Principle Of Ray Tracing Research Articles

A broadband and high‐efficiency folded transmitarray antenna

AbstractA folded transmitarray antenna (FTA) with low profile, high efficiency, and broadband is proposed. The transmission unit‐cell is composed of two metallic layers of bowknot‐shaped patches printed on a single layer of dielectric substrate. By regulating bowknot‐shaped patches' dimension and mirroring elements' top and bottom layers, 360° phase swing and high transmission magnitudes are obtained. With the introduction of a reflectarray integrated with a feed horn in the middle, an FTA is designed based on ray tracing principle, leading to a profile reduced to 1/3 of the focal distance of traditional transmitarrays. According to testing results, 15.5% 1 dB gain bandwidth, 30.9% 3 dB gain bandwidth, and 42.3% peak aperture efficiency are achieved. These outstanding performances demonstrate its good potential for a wide range of high‐gain applications.

Anatomical and optical origins of negative dysphotopsia

Negative dysphotopsia (ND) is a complaint after, an otherwise uneventful, cataract surgery with intraocular lens (IOL) implantation. It is generally described as a shadow in the temporal peripheral visual field. Approximately 3% of the patients suffer from this condition and complaints range from mild visual field defects to a significant loss of peripheral vision that disturbs daily life. Originally, this condition was poorly understood as conventional ophthalmic techniques are not designed for a comprehensive evaluation of the peripheral vision. In the last years, however, a combination of dedicated anatomical measurements and optical ray tracing simulations have revealed the cause of ND and proposed different treatments.In this presentation the basic principles of ray tracing of the eye will be presented, followed by the main results of the ESCRS vRESPOND study. In this study, a detailed anatomical assessment of the pseudophakic population with and without ND was made. The distinct differences between both groups, such as a smaller (p = <0.01) and more decentered (p < 0.01) pupil and an increased temporal‐tilted iris (p < 0.01), will be discussed. Interestingly, high‐resolution ocular MRI revealed that the in‐the‐bag IOL position and retinal shape did not differ significantly between both groups. The impact of these differences on the patient's peripheral vision will be shown through ray tracing simulations. First the optical origin of the shadow, caused by light rays missing the IOL, will be presented, followed by a quantitative analysis of the effect the different anatomical and IOL‐design parameters on the severity of this shadow. At the end of the presentation, the optical rationale behind some of the treatments of ND will be discussed.

A Method for Transmitarray Antenna Profile Reduction Based on Ray Tracing Principle

In this letter, a method named double phase-compensation is first proposed to drastically reduce the profile of traditional transmitarray antenna (TA) based on ray tracing principle. Previously, the folded transmitarray antenna (FTA) has realized the profile reduction to 1/3. It is known that there is an urgent need for more compact antenna nowadays. If the FTA's profile is further reduced, the focus-to-diameter ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> ) ratio should be decreased which will result in obvious aperture efficiency reduction. To further reduce the FTA's profile with unchanged <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> for keeping high efficiency, the extra phase compensation is innovatively added on the FTA's reflector. Hence the TA's profile can be reduced to lower than 1/3 and be flexibly adjusted as needed. Three FTA models are designed for comparison and demonstration. The simulation and experimental results indicate that the extra phase compensation successfully alleviates the efficiency drop caused by directly reducing the profile of FTA. Significantly, the method provides an efficient approach to further improve the compactness of antenna system and is very meaningful for TA miniaturization.

Dislocation Contrast Analysis in Weak Beam Synchrotron X-Ray Topography

Synchrotron monochromatic beam X-ray topography has been widely applied to characterize structural defects in SiC crystals. Using ray tracing simulations, the dislocation contrast in X-ray topography under strong diffraction conditions (diffraction takes place at or near Bragg angle) has been intensively investigated. However, the contrast and the configurations of the dislocation images recorded under weak diffraction conditions have not been fully investigated. Recently, we demonstrated that the contrast of dislocations in synchrotron grazing incidence topography under weak diffraction conditions can also be analyzed and interpreted by applying ray tracing principles. In this study, we have extended the application of the ray tracing method to analyze the dislocation contrast in weak beam synchrotron back reflection and rocking curve topography. The ray tracing method is shown to successfully simulate and correlate the contrast of threading screw dislocations at various positions on the rocking curve and thus allow to determine the signs of Burgers vectors.

Comparing the accuracy of new intraocular lens power calculation formulae in short eyes after cataract surgery: a systematic review and meta-analysis.

Calculating the intraocular lens (IOL) power in short eyes for cataract surgery has been a challenge. A meta-analysis was conducted to identify, among several classic and new IOL power calculation formulae, which obtains the best accuracy. All studies aiming at comparing the accuracy of IOL power calculation formulae in short eyes were searched up in the databases of PubMed, EMBASE, Web of Science and the Cochrane library from Jan. 2011 to Mar. 2021. Primary outcomes were the percentages of eyes with a refractive prediction error in ± 0.25D, ± 0.5D and ± 1.0D. Totally 1,476 eyes from 14 studies were enrolled in comparison of 13 formulae (Barrett Universal II, Castrop, Haigis, Hoffer Q, Holladay1, Holladay2, Kane, Ladas Super Formula, Okulix, Olsen, Pearl-DGS, SRK/T and T2). Pearl-DGS had the highest percentage within ± 0.25D. In the ± 0.5D range, Pearl-DGS obtained the highest percentage again, and it was significantly higher than Barrett Universal II, Haigis, Hoffer Q, Holladay1, Holladay2 and Olsen (P = 0.001, P = 0.02, P = 0.0003, P = 0.01, P = 0.007, P = 0.05, respectively). In the ± 1.0D range, Okulix possessed the highest percentage, and it was significantly higher than Barrett Universal II, Castrop, Hoffer Q and Holladay2 (P = 0.0005, P = 0.03, P = 0.003, P = 0.02, respectively). The new generation formulae, based on artificial intelligence or ray-tracing principle, are more accurate than the convergence formulae. Pearl-DGS and Okulix are the two most accurate formulae in short eyes.

Design of Wideband High-Efficiency Circularly Polarized Folded Reflectarray Antenna

This communication presents a wideband high-efficiency circularly polarized (CP) folded reflectarray antenna (FRA) based on the CP selective surface (CPSS). The proposed CPFRA is comprised of a simple CPSS on the top layer, a wideband reflectarray plane on the bottom layer, and a wideband planar CP antenna as the primary source. First, the simple CPSS based on the traditional Pierrot structure is designed. The CPSS can reflect one CP wave, while it can transmit its orthogonal CP wave. Then, a subwavelength element is used to design the wideband reflectarray, and a wideband planar CP microstrip patch array is selected as the feed. According to the ray tracing principle, the distance between the upper CPSS and the bottom planar reflectarray is reduced to half of the distance between the planar reflectarray and the imaginary feed approximately. At last, we design a wideband high-efficiency CPFRA. Measured results of the fabricated prototype reveal that its maximum gain at 10 GHz is 27.8 dBic, its 3 dB gain bandwidth is 15%, its 3 dB axial-ratio (AR) bandwidth is 23%, and its maximum aperture efficiency is about 45.4%. Good broadband and low-profile characteristics make the proposed CPFRA have potential value in some wireless communication system.

Analysis of the acoustical environment of classrooms in three brazilian public schools through measurements and 3d simulation

The present study analyses the outdoor and indoor sound pressure levels (SPL) and the reverberation time (RT) measured in three Brazilian public classrooms. For the SPL, a sound level analyzer (class II) was used, and for the RT it was used a smartphone for the measurements. The sound sources were the impulses of bursting balloons and the data was processed in a MatLab toolbox (ITA-Toolbox). The classrooms were also simulated in an open source modeling software (I-SIMPA), using ray-tracing principles. Based on the results of the simulations, supported by the low-cost measurements, it was observed that the classroom didn't reach the national standards for classroom acoustics. Some improvements were designed with sustainable materials in order to reach the lower limits of the standards using the same room acoustics software. It was observed that the low-cost measurements helped on the diagnosis of classroom's acoustic issues which was also verified in the 3D simulation. This procedure showed itself as a cheap solution for classroom acoustic designs.

Optical design and simulation of Einstein Probe satellite follow-up x-ray telescope

The Follow-up X-ray Telescope (FXT), a key payload onboard the Einstein Probe sallite (EP), is equipped with a Wolter-I x-ray focusing mirror system. We introduce the principle of such a mirror system and analyze the influence of the mirror gap in the multishell nested mirror of the FXT on the effective area, stray-light ratio, and vignetting. To ensure that no occlusion occurs within adjacent shells and minimize stray-light ratio, the size of the gap is set to a optimized value for corresponding shell. We finished a design of a 54-shell mirror system according to these results. The optical performance of the design was then simulated using a Monte Carlo algorithm and the ray-tracing principle. The simulation shows that the effective area is 414.5 ± 0.2 cm2 at 1.25 keV (considering the spider), and the field of view is 64 arcmin in diameter. These parameters meet the optical requirements of the FXT.

A simulation model and experimental study of X-ray transmission through a polycapillary focusing X-ray lens

A simulation model is established to simulate the X-ray transmission performance through a polycapillary focusing X-ray lens whose configuration curve was described by a piecewise function. The shape of the lens is segmented, and each segment uses different function curve. The ray tracing principle is used to simulate the transmission performance of X-rays through the polycapillary focusing X-ray lens. And the simulation results were compared with the experimental results.

Relationship Between Basal Plane Dislocation Distribution and Local Basal Plane Bending in PVT-Grown 4H-SiC Crystals

The inhomogeneous distributions of basal plane dislocations (BPDs) in PVT-grown 4H-SiC crystal boule due to internal stresses cause lattice plane bending, which strongly affect SiC-based device fabrication. The relationship between BPDs and local basal plane bending in 6-inch 4H-SiC substrates has been investigated. Synchrotron monochromatic beam x-ray topography (SMBXT) imaging shows black and white contrast of BPDs with Burgers vectors of opposite signs based on the principle of ray tracing. We have evaluated the net difference of BPDs with black and white contrast along both [11$$ \bar{2}$$0] and [1$$ \bar{1}$$00] radial directions on the Si face across multiple 6-inch diameter 4H-SiC substrates sliced from the same and different boules and predicted the nature (concave/convex) and amount of bending of the basal plane in these wafers. Line scans of 0008 reflection using high resolution x-ray diffractometry (HRXRD) has been carried out along the two directions to verify the nature of bending in these wafers. Results show quite different bending behavior along [11$$ \bar{2} $$0] and [1$$ \bar{1}$$00] directions, indicating that the Si face of 6-inch substrates creates non-isotropic bending on the basal plane. These observations are correlated quite well with net BPD density analysis. The physical shapes of the wafers were also measured to be not flat due to the surface effect. Quantitative analysis of the degree of basal plane bending based on the SMBXT data was carried out and found to be correlating well with the measured tilt angle from HRXRD. Existence of a high stress center was observed in one of the 6-inch wafers resulting in severe bending which is associated with both large bending angles and abrupt changes in lattice constants a and c.

Imaging Velocity Fields Analysis of Space Camera for Dynamic Circular Scanning

Compared with traditional push-broom imaging, the space camera that performs the new circular scanning imaging can effectively enlarge the imaging area and obtain high-resolution images. However, the imaging velocity fields of space camera will seriously deteriorate the image quality in the circular scanning imaging process. And the velocity fields are anisotropically distributed due to various factors, including attitude maneuvering, satellite precession, earth curvature, and earth rotation. Therefore, this paper proposes a mathematical model of the velocity field to analyze the effect of circular scanning imaging. Based on the principle of ray tracing, the expression of the instantaneous velocity field on the ground is first derived, and then the corresponding image velocity field is obtained by mapping the velocity vector to the focal plane. In addition, numerical simulations and image simulations are performed to analyze the anisotropy distribution of the velocity vectors. Moreover, the dynamic characteristics of the space camera are analyzed to evaluate the performance of this new imaging. The simulation results show that the higher velocity leads to worse imaging quality. The study of this paper provides guidance for attitude planning and imaging assessment for new remote sensing imaging of space cameras.

Relationship between Basal Plane Dislocation and Local Basal Plane Bending in PVT-Grown 4H-SiC Crystals

Efforts to improve the quality and size of 4H-SiC wafers have resulted in size of 6” and dislocation densities of the order of 103 cm-2. The presence of significant quantities of crystallographic defects in bulk 4H-SiC crystals continues to be a major obstacle for achieving high-quality 4H-SiC substrates. Of particular note is the nucleation and distribution of basal plane dislocations (BPDs). BPDs are deformation-induced and are mostly generated during post-crystal growth cooling or high temperature annealing processes. BPDs have been associated with the formation of Shockley stacking fault leading to an increase in forward voltage degradation and are undesirable. Depending on the PVT growth conditions, internal stresses due to non-uniformity of temperature field cause lattice plane bending. During cooldown, this bending is accommodated by the inhomogeneous distribution of BPDs in a PVT grown 4H-SiC boule and persists in wafers sliced from the boule. Crystal bending affects subsequent wafer processing especially polishing and device fabrication. Therefore, analysis of the BPD distribution (sign and density) enables us to better understand basal plane bending, which provides insight into further improvement of the crystal growth process. Synchrotron Monochromatic Beam X-ray Topography (SMBXT) studies in grazing incidence geometry reveal the appearance of black and white contrast of BPDs which are associated with opposite sign of Burgers vectors. Based on the principle of ray tracing, black contrast BPDs are generated by focusing of diffracted X-rays when the extra half plane is extending away from the imaged surface, while defocusing of X-rays contribute to the generation of white contrast BPDs due to the extra half plane extending towards the surface [1]. The inhomogeneous distribution of the two types of BPD contrast will thus result in concave/convex shape of the basal planes. In our study, we have evaluated the ratio of the black/white contrast of BPDs along 11-20 direction across multiple 6-inch diameter 4H-SiC substrates sliced from the same and different boules and predicted how the lattice is tilted in different substrate wafers. High resolution X-ray diffraction measurements are currently underway to investigate the variation of rocking curve peak shift along 11-20 direction and thus to further verify our result.

Relationship between Basal Plane Dislocation and Local Basal Plane Bending in PVT-Grown 4H-SiC Crystals

Synchrotron monochromatic beam x-ray topography (SMBXT) shows black and white contrast of BPDs for Burgers vectors of opposite signs based on the principle of ray tracing. We have evaluated the ratio of black and white contrast of BPDs along both [1120] and [1100] directions across multiple 4-inch and 6-inch diameter 4H-SiC substrates. Results show the predominance of white contrast BPDs along both radial directions indicating that the basal planes on Si face are bent in a convex manner. Line scans of 0004 reflection using HRXRD was carried out which further confirmed the nature of basal plane bending in these wafers. Detailed analysis on the subsequent wafers across the crystal boule reveals the inheritance of basal plane bending behavior in these wafers. The radius of curvature in 6-inch wafers was found to be larger than the 4-inch wafers. Additional studies on the effect of low angle grain boundaries were also discussed.

Virtual wavefront calibration method based on ray tracing for alignment error compensation in the interferometric bearing ball measurement system

The accuracy of laser interferometry for measuring bearing balls is limited because it is challenging to realize null positioning of the ball being assessed. Even a slight alignment error causes the reflected wavefront to carry an uncertain aberration, which results in the surface error being obscured by the wavefront aberration. To effectively separate the surface error from the reflected wavefront, a virtual wavefront calibration method of ray tracing for alignment error compensation in the interferometric bearing ball measurement system is proposed. A virtual wavefront measurement model with variable alignment vector of the system is established based on the ray tracing principle and coordinate transform theory. According to the virtual wavefront, a calibration process is achieved in the virtual model with a known regularization and optimization method; as a result, no accurate adjustment mechanism is required to adjust the position of the bearing ball in the actual measurement system. Simulation and experiment results indicate that the proposed method is effective, and the repeatability of this measurement system is better than λ/40 peak–valley value. The final results may promote the application of this method in other fields of optical measurement.

An optimization method of dynamic patterns based on aspheric microlens array

An optimization method is proposed to improve the image quality of dynamic patterns in this paper. In order to obtain parallel emergent beam of high quality, aspheric microlens array is used in the optical system. Besides, an analytical model of the substrate and a single aspheric lens of MLA is presented based on the principle of ray tracing which is used in optical design for virtually tracing rays through an optical system. Moreover, how do the parameters influence the image quality is analyzed and the relationship between the conic constant and the divergence angle of emergent beam is derived. Preliminary optimization results with a second order aspheric lens are compared with the simulation results obtained by ZEMAX. The ray tracing method in this article helps improve the image quality of dynamic patterns and has the potential to be used in designing aspheric surface because it offers a way to improve the parallel rays and optimize the parameters of the optical system.

The Focal Heat Flux Distribution Measurement of High-times Concentrating Directional Transmission System

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基于光线追迹的LED裸眼三维显示技术准直性研究

In the integrated imaging naked eye 3D display based on LED, the divergence angle of the pixel point of LED large screen was very large. Flat convex and double convex lens are often employed. The reconstructed light of the image diverges and the pixel crosstalk between adjacent lens units was large, resulting in unclear images during the reproduction of the three-dimensional scene with the reduced imaging quality. The imaging process of integrated imaging based on LED was analyzed according to the principle of ray tracing. The relationship of crosstalk between different shapes of the lens array and adjacent lens units of LED integrated imaging was investigated. A single meniscus lens was used to effectively control the divergence of the reconstructed light. The reconstructed light passing through the lens was more convergent and collimated. The emergent rays through the lens becomes more parallel and the crosstalk between adjacent lens units was reduced effectively. By comparing the simulation result of the letter model, the meniscus lens was more suitable for LED integrated imaging. The imaging effect of the meniscus lens is better than that of the other lens.

Simulation and application of micro X-ray fluorescence based on an ellipsoidal capillary

A micro X-ray fluorescence setup was presented, based on an ellipsoidal capillary and a traditional laboratorial X-ray source. Using Ray-tracing principle, we have simulated the transmission path of X-ray beam in the ellipsoidal capillary and designed the optimal parameters of the ellipsoidal capillary for the micro X-ray fluorescence setup. We demonstrate that ellipsoidal capillary is well suited as condenser for the micro X-ray fluorescence based on traditional laboratorial X-ray source. Furthermore, we obtain the 2D mapping image of the leaf blade sample by using the ellipsoidal capillary we designed.

A Novel PRAMC-Based Ultralow-Profile Transmitarray Antenna by Using Ray Tracing Principle

In this paper, a novel ultralow-profile transmitarray (TA) is proposed by using multifolded ray tracing principle. The proposed TA unit cell would reflect the incident wave of x-polarization as a ground and transmit the incident wave of y-polarization with arbitrary phase shift in the operating frequency band. A broadband polarization rotation reflection surface based on artificial magnetic conductor with small phase difference in wide range of incidence angle is applied to transform the polarization of incident wave. Two kinds of TA antennas at 28 GHz are studied, where the distances between the source and the TA are, respectively, reduced to 1/3 and 1/4 of the focal length (named as TA antennas I and II), which are much less than that of the conventional TA antennas. The simulated results show that the proposed TA antennas can achieve −1 dB gain drop bandwidth of 5% and cross-polarization level of less than −30 dB, and the maximum aperture efficiencies can achieve 46% and 40%, respectively. For demonstration, the TA antenna I is fabricated and measured. Good agreement can be observed between the measurement and simulation.

Simulation of the Golay3 multiple mirror telescope with a conicoidal primary mirror by extending the optical design program

The notion of a sparse aperture system offers a novel solution to decrease the volumes and weight of space telescopes while pursuing higher resolutions. A simulation of the applicable sparse aperture systems is studied. First, the principle of ray tracing used in the optical design program is analyzed. It is pointed out that surface models representing the primary mirror of a sparse aperture system can be established by programming and creating Dynamic Link Library files to define the propagation properties of the passing rays. The method of simulating the Golay3 multiple mirror telescope (MMT) with a conicoidal primary mirror is proposed. Second, the structure of the conicoidal primary mirror of the Golay3 MMT is investigated. Formulas to define the directions, optical path lengths and intensities of rays passing through the primary mirror are deduced. Finally, two Golay3 MMT systems are simulated as examples. Their simulation results are presented and analyzed. The theoretical fill factors, the simulative fill factors, and the normalized modulation transfer functions of the simulated system are calculated to verify the proposed simulation method. They are proved to be in accordance with each other.