Symmetric Lens Research Articles

High-speed terahertz reflection three-dimensional imaging using beam steering.

High-speed terahertz (THz) reflection three-dimensional (3D) imaging is demonstrated using electronically-controlled optical sampling (ECOPS) and beam steering. ECOPS measurement is used for scanning an axial range of 7.8 mm in free space at 1 kHz scan rate while a transverse range of 100 × 100 mm(2) is scanned using beam steering instead of moving an imaging target. Telecentric f-θ lenses with axial and non-axial symmetry have been developed for beam steering. It is experimentally demonstrated that the non-axially symmetric lens has better characteristics than the axially symmetric lens. The total scan time depends on the number of points in a transverse range. For example, it takes 40 s for 200 × 200 points and 10 s for 100 × 100 points. To demonstrate the application of the imaging technique to nondestructive testing, THz 3D tomographic images of a glass fiber reinforced polymer sample with artificial internal defects have been acquired using the lenses for comparison.

Gradient index lenses for flexural waves based on thickness variations

This work presents a method for the realization of gradient index devices for flexural waves in thin plates. Unlike recent approaches based on phononic crystals, the present approach is based on the thickness-dependence of the dispersion relation of flexural waves, which is used to create gradient index devices by means of local variations of the plate's thickness. Numerical simulations of known circularly symmetrical gradient index lenses have been performed. These simulations have been done using the multilayer multiple scattering method and the results prove their broadband efficiency and omnidirectional properties. Finally, finite element simulations employing the full three-dimensional elasticity equations also support the validity of the designed approach.

Negative refraction and planar focusing based on parity-time symmetric metasurfaces.

We introduce a new mechanism to realize negative refraction and planar focusing using a pair of parity-time symmetric metasurfaces. In contrast to existing solutions that achieve these effects with negative-index metamaterials or phase conjugating surfaces, the proposed parity-time symmetric lens enables loss-free, all-angle negative refraction and planar focusing in free space, without relying on bulk metamaterials or nonlinear effects. This concept may represent a pivotal step towards loss-free negative refraction and highly efficient planar focusing by exploiting the largely uncharted scattering properties of parity-time symmetric systems.

Asymptotic solutions for the case of SIE lens models and application to the quadruply imaged quasar Q2237+0305

Considering a small misalignment between a point-like source, a singular isothermal ellipsoid deflector and an observer, we derive to first order simple relations between the model parameters and the lensed image positions, and an expression for the time delay between pairs of opposed images which is analogue to the one previously derived for the case of e − γ models. Combined with the first-order astrometric relations, we retrieve a simple expression for the time delays, in agreement with Witt, Mao & Keeton, which solely depends on the lensed image positions. The real advantage of using the first-order equations when dealing with symmetric gravitational lens systems is to directly test the validity of the adopted lens model without having to perform any accurate numerical fit. In this paper, we present in detail the calculations which lead to those relations between the singular isothermal ellipsoid lens model parameters and the lensed image positions. In addition, we model the well-known Einstein cross Q2237+0305 with three families of models: e − γ, singular isothermal ellipsoid and non-singular isothermal ellipsoid plus shear, using a genetic algorithm from the Qubist Optimization Toolbox. We conclude that although the non-singular isothermal ellipsoid plus shear model shows the best agreement between the calculated and the observed image positions (��x �= 0.0026 arcsec), the more simple singular isothermal ellipsoid also leads to quite satisfactory and acceptable results (��x �= 0.0059 arcsec).

Refractive laser beam shaping by means of a functional differential equation based design approach

Many laser applications require specific irradiance distributions to ensure optimal performance. Geometric optical design methods based on numerical calculation of two plano-aspheric lenses have been thoroughly studied in the past. In this work, we present an alternative new design approach based on functional differential equations that allows direct calculation of the rotational symmetric lens profiles described by two-point Taylor polynomials. The formalism is used to design a Gaussian to flat-top irradiance beam shaping system but also to generate a more complex dark-hollow Gaussian (donut-like) irradiance distribution with zero intensity in the on-axis region. The presented ray tracing results confirm the high accuracy of both calculated solutions and emphasize the potential of this design approach for refractive beam shaping applications.

Side-illuminating LED luminaires with accurate projection in high uniformity and high optical utilization factor for large-area field illumination.

A novel light luminaire is proposed and experimentally analyzed, which accurately projects light into a large rectangular area to achieve uniform illumination and a high optical utilization factor at the target. Side-illuminating luminaires for large-scale illuminated area are typically set with an elevated tilt angle to enlarge the illuminated area. However, the light pattern is bent thereby reducing the uniformity and optical utilization factor at the target. In this paper, we propose an efficient and useful approach with a rotationally symmetric projection lens that is trimmed to adjust the bending effect and to form a rectangular illumination light pattern on the ground. The design concept is demonstrated and verified. Several potential applications such as highly uniform illumination with fitting shapes for sport courts are analyzed and discussed.

A two-step design method for high compact rotationally symmetric optical system for LED surface light source.

A two-step optimization method is proposed to design a compact single-surface far-field illumination system, satisfying the requirements of illuminance uniformity and light control efficiency with h/D less than 3:1. In the first step, the conventional tailored edge-ray design (TED) method is employed to generate prescribed illumination distribution for the rotationally symmetric optical system, and an optimization process is added to reach a balance between illuminance uniformity and light control efficiency. Based on the improved TED method, we can construct an initial optical system more accurate than that obtained by point source assumption. In the second step, an iterative feedback modification process is employed to optimize the initial optical system, so that the degradation of performance due to insufficient control of skew rays is mitigated. Because the initial optical system constructed in the first step is accurate enough, the second-step feedback modification can converge to a satisfactory result within several iterations. As an example, a free-form rotationally symmetric lens with the height of h = 25 mm is designed for a discoidal LED source with the diameter of D = 10 mm. Both high illuminance uniformity of 0.75 and high light control efficiency of 0.86 are obtained simultaneously. The method can be further used to achieve more complex non-uniform illumination distributions. The design of an optical system with h/D = 2.5:1 and a circular linear illumination distribution is demonstrated.

Expert system of single magnetic lens using JESS in Focused Ion Beam

This work shows expert system of symmetrical single magnetic lens used in focused ion beam optical system. Java expert system shell(JESS) programming is proposed to build the intelligent agent MOPTIONfor getting an optimum magnetic flux density , and calculate the ion optical trajectory. The combination of such rule based engine and SIMION 8.1 has configured the reconstruction process and compiled the data retrieved by the proposed expert system agent to implement the pole-pieces reconstruction for lens design. The pole pieces reconstruction has been resulted in 3D graph , and under the infinite magnification conditions of the optical path, aberration (spherical / chromatic and total) disks diameters have been obtained and got the values (0.03,0.13 and 0.133) micron (µm) respectively.

Potential benefits of free-form optics in on-axis imaging applications with high aspect ratio

Including free-form optical components in imaging systems provides numerous opportunities for enhanced performance and compact, lightweight packaging. This applies especially to the use of free-form optics in off-axis imaging applications. In case of on-axis imaging, rotationally symmetric lenses are typically used, as they greatly simplify the design and manufacturing process. However, for imaging applications with high aspect ratio, free-form optics can help to provide solutions with clearly better overall imaging performance. For such cases, the ray tracing simulations in this work demonstrate superior imaging performance of basic free-form lenses in comparison to conventional rotationally symmetric lenses, each consisting of two surfaces.

Use of the Fourier transform to derive simple expressions for the gravitational lens deflection angle

Knowing that the gravitational lens deflection angle can be expressed as the convolution product between the dimensionless surface mass density |$\kappa (\boldsymbol {x})$| and a simple function of the scaled impact parameter vector |$\boldsymbol {x}$|⁠, we make use of the Fourier transform to derive its analytical expression for the case of mass distributions presenting a homoeoidal symmetry. For this family of models, we obtain the expression of the two components of the deflection angle in the form of integrals performed over the radial coordinate ρ. In the limiting case of axially symmetric lenses, we obviously retrieve the well-known relation |$\hat{\boldsymbol {\alpha }}(\boldsymbol {x})\ \propto M(\le |\boldsymbol {x}|) \boldsymbol {x}/|\boldsymbol {x}|^2$|⁠. Furthermore, we derive explicit solutions for the deflection angle characterized by dimensionless surface mass density profiles such as |$\kappa \propto (\rho _{\rm c}^{2}+ \rho ^{2})^{-\nu }$|⁠; corresponding to the non-singular isothermal ellipsoid model for the particular case ν = 1/2. Let us insist that all these results are obtained without using the complex formalism introduced by Bourassa and Kantowski. Further straightforward applications of this Fourier approach are suggested in the conclusions of this work.

Building a New Software of Electromagnetic Lenses (CADTEL)

The Computer Aided designing Tools for Electromagnetic Lenses (CADTEL) is a new software as application package of programs concept to aid both users and professionals in symmetric and asymmetric electromagnetic lenses with single, double, and multipole piece in electron microscope of electron optics field. The CADTEL software has been designed to run on several computer platforms and includes two types of design procedure. The first one named, analysis procedure (which is based on trial and error) where consist of three sorts called; H1 programs for magnetic scalar potential by solving Laplace's equation [1,2], H2 and H3 programs for magnetic vector potential by solving Poisson's equation [3,4] in linear and non linear media respectively. While the second part, named H4 programs for the synthesis procedure (inverse design). The previous types differ by the obtaining the magnetic flux density, and poles shape, while it is analog by compute and plot the lens properties which are operating at zero, low, high, and infinite magnification conditions (operation modes). CADTEL software consist of computational and plot steps of magnetic field, equipotential surfaces, flux lines, objective and projector properties, and poles shape for proposed lens design which are appear in auto visual interfaces, that are coded in visual basic language [5].

Polarization-sensitive diffractive optical elements fabricated in BR films with femtosecond laser

Multi-photon product (F540-state) of bacteriorhodopsin (BR) polymeric films excited by femtosecond laser shows permanently photoinduced birefringence and dichroism. Based on this property, polarization-sensitive diffractive optical elements (PDOEs), e.g., gratings, two-dimensional optical lattice, Bessel zone plate, were firstly fabricated and investigated in BR films by femtosecond laser multi-beam interference with rotationally symmetric pyramid lenses. These fabricated PDOEs are completely stable at room temperature. The dependence of diffraction efficiency on the incident polarization state was measured. The micro-structures of PDOEs were observed under polarization microscope, and the selective readout diffraction patterns from the polarization-multiplexed PDOEs were demonstrated.

Plenary Special Lectures

The correction of the aberrations of electron lenses is the long story of many seemingly fruitless efforts to improve the resolution of electron microscopes by compensating for aberrations of round electron lenses over a period of 50 years. The problem started in 1936 when Scherzer demonstrated that the chromatic and spherical aberrations of rotationally symmetric electron lenses are unavoidable. Moreover, the coefficients of these aberrations cannot be made sufficiently small. As a result, the resolution limit of standard electron microscopes equals about one hundred times the wavelength of the electrons, whereas modern light microscopes have reached a resolution limit somewhat smaller than the wavelength. In 1947, Scherzer found an ingenious way for enabling aberration correction. He demonstrated in a famous article that it is in theory possible to eliminate chromatic and spherical aberrations by lifting any one of the constraints of his theorem, either by abandoning rotational symmetry or by introducing time-varying fields, or space charges. Moreover, he proposed a multipole corrector compensating for the spherical aberration of the objective lens.

Algebraic and numerical analysis of imaging properties of thin tunable-focus fluidic membrane lenses with parabolic surfaces

The theory of third-order aberrations for a system of rotationally symmetric thin tunable-focus fluidic membrane lenses with parabolic surfaces is described. A complex analysis of the third-order design of tunable fluidic lenses is performed considering all types of primary aberrations. Moreover, formulas are derived for the calculation of the change of aberration coefficients of the parabolic tunable fluidic membrane lens with respect to the wavelength. It is shown that spherical aberration of a simple tunable-focus fluidic membrane lens with parabolic surfaces can be corrected, which is not possible with a classical spherical lens. The presented analysis is explained on examples. Derived formulas make possible to calculate parameters of optical systems with fluidic membrane lenses with small residual aberrations.

Building a New Software of Electromagnetic Lenses (CADTEL)

The Computer Aided designing Tools for Electromagnetic Lenses (CADTEL) is a new software as application package of programs concept to aid both users and professionals in symmetric and asymmetric electromagnetic lenses with single, double, and multipole piece in electron microscope of electron optics field. The CADTEL software has been designed to run on several computer platforms and includes two types of design procedure. The first one named, analysis procedure (which is based on trial and error) where consist of three sorts called; H1 programs for magnetic scalar potential by solving Laplace's equation [1,2], H2 and H3 programs for magnetic vector potential by solving Poisson's equation [3,4] in linear and non linear media respectively. While the second part, named H4 programs for the synthesis procedure (inverse design). The previous types differ by the obtaining the magnetic flux density, and poles shape, while it is analog by compute and plot the lens properties which are operating at zero, low, high, and infinite magnification conditions (operation modes). CADTEL software consist of computational and plot steps of magnetic field, equipotential surfaces, flux lines, objective and projector properties, and poles shape for proposed lens design which are appear in auto visual interfaces, that are coded in visual basic language [5].

数控超光滑加工高次回转对称非球面镜

数控超光滑加工高次回转对称非球面镜

Lensing and dynamics in two simple steps

Abstract We present a ready-to-use method to constrain the density distribution in spherically symmetric early-type galaxy lenses. Assuming a power-law density profile, then joint use of the virial theorem and the lens equation yields simple formulae for the power-law index (or logarithmic density gradient). Any dependence on orbital anisotropy can be tightly constrained or even erased completely. Our results rely just on surface brightnesses and line-of-sight kinematics, making deprojection unnecessary. We revisit three systems that have already been examined in the literature (the Cosmic Horseshoe, the Jackpot and B1608+656) and provide our estimates. Finally, we show that the method yields a good approximation for the density profile even when the true profile is a broken power law, albeit with a mild bias towards isothermality.

Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs

Monocentric lenses have recently changed from primarily a historic curiosity to a potential solution for panoramic high-resolution imagers, where the spherical image surface is directly detected by curved image sensors or optically transferred onto multiple conventional flat focal planes. We compare imaging and waveguide-based transfer of the spherical image surface formed by the monocentric lens onto planar image sensors, showing that both approaches can make the system input aperture and resolution substantially independent of the input angle. We present aberration analysis that demonstrates that wide-field monocentric lenses can be focused by purely axial translation and describe a systematic design process to identify the best designs for two-glass symmetric monocentric lenses. Finally, we use this approach to design an F/1.7, 12 mm focal length imager with an up to 160° field of view and show that it compares favorably in size and performance to conventional wide-angle imagers.

Focus on software and semiconductors

Focus on software and semiconductors

Asymptotic solutions for the case of nearly symmetric gravitational lens systems

Gravitational lensing provides a powerful tool to determine the Hubble parameter H0 from the measurement of the time delay Δt between two lensed images of a background variable source. Nevertheless, knowledge of the deflector mass distribution constitutes a hurdle. We propose in the present work interesting solutions for the case of nearly symmetric gravitational lens systems. For the case of a small misalignment between the source, the deflector and the observer, we first consider power-law (ɛ) axially symmetric models for which we derive an analytical relation between the amplification ratio and source position which is independent of the power-law slope ɛ. According to this relation, we deduce an expression for H0 also irrespective of the value ɛ. Secondly, we consider the power-law axially symmetric lens models with an external large-scale gravitational field, the shear γ, resulting in the so-called ɛ−γ models, for which we deduce simple first-order equations linking the model parameters and the lensed image positions, the latter being observable quantities. We also deduce simple relations between H0 and observables quantities only. From these equations, we may estimate the value of the Hubble parameter in a robust way. Nevertheless, comparison between the ɛ−γ and singular isothermal ellipsoid (SIE) models leads to the conclusion that these models remain most often distinct. Therefore, even for the case of a small misalignment, use of the first-order equations and precise astrometric measurements of the positions of the lensed images with respect to the centre of the deflector enables one to discriminate between these two families of models. Finally, we confront the models with numerical simulations to evaluate the intrinsic error of the first-order expressions used when deriving the model parameters under the assumption of a quasi-alignment between the source, the deflector and the observer. From these same simulations, we estimate for the case of the ɛ−γ family of models that the standard deviation affecting H0 is which merely reflects the adopted astrometric uncertainties on the relative image positions, typically arcsec. In conclusions, we stress the importance of getting very accurate measurements of the relative positions of the multiple lensed images and of the time delays for the case of nearly symmetric gravitational lens systems, in order to derive robust and precise values of the Hubble parameter.