Axisymmetric Lens Research Articles

Surface profiling of an aspherical liquid lens with a varied thickness membrane.

Inspired by crystalline lenses in human eyes, liquid lenses have a simple yet elegant working principle, and result in compact optical systems. Recent numerical studies showed that membranes with variable thicknesses could affect the lens profile. However, fabrication and assembly of a liquid lens with an inhomogeneous membrane is difficult. There is also a lack of experimental studies about the changes of a lens profile during deformation. In this paper, we provided a new experimental approach for characterizing the performance of a liquid lens with an inhomogeneous membrane. A 2D axisymmetric lens model was built in finite element analysis software to theoretically study the non-linear deformation behavior of the inhomogeneous membrane. Then we provided a new approach to fabricate inhomogeneous membranes using a pre-machined aluminum mold. An optical coherence tomography (OCT) system was used to dynamically measure the changes of a lens profile without contact. Both simulation and the experiments indicated that the variation of the thickness of the membrane could affect the lens profile in a predictable manner. A negative conic constant was achieved when a plano-concave membrane was adopted in a liquid lens. Larger increments of the thickness of the membrane in the radial direction resulted in a larger contribution of a conic constant to the lens profile. The presented study offers guidance for image-quality analysis and optimization of a liquid-lens-based optical system.

Investigation of waviness error in surface grinding of large axisymmetric aspheric lenses

Waviness error is one of the most critical errors in the large aspheric lenses grinding and one that has a strong impact on the performance of the optical system. In this article, the waviness error of large axisymmetric aspheric lenses for X-axis direction as well as Z-axis direction is analyzed by employing grate parallel grinding method. The grinding wheel vibration and Z-axis interpolation pace are regarded as the main causes of the surface waviness error. Furthermore, to reduce the waviness error, the influence of grinding parameters on waviness error is investigated. The waviness errors measured during grinding experiments are in good agreement with the theoretical results and the appropriate grinding parameters are recommended.

Complementary optimization method of freeform lens design for uniform illumination with extended light-emitting diode sources

A freeform lens design method based on energy mapping and complementary optimization approaches is proposed to achieve uniform illumination with extended light-emitting diode (LED) sources. This method is primarily derived from a simple source–a target energy mapping approach, while a complementary illuminance on the target plane is introduced to optimize the primary axisymmetric lens so that the profile of the lens can be reformed to produce uniform illumination when applying an extended LED source. By using this optimization method, the illuminance uniformity and optical efficiency of the lens can be improved, respectively, from 0.56 to 0.85 and from 92.4% to 94.3% for an LED light source with chip diameter of 8.9 mm, while the aspect ratio of the lens clear aperture to the source diameter is only 3.8.

Source-position transformation: an approximate invariance in strong gravitational lensing

The main obstacle for gravitational lensing to determine accurate masses of deflectors, or to determine precise estimates for the Hubble constant, is the degeneracy of lensing observables with respect to the mass-sheet transformation (MST). The MST is a global modification of the mass distribution which leaves all image positions, shapes and flux ratios invariant, but which changes the time delay. Here we show that another global transformation of lensing mass distributions exists which almost leaves image positions and flux ratios invariant, and of which the MST is a special case. Whereas for axi-symmetric lenses this source position transformation exactly reproduces all strong lensing observables, it does so only approximately for more general lens situations. We provide crude estimates for the accuracy with which the transformed mass distribution can reproduce the same image positions as the original lens model, and present an illustrative example of its performance. This new invariance transformation most likely is the reason why the same strong lensing information can be accounted for with rather different mass models.

光学部品用金型加工向け超精密5軸加工機の開発

The machining of lens array mold for optics is attracting attention for fabricating camera lens modules. The profiles of axisymmetric aspheric lenses ranging from 1 to 5 mm in diameter are regularly arranged on lens array molds, allowing multiple optical lenses to be molded simultaneously. An ultra-precision machine tool for machining the lens array mold that has high-speed motion and high-accuracy positioning is needed. To solve this problem, we developed an ultra-precision 5-axis machine tool. In this paper, this machine tool was evaluated by high speed machining of the lens array mold. A surface roughness of within 2 nm and a form accuracy of within 0.1μm have been achieved using the shaper machining. The performance of the machine tool and the evaluation results for the machined mold are reported herein.

Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses

The symmetry matching between the source and the lens results in fundamental interest for lensing applications. In this work, we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.

Discussions on on-machine measurement of aspheric lens-mold surface

At present, regarding to the machining of aspheric lens mold, there are two major methods to carry out the on-machine measurement (OMM) — contacting method (CM) and non-contacting method (NCM). Here such two methods are reviewed in detail. CM is mainly based on the contacting probe which is scratching aspheric surface of lens mold to achieve profile data. To be efficient, an idea with 45° tilt of probe is proposed for OMM of lens mold by Suzuki. But generally speaking, the contacting OMM is not so efficient and can only deal with axisymmetric aspheric lens mold. On the contrary, NCM mostly uses laser to achieve aspheric profile without any contact. On ultra-precision lathe, laser scanning system or laser interferometer is mounted on the frame of lathe and transfers measurement data to machining system efficiently. However, most NCMs need stable environment and low working noise except instantaneous phase-shifting shearing interferometry (IPSSI). Therefore, a new idea about IPSSI is proposed in this paper to realize OMM of lens molds. Unfortunately, it's also difficult to test the high numerical aperture aspheric or free-form lens molds. By comparison, the newly-developed fringe reflection (FR) method is becoming the promising method because it features the high efficiency and high accuracy. However, this method has not been used for OMM system yet. Much research should be conducted for FR OMM technology.

Studying properties of polymer X-ray lenses

The focusing properties and radiation resistance of refractive polymer X-ray lenses have been experimentally studied on an ESRF synchrotron. The axisymmetric X-ray lenses with parabolic profile have been manufactured by “imprinting” a high-precision stamp into a photocurable polymer. Results of measurements of the characteristics of lenses for 9.9-keV X-rays with an intensity of 1013 ph/(mm2 s) are presented and discussed.

Focussing light through a stack of toroidal channels in PMMA

We propose a transformational design of an axi-symmetric gradient lens for electromagnetic waves. We show that a metamaterial consisting of toroidal air channels of diameters ranging from 23 nm to 190 nm in a matrix of Polymethylmethacrylate (PMMA) allows for a focussing effect of light over a large bandwidth i.e. [600-1000] nm. We finally propose a simplified design of lens allowing for a two-photon lithography implementation.

On the Geostrophic Adjustment of an Isolated Lens: Dependence on Burger Number and Initial Geometry*

Abstract Geostrophic adjustment of an isolated axisymmetric lens was examined to better understand the dependence of radial displacements and the adjusted velocity on the Burger number and the geometry of initial conditions. The behavior of the adjustment was examined using laboratory experiments and numerical simulations, which were in turn compared to published analytical solutions. Three defining length scales of the initial conditions were used to distinguish between various asymptotic behaviors for large and small Burger numbers: the Rossby radius of deformation, the horizontal length scale of the initial density defect, and the horizontal length scale of the initial pressure gradient. Numerical simulations for the fully nonlinear time-dependent adjustment agreed both qualitatively and quantitatively with analogous analytical solutions. For large Burger numbers, similar agreement was found in laboratory experiments. Results show that a broad range of final states can result from different initial geometries, depending on the values of the relevant length scales and the Burger number computed from initial conditions. For Burger numbers much larger or smaller than unity, differences between different initial geometries can readily exceed an order of magnitude for both displacement and velocity.

Axisymmetric Resonant Lens Antenna With Improved Directivity in Ka-Band

A compact-size shaped dielectric lens antenna (DLA) is designed and optimized in Kα-band (29.5 GHz) using a new synthesis tool based on the combination of a genetic algorithm and BoR-FDTD solver. The antenna is fabricated in Rexolite and fed by a circular waveguide with a flange and an optimized integrated dielectric taper. As demonstrated, the proposed antenna combines features intrinsic to lens, resonant, and reflector antennas. The attractive performance of the antenna (in terms of directivity and sidelobe level) is demonstrated numerically and experimentally by comparison to a conventional extended hemispherical DLA.

Electron-optical characteristics of a combined electrostatic lens

The load characteristics of an electrostatic lens consisting of three coaxial cylinders are calculated. The lens is capable of focusing to one point both paraxial annular beams and annular beams away from the axis. In addition, it increases the intensity of a charged particle beam by roughly an order of magnitude compared with a commonly used single axisymmetric lens.

Effects of Grinding Wheel Vibration on Surface Quality of Axisymmetric Aspheric Lens

Minute vibration of grinding wheel greatly restricts machining accuracy of axisymmetric aspheric surface in precision grinding. This paper is dedicated to analysis micro-topography of grinding surface under grinding wheel vibration. The relative motion track of wheel to ideal lens surface and the interference of them are involved to study the effects of grinding wheel vibration on surface quality. For different operation parameters, the processed surface presents various micro-topography, and the restriction extent of vibration to surface quality is also different. Vibration waveform in the region near lens center is smoothed greatly by the interference of wheel and the processed surface. Therefore, surface quality gets some improvement from edge to center for axisymmetric aspheric lens. Experiment results verified the validity of the theoretical analysis.

77 GHz Stepped Lens With Sectorial Radiation Pattern as Primary Feed of a Lens Based CATR

We describe the design, fabrication and measurements of an axisymmetric dielectric lens, featuring a sectorial radiation pattern at 77 GHz. It will be used as the primary feed of a lens-based compact antenna test range (CATR). Due to symmetry of revolution, the sectorial lens profile can be designed in one dimension by using phase only control. The phase variation is echoed on the lens depth. The resulting stepped lens is simulated using France Telecom Orange Labs SRSRD software (¿in-house¿ software developed for dielectric axisymmetric radiating structures) and measured in an anechoic chamber at 77 GHz. Two lenses were fabricated with different materials: PVC and polyurethane, respectively. Good agreements were obtained between simulations and measurements. Less than 0.2 dB ripple in the central beam are obtained for the polyurethane lens although relatively high secondary lobes occur at 11°. Comparisons between the near field of a CATR illuminated by a small horn providing a uniform amplitude taper and the sectorial lens are conducted using numerical simulations. Results show that on-axis oscillations are reduced from 6 to 1 dB with the sectorial lens.

A combined electrostatic lens

With a view to increasing the intensity of charged particle beams, a combined electrostatic lens consisting of three coaxial cylinders has been theoretically studied. The proposed lens is capable of focusing both paraxial beams (by an axisymmetric lens) and nonparaxial beams (by a coaxial cylindrical lens). The parameters of this combined lens have been evaluated by numerical methods. The gain in the beam intensity provided by the proposed lens in comparison to the widely used single axisymmetric lens is determined.

Surface Waviness Analysis for Axisymmetric Aspheric Lens in Precision Grinding

For precision grinding, especially the aspheric grinding, the vibrations of wheel and workpiece have great impact on workpiece accuracy and roughness with special waviness. This paper firstly studies the relationship between grinding parameters and surface quality. Then according to the two kinds of aspheric machining mode: grinding with equal step feeding and grinding with equal angle feeding, the corresponding surface equations and vibration equations after grinding are given in this paper. Moreover, the specific analysis of aspheric surface model and surface waviness are also discussed for parameters optimization. The grinding experiments are done to support the theoretical research. The comparison between theoretical waviness analysis and experimental results shows good matching.

Synthesis of an inhomogeneous dielectric axisymmetric lens

The problem of determining the index of refraction as a function of the distance from the axis of symmetry of an inhomogeneous dielectric lens is considered for the input and output wave fronts. An analytical method of obtaining a solution for a layered lens is proposed, which is based on the geometric optics approximation and the assumption that the index of refraction within each layer is constant. It is demonstrated that this method is applicable to both layered and gradient lenses (provided that the number of layers is sufficiently large).

Nano-topography on axisymmetric aspherical ground surfaces

Recently, axisymmetric aspherical lenses are being increasingly installed in optical devices such as digital cameras. As the pixel number of digital image sensors increases, both high form accuracy and fine surface roughness are required, compared with conventional products. However, distortion in an optical image occurs even if an axisymmetric aspherical lens, which has high form accuracy and fine surface roughness, is used. The distortion of the optical image is caused by the surface nano-topography, which is generated in the grinding process. In this paper, the relationship between grinding conditions and the distribution of the nano-topography is investigated. In addition, a fluctuation-free grinding machine was developed to control the nano-topography.

New Compensation Grinding of Axisymmetric Aspherical Lenses with High NA Value

Aspherical parts are installed in various optical instruments. At present, a higher form accuracy is required for aspherical parts to improve the resolution of the optical instruments. To meet this demand, an arc envelope grinding method has been developed. In the arc envelope grinding process, a spherical shaped grinding wheel is used and the form error of the cross-sectional profile of the grinding wheel is transcribed to the workpiece profile. Therefore, the grinding wheel should be trued previously. However, the form error of the grinding wheel cannot be removed perfectly. To reduce the affect of the form error of the grinding wheel, compensation grinding must be carried out. In this work, the wheel path of a new compensation grinding method is proposed for a high NA value of the workpiece. Tests using the new compensation grinding method demonstrate the reduction in the form error of aspherical parts.

Nucleation in cylindrical capillaries.

We use a local density functional theory in the square gradient approximation to explore the properties of critical nuclei for the liquid-vapor transition of van der Waals fluids in cylindrical capillaries. The proposed model allows us to investigate the effect of pore size, surface field, and supersaturation on the behavior of the system. Our calculations predict the existence of at least three different pathways for the nucleation of droplets and bubbles in these confined fluids: axisymmetric annular bumps and lenses, and asymmetric droplets. The morphological transition between these different structures is driven by the existence of states of zero compressibility in the capillary. We show that the classical capillarity theory provides surprisingly accurate predictions for the work of formation of critical nuclei in cylindrical pores when line tension contributions to the free energy are taken into account.