness, and an increase in optimal focal length, consistent with a hyperopic shift. This system may serve as a model to study changes that occur with advanced aging rather than nuclear cataract formation per se.