Annular Lens Research Articles

FDTD simulation and measurement of a 90 GHz quasi-optical annular slot receiver

The authors describe the full design, modelling and measurement of a quasi-optical annular slot lens receiver at 90 GHz. The annular slot antenna mounted on an elliptical lens with a planar Schottky diode acts simultaneously as an antenna and a mixer. Measurement of input impedance, radiation pattern and conversion loss of the annular slot lens receiver is performed and compared with in-house finite-difference time-domain simulations at 90 GHz. A thru-reflect-line (TRL) manufactured on the same wafer is used as the calibration standard for de-embedding in the impedance measurements. In mixer designs, an important feature is to match the antenna with the diode for the mixer to have optimum performance. Two configurations are considered whereby an extra matching stub is added to one of the designs to conjugate match the diode. The optimum conversion loss for the design without matching stub is 17.4 dB with bias at 0.65 mA and LO power of −7.3 dBm while the optimum conversion loss for the design with the matching stub is 16.7 dB with bias at 0.36 mA and available LO power of −7.5 dBm. This antenna is well suited for use in millimetre-wave imaging arrays.

SABCMS, a new approach to higher lateral resolution of laser probe measurement system

In order to achieve a high lateral resolution required for ultraprecision measurement of microstructural workpieces, shaped annular beam confocal measurement system (SABCMS), a new approach is proposed for ultraprecision measurement of 3D microstructures. SABCMS uses a binary optical element based on the diffraction principle to shape a Gauss laser beam into an annular beam, and optimizes the normalized inner radius of annular beam aperture ɛ to decrease the main lobe of airy spot, to increase the lateral resolution and measurement range. In comparison with an annular beam shaping technique used in a conventional annular lens confocal measurement system, the annular beam shaping technique used in SABCMS reduces the energy loss, and eliminates the effect of the inner ring edges diffraction of annular lens on the measurement system and improves the defocused property. Experimental comparison and analysis indicate that, as ɛ increases, both the lateral resolution and measurement range of SABCMS increase, and the spatial resolution improves, too, while the axial resolution of SABCMS reduces; the lateral resolution of SABCMS is better than 0.2 μm when wavelength of incidence laser beam λ = 632.8 nm, numerical aperture of measuring lens NA = 0.85, and ɛ = 0.5. It is therefore concluded that SABCMS is a new approach to further improvement of lateral resolution in laser probe measurement systems.

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.

Focusing of flattened Gaussian beams by an annular lens

Focusing properties of flattened Gaussian beams (FGBs) passing through an annular lens is studied based on the Collins formula. It is found that the on-axis irradiance distributions of focused FGBs are unsymmetrical with respect to the geometrical focal plane even for large values of Fresnel number F w associated with the beam, so that there exist focal shifts in general. Detailed numerical results show the dependence of focal shifts on the beam and system parameters. Focal shifts of FGBs by a lens without central obscuration and focal shifts of Gaussian beams by an annular lens can be treated as special cases of the obscure ratio ε=0 and beam order N=0, respectively. Furthermore, focal shifts of plane waves by an annular lens can also be treated as a special case of N=0 and F w →∞.

A study of the optical transfer function for annular binary filters

Summary The annular binary pupil filters consist of two transparent annuli obstructed by an annular mask. The optical transfer functions for them are analytically derived under paraxial approximation, and three- and two- as well as one-dimensional numerical plots are presented. It is shown that by changing the parameters of transparent regions it is possible to improve the axial resolution whilst the transverse resolution remains unchanged, compared with an annular lens. Results indicate, as is well known, that this kind of filters can be applied to three-dimensional confocal microscopy.

Advantages of two-color excitation fluorescence microscopy with two confocal excitation beams

We establish the advantages of two-color excitation (2CE) fluorescence microscopy where the two confocal excitation beams are separated by an angle, θ [Opt. Lett. 24 (1999) 1505]. The two excitation wavelengths λ 1 and λ 2 are related according to 1/ λ e=1/ λ 1+1/ λ 2, where λ e is the single-photon excitation wavelength of the sample. Both circular and annular pupils are considered in the calculation of the three-dimensional point spread function of the 2CE microscope. When λ 1≠ λ 2, the 2CE fluorescence intensity is proportional to the product of the two excitation intensities and is generated only in regions where the excitation beams overlap with each other in both space and time. Two-photon excitation fluorescence (2PE) microscopy is a special case of 2CE microscopy with λ 1= λ 2=2 λ e= λ 2p. With focusing lenses of low-to-moderate numerical apertures, the main advantage of 2CE microscopy over its 2PE counterpart is not in improved imaging resolution, but in the observation of microscopic objects through highly scattering media. In 2CE imaging, scattering decreases the in-focus fluorescence but only minimally increases the unwanted fluorescence background unlike in the 2PE case. Furthermore, annular lenses with their very long depths of field offer an easier way for maintaining the alignment of the two confocal excitation beams in applications involving the imaging of irregularly shaped, thick samples.

PALLAS: a novel optical measurement technique in air pollutant transport studies

This paper presents the principles of a novel laser optical method in the measurement of concentration distribution of air pollutants. It is based on a concerted application of panoramic annular lens (PAL) optical detection system and a laser sheet illumination equipment (PALLAS). The PAL optic provides full 360° angle of panoramic view information. This is the most important property which makes the PALLAS especially suitable for extensive investigation of concentration field around models of buildings and features of terrain. This paper presents the advantages of this system in comparison to the conventional laser sheet technique. The first results are also presented and measurement technical improvement of PALLAS method is summarised.

Development of a phase-displacement equation for panoramic interferometry

We developed the parametric equations that are needed to quantify the modulations in the sensitivity vector that occur when the phase-displacement equation is applied to make panoramic interferometric measurements. The measurement system relies on two collinear panoramic annular lenses, one to illuminate and the other to image their surroundings. When a coherent light source is used and a reference beam is added, interference occurs over the region of interest defined by the illuminating and viewing lenses. A holographic system is used to demonstrate the approach and quantify the analysis. We obtained interference fringes in real time by comparing holograms recorded before and after a section of cylindrical pipe is displaced relative to the measurement system. The annular images and the holographic fringes are acquired and stored digitally in a computer system, and image transformation algorithms are applied to remove optical distortions in the holographic patterns. Excellent agreement is obtained when the fringe loci are compared with those predicted on the basis of theory.

Annular tinted contact lenses caused irregular corneal astigmatism.

Annular tinted contact lenses caused irregular corneal astigmatism.

Investigation of Light Distribution with an Annular Lens Light Guide

Investigation of Light Distribution with an Annular Lens Light Guide

An Optical Head with Special Annular Lens for Laser Disc-Compatible Digital Versatile Disc Pickup

A compact and inexpensive design for a laser disc(LD)-compatible digital versatile disc(DVD) pickup that uses a special annular lens is presented and the measurement technique of the lens is described. One objective lens having a special annular area functions as an aberration-corrected lens for reading LD, compact disc recordable(CDR) and DVD regardless of differences in substrate thickness. The special area has an aspherical surface optimized for a thick substrate. This lens can also be used for compact disc rewritable(CDRW).

Focusing Gaussian beams by an annular lens with spherical aberration

In this paper, focusing Gaussian beams by an annular lens with spherical abberation is discussed. The expressions for the axial light intensity of Gaussian beams focused by an annular lens with primary spherical aberration have been derived. The numerical calculation shows that, for the annular lens with negative spherical aberration, the axial maximum focused intensity can be made larger than that of aberration-free cases. By choosing suitable values of central obstruction ratio of the annular lens with negative spherical aberration, one can obtain an axial maximum focused intensity much greater than that of aberration-free cases. In addition, the positive spherical aberration can shift the best focal position (z/f)m (the position where the axial focused inensity is maximum) far away from the lens so that the positive focal shift can be achieved (i.e. Δz/f = (z/f)m − 1 > 0). It is shown that, when the Fresnel number of the outer radius of the annular lens is small (e.g. Na ≤ 1), the effect of the spherical aberration on focusing Gaussian beams can be neglected.

Focusing Gaussian beams by an annular lens with spherical aberration

Focusing Gaussian beams by an annular lens with spherical aberration

Effects of Fresnel diffraction on confocal imaging with an annular lens

yOptoelectronic Imaging Group, Department of Applied Physics, Victoria Universityof Technology, PO Box 14428, MCMC, VIC 8001, AustraliazDepartment of Physical Optics, University of Sydney, NSW 2006, AustraliaSubmitted 9 January 1997, accepted 26 June 1997Abstract. The effect of the Fresnel diffraction on the imaging properties of confocalmicroscopy with one circular aperture and one annular aperture is investigated. Theresults show that the Fresnel diffraction patterns alter the axial imaging properties moreseriously than the transverse imaging properties. The axial response of such a confocalmicroscope is sharpened, but severely distorted.Keywords: Fresnel diffraction, annular pupil, confocal microscopy1. IntroductionAnnular aperture is a widely used spatial filter in confocalmicroscopy. It gives some improvement in transverseresolution, but a degradation in axial resolution appears ina confocal system with an annular structure [1,2]. Recentresearch suggests that the use of annular apertures as spatialfilters can suppress the scattered photons [3]. For example,a reflection-mode confocal system with an annular aperturein the illumination path is reported to show a significantenhancement in signal-to-noise ratio for imaging through ahighly scattering medium [4].In practice, an annular aperture cannot be placed exactlyat the back focal plane of an objective. In this case,Fresnel diffraction by the annular aperture exists. Fresneldiffraction of a finite-sized aperture can produce bright anddark fringes because of the interference of the waveletscontributed from points over the aperture [5,6]. Theintensity modulation caused by the interference fringes canalter the imaging properties of confocal microscopy, sincethe effective pupil function of the objective illuminatedby the Fresnel patterns changes accordingly, resulting inthe alteration of the intensity in the focal region [7–10].Therefore, it is important to investigate the effect of Fresneldiffraction on the imaging performance of a confocalsystem with an annular aperture.This paper is organized as follows. Section 2 presentsthe Fresnel diffraction of an annular aperture. The effectof Fresnel diffraction patterns of an annular aperture on theimaging properties of confocal microscopy is discussed insection 3.2. Fresnel diffraction of an annular apertureIf an aperture is placed in the back focal plane of anobjective then focusing is described by Debye theory. TheFresnel number is infinity in this situation. However, ifthe aperture is placed away from the back focal plane by adistance

5574373 Local gradient coil arrangement for nuclear magnetic resonance tomography apparatus

A system for applying local hyperthermia employing ultrasonic transducers with annular focusing lenses gave better temperature uniformity in small fibrosarcomas than conventional unfocused transducers. The lenses were designed for ultrasonic frequencies of 3,4,5 and 9 MHz for tumors approximately 6 mm dia. Tests in degassed water indicated that the focusing lenses concentrated approx. 80% of the ultrasonic energy into an annular-shaped focus of 6 mm dia. located at a distance of 3 cm in front of the lens. These transducers were used to heat subcutaneous PARA-7 fibrosarcomas in hamsters. Steady-state temperature measurements indicated temperature gradients within tumors of 0.5–1.0°C when transducers employing annular-focused lenses were used, versus gradients of 2.0–2.3°C with 10 mm dia. unfocused transducers.

Characterization of the panoramic annular lens

The panoramic annular lens (PAL) consists of a single piece of glass, with spherical surfaces, that produces a flat annular image of the entire 360-deg surround of the optical axis of the lens. This paper describes the attributes of the PAL and shows that the lens maps elements from object to image space via a constant aspect ratio polar mapping. A panoramic video system (PVS) is described to illustrate how the characterization can be applied in experimental mechanics for cavity inspection and measurement.

Axial imaging behaviour of a single lens illuminated by an ultrashort pulsed beam

For an incident pulsed laser beam of femtoseconds, the axial imaging performance of an imaging system consisting of a single lens is discussed. Both the point spread function and the transfer function for the lens are examined for both circular and annular pupils. While an annular lens can be used for compensation for the temporal broadening of the pulse in the focal plane, imaging resolution in the axial direction is strongly degraded.

Improved axial resolution in confocal fluorescence microscopy using annular pupils

The axial image of a thick fluorescent layer is studied in a confocal microscope consisting of either circular or annular pupils. The response for circular pupils is sharper than that for annular pupils if a small pinhole detector is used. But when the size of the pinhole is larger than a certain value, the response in the latter case can become sharper than that in the former. This result implies that for a given detector of finite size, axial resolution in confocal fluorescence microscopy can be improved when an annular lens is used. Our experimental results qualitatively demonstrate the theoretical prediction. The strength of optical sectioning and the axial cross-section of the three-dimensional optical transfer function are also derived from the measured data.

Three-dimensional optical transfer function for circular and annular lenses with spherical aberration and defocus

The three-dimensional optical transfer function for both circular and annular lenses in the presence of combined spherical aberration and defocus is investigated, with attention centered on its phase. Results show that it is possible to reduce the phase variation of the optical transfer function optimally for a circular lens by introducing defocus according to the condition of least confusion. In the appendixes it is shown how to calculate the in-focus and on-axis transfer function from the three-dimensional optical transfer function.

Femtosecond pulses in the focal region of lenses.

A systematic theoretical and experimental study of focusing femtosecond light pulses by single lenses is presented. By evaluation of the diffraction integral the interplay of spherical and chromatic aberration is shown to determine the temporal as well as the spatial intensity distribution in the focal region of a lens. Conditions are derived under which the effect of spherical aberration dominates. Here a temporally unbroadened, in-focus pulse occurs while the spatial distribution is that expected from an annular lens aperture. If chromatic aberration is the major aberration, the in-focus pulses are considerably broadened. Both effects could clearly be measured with 100-fs pulses using a modified Michelson interferometer. In an intermediate parameter range both chromatic and spherical aberration contribute to the pulse broadening and to the spatial intensity pattern in a given plane in the focal region. From Fresnel diffraction we expect a weak-intensity distribution to precede the in-focus pulse on the axis. Another weak intensity peak is produced by the pulse traveling on axis. By measuring its separation from the main pulse in the marginal focal plane one can estiamte the aberration parameters.