Vector Ray Tracing Research Articles

Möbius shifts associated with the third-order and the fourth-order rainbows of a spheroidal droplet computation.

Vector-ray tracing (VRT) is employed to calculate Möbius shifts of the third-order and the fourth-order rainbows for a spheroidal droplet. When the aspect ratio of a spheroidal droplet is small, approximation expressions for calculating the Möbius shift (i.e., deviation of the geometrical rainbow angle for a spheroidal droplet and that for a spherical droplet) were given by Lock and Können [Appl. Opt.56, G88 (2017)APOPAI0003-693510.1364/AO.56.000G88]. The assessment of applicability ranges of the Lock approximation is obtained by comparing with a VRT simulation for a water droplet with the refractive index m=1.333. For this, a parameter ΔD is defined that measures the disagreement between the two methods. A threshold value of 5% for ΔD is chosen below which the agreement is considered to be good. For the third-order rainbow, it is shown that this is the case for the Lock approximation for water droplets (m=1.333) with aspect ratios in the range of 0.97≤a/c≤1.03. For the fourth-order rainbow, the application range of the Lock approximation is 0.99≤a/c≤1.01 for water droplets. For the first-order and second-order rainbows, the application ranges are briefly revisited with the current method. The influence of the droplet refractive index on the Möbius shift is also investigated.

Geometric optics applied to drops passing through a focused Gaussian beam.

The present study examines the scattered light intensity from a drop passing through a Gaussian beam of a diameter comparable to or smaller than the drop. This is the situation encountered when using the time-shift technique, an optical technique used to characterize drops and aerosols according to the size and the velocity. In simulating the signals received by such an instrument, the computational effort involved when using, for instance, the Generalized Lorenz-Mie Theory or vector ray-tracing, is immense and hardly practical for use in instrument design and/or optimization. In this study theoretical expressions based on geometric optics are derived as an alternative, and they are shown to adequately capture the main features of the time-shift signals. These solutions require little computational effort and can be effectively used to explore the dependencies of the signals on various input factors, thus allowing further instrument development. On the other hand, these relations are also of general interest in the field of light scattering from drops and aerosols.

Design of optical engines for stellar simulation systems with low extinction ratios

An optical engine (OE) for stellar simulation systems with low extinction ratios (ERs) is proposed. This engine combines two orthogonal polarizers with a non-polarizing beam splitter to suppress the leakage of dark silicon-based liquid crystals (LCOS) in traditional systems. In this paper, a method to calculate the ER based on vector ray tracing is used. The new optical engine (OE) is demonstrated to have lower ERs than traditional systems. The calculations show that the maximum ER is 5×10−5 in the range of ±8°, which is much lower than the ERs of traditional optical engines of 2.5×10−2 . It reduces the ER by three orders of magnitude. The experimental results show that the new OE improves the ERs by 92.68% compared with the traditional system.

Updated Fast Solution for Quasi-Optical Beam Waveguides With Tilted FFT Beam Propagator

An updated fast solution in modeling quasi-optical beam waveguides is reported, where several mirror reflectors are utilized for the beam transformation. The fast Fourier transform Poynting vector ray tracing between virtual apertures (FFT-PVVAs) algorithm has been introduced and applied in modeling the reflected beam, based on the FFT-accelerated beam propagator between parallel apertures, and the Poynting vector ray tracing for the mirror reflection. However, for designing and optimizing a beam path with multireflectors, it is desired that the accumulated precision loss due to the Poynting vector ray tracing can be further reduced. As a modification, angular spectrum transform-based beam propagator between oblique apertures is introduced, so as to reduce the ray tracing path length. The improved method is named as FFT-PVVA-tilted propagation (FFT-PVVA-TP). As validation, beam propagation in a four-mirror beam waveguide is simulated by FFT-PVVA, FFT-PVVA-TP, and physical optics integration. Numerical results suggest that FFT-PVVA-TP provides clearly better accuracy after four times of beam reflection.

Poynting Vector Method for Reflector Beam Shaping

A reflector beam shaping method is presented, which includes an efficient algorithm. This efficient algorithm based on the Poynting vector tracing method is employed to analyze the procedure of beam propagation and reflection. The Poynting vector ray tracing method is naturally integrated into the reflector reshaping procedure, which brings significant advantage over existing beam shaping methods. The beam shaping process by this algorithm also shows distinct advantage in efficiency over competing integration theories. It has comparable accuracy with typical physical optics. The validity of this reflector shaping method is demonstrated by performing iterative phase correction toward a gyrotron quasi-optical mode converter.

Simulation of optical caustics associated with the tertiary rainbow of oblate droplets.

In this paper, a vector ray tracing (VRT) model is used to simulate optical caustic structures, including rainbow and hyperbolic umbilic (HU) fringes, in the tertiary rainbow region of light scattering from oblate spheroidal droplets. In order to apply the optical caustic structures to particle diagnostics, the evolution of rainbow and HU fringes with an increase in the aspect ratio of oblate spheroidal droplets is investigated in detail, and the curvature of rainbow fringes are calculated. Next, on the basis of the VRT model, the location of cusp caustics is calculated and compared with theoretical prediction.

Application of vector ray tracing to the computation of Möbius shifts for the primary and secondary rainbows.

The Möbius approximation for the primary rainbow and the Können approximation for the secondary rainbow have been modified to yield consistent predictions of the Möbius shift of the top and bottom rainbows, respectively. The applicability ranges of the Möbius and Können approximations are investigated by comparison to vector ray tracing (VRT) simulations. For the primary rainbow, these results indicate that the Möbius approximation is valid for spheroidal water droplets (m=1.333) in the range of aspect ratios 0.98≤a/c≤1.02. For the secondary rainbow, the Können approximation predicts the Möbius shift well for spheroidal water droplets within the range 0.99≤a/c≤1.01. For a spheroidal droplet with side-on incidence, the difference between the approximations and VRT simulations are discussed. Furthermore, the dependence of Möbius shifts on the relative refractive index of droplet is discussed.

航天TDI CCD相机成像拼接快速配准算法设计与分析

In order to solve the problem of multi pieces of TDI CCD stitching pixel mismatch in satellite flexible transformation multimodal imaging, a kind of pixel matching algorithm which can realize overlapping and displacement pixel fast assembly and registration of TDI CCD camera is proposed. Through the analysis of multi pieces of TDI CCD assembly imaging pixel mismatch phenomenon caused by the variation of image motion velocity vector in focal plane during the process of satellite side swing imaging, the imaging velocity vector ray tracing and the homogeneous coordinate transformation method is designed. Based on this method, the image motion velocity and drift angle which influence image mismatch during the process of satellite side swing imaging and the number of pixel in direction of longitudinal displacement and transverse overlapping of two pieces of TDI CCD assembly imaging are calculated. Three-axis air flotation turntable attitude simulation system and a TDI CCD camera are used in experiment to verify the pixel matching algorithm of two pieces of TDI CCD assembly imaging. TDI CCD camera of viewing angle of 10, after an assembly period, the original number of longitudinal displacement and transverse overlapping pixels of two pieces of TDI CCD assembly imaging turns from 148.5 and 50 to 137 and 49, respectively, which is consistent with theoretical result in longitudinal displacement direction and has a deviation of only 0.1 pixel in transverse overlapping direction. Compared with the theoretical and experimental result, the design of fast registration algorithm of calculation of longitudinal displacement and transverse overlapping pixel can solve the accuracy of TDI CCD assembly imaging, which guarantees image pixel matching and obtain high quality images.

Simulation of optical caustics associated with the secondary rainbow of oblate droplets

A vector-ray tracing (VRT) model is employed to simulate optical caustic structures [in terms of rainbow and hyperbolic umbilic (HU) fringes] in the secondary rainbow region of light scattering from oblate droplets. The changes of the rainbow fringe and HU fringe in response to shape deformation of oblate droplets are investigated and the curvature of the rainbow fringe is calculated. Then the location of cusp caustics is calculated from VRT simulations and compared with analytic solutions.

Optical caustics associated with the primary rainbow of oblate droplets: simulation and application in non-sphericity measurement

A vector ray tracing (VRT) model is developed to simulate optical caustic structures in the primary rainbow region of light scattering from oblate droplets. The changes of the optical caustic structures in response to shape deformation of oblate droplets are investigated. Then the curvature calculated from the simulated rainbow fringes is compared with that from the measured rainbow fringes and good agreement is found. Furthermore, according to the generalized rainbow patterns and the relation between aspect ratio and curvature of the rainbow fringe, non-sphericities in terms of aspect ratio of an oblate water droplet is measured with high measurement accuracy.

Simplification of vector ray tracing by the groove function

Tracing rays through arbitrary diffraction gratings (including holographic gratings of the second generation fabricated on a curved substrate) by the vector form is somewhat complicated. Vector ray tracing utilizes the local groove density, the calculation of which highly depends on how the grooves are generated. Characterizing a grating by its groove function, available for almost arbitrary gratings, is much simpler than doing so by its groove density, essentially being a vector. Applying the concept of Riemann geometry, we give an expression of the groove density by the groove function. The groove function description of a grating can thus be incorporated into vector ray tracing, which is beneficial especially at the design stage. A unified explicit grating ray-tracing formalism is given as well.

The Velocity Tomography with Crosshole Seismic Data

In this paper we calculate the ray–path and traveltimes of seismic wave with vector ray tracing, and then develop a technique to reconstruct the velocity image of acoustic media from dircet traveltimes of crosshole data. The images of seismic velocity with two typical and complex geological models are presented, which demonstrate that it is a quick and highly precise technique for velocity reconstruction by crosshole data.

Design and Fabrication of a Holographic Solar Concentrator

The main purpose of this paper is to present the potential of photovoltaic systems using holographic solar concentrators. A hologram used here focuses light, spectrally splits it and diverts unwanted infrared heat away from the solar cell. The output of the hologram appears as a perpendicular thin spectral line and is displaced to solar cells on both sides. To obtain optimum design conditions we used the coupled wave theory and the vector ray tracing method. The measured data showed that the diffraction efficiency was 75 ％ and the spectral bandwidth was 350 nm.

Computer analysis of holographic systems by means of vector ray tracing: authors’ reply to comment

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text H. W. Holloway and R. A. Ferrante, "Computer analysis of holographic systems by means of vector ray tracing: authors’ reply to comment," Appl. Opt. 21, 974-974 (1982) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Computer analysis of holographic systems by means of vector ray tracing: comment

Computer analysis of holographic systems by means of vector ray tracing: comment

Computer analysis of holographic systems by means of vector ray tracing

This paper describes a computer program based on Welford's vector analysis approach capable of ray tracing through hybrid optical systems containing both conventional and diffractive elements. Results are compared to experimental data and the calculations of two other holographic computer design codes.

Analysis of He–Ne Laser Surface Reflections from an Off-Axis Parabolic Mirror

Surface reflections from an off-axis parabolic mirror are analyzed in three dimensions applying the techniques of vector analysis and ray tracing. A He-Ne laser is directed onto the mirror surface and held fixed while the parabolic mirror is rotated through an angle of 360 degrees on an axis that is parallel to that of the original paraboloid. The reflection from the mirror traces a closed figure in a plane perpendicular to the paraboloidal axis when the mirror undergoes one complete revolution about its center axis. The shape of this figure depends on the value of the off-axis distance and the focal length; consequently, this figure yields information about the parameters specified in the construction of off-axis parabolic mirrors.