Particular solution of the discrete-ordinate method

We present two methods that can be used to derive the particular solution of the discrete-ordinate method (DOM) for an arbitrary source in a plane-parallel atmosphere, which allows us to solve the transfer equation 12-18% faster in the case of a single beam source and is even faster for the atmosphere thermal emission source. We also remove the divide by zero problem that occurs when a beam source coincides with a Gaussian quadrature point. In our implementation, solution for multiple sources can be obtained simultaneously. For each extra source, it costs only 1.3-3.6% CPU time required for a full solution. The GDOM code that we developed previously has been revised to integrate with the DOM. Therefore we are now able to compute the Green's function and DOM solutions simultaneously.     

Particular solutions for axisymmetric Helmholtz-type operators

In this paper, we consider the solution of the axisymmetric heat equation with axisymmetric data in an axisymmetric domain in R³. To solve this problem, we remove the time-dependence by various transform or time-stepping methods. This converts the problem to one of a sequence of modified inhomogeneous Helmholtz equations. Generalizing previous work, we consider solving these equations by boundary-type methods. In order to do this, one needs to subtract off a particular solution, so that one obtains a sequence of modified homogeneous Helmholtz equations. We do this by modifying the usual Dual Reciprocity Method (DRM) and approximating the right-hand sides by Fourier-polynomials or bivariate polynomials. This inevitably leads to analytical solving a sequence of ordinary differential equations (ODEs.) The analytic formulas and their precision are checked using mathematica. In fact, by using an infinite precision technique, the particular solutions can be obtained with infinite precision themselves. This work will form the basis for numerical algorithms for solving axisymmetric heat equation.     

Paraxial theory for birefringent lenses

The generalized ray tracing for the extraordinary ray through uniaxial crystals developed by Avenda?o-Alejo and Stavroudis [J. Opt. Soc. Am. A 19, 1674 (2002)] has been applied to derive paraxial refracting equations. Paraxial equations are derived for three cases where the incident, ordinary, and extraordinary rays lie in the incident plane: (a) the crystal axis is parallel to the optical axis, (b) the crystal axis is orthogonal to the optical axis and lies in the plane of incidence, and (c) the crystal axis is orthogonal to both the optical axis and the incident plane. The paraxial ray-tracing equations for the extraordinary ray are represented by matrix operators. The elements of the matrix system give all the information of the focal points and of the principal points. Gaussian formulas are derived, and some examples are presented.     

Diffractive lenses for chromatic confocal imaging

A diffractive zone plate provides a highly linear wavelength-to-depth coding, allowing for nonmechanical depth scanning in a confocal microscope. This chromatic confocal microscope, constructed with 40x and 60x objectives, achieves axial position changes of 55 and 25 mum, respectively, for a wavelength tuning range of 100 nm. The corresponding longitudinal point-spread functions are measured and shown to possess full-width half-maximums of 2.52 and 2.23 mum, respectively. Two-dimensional profiles of a two-phase-level grating and a four-phase-level diffractive structure are given. The performance of the chromatic confocal microscope is consistent with that of the conventional confocal operation of the microscope.     

Desired concentration-dependent ion exchange for micro-optic lenses

The required concentration-dependent diffusion coefficients for both ideal one-dimensional and ideal radial gradient-index profiles are determined. The modified quasi-chemical diffusion model is used to relate the diffusion coefficient to optimum glass composition. Adding aluminum to sodium silicate glasses facilitates the approach to the desired concentration dependence of the diffusion coefficient for silver-sodium ion exchange. A parabolic one-dimensional index profile is fabricated in one of the glasses. It deviates from ideal values by less than 2%.     

Model eyes for evaluation of intraocular lenses

In accordance with the present international standard for intraocular lenses (IOLs), their imaging performance should be measured in a model eye having an aberration-free cornea. This was an acceptable setup when IOLs had all surfaces spherical and hence the measured result reflected the spherical aberration of the IOL. With newer IOLs designed to compensate for the spherical aberration of the cornea there is a need for a model eye with a physiological level of spherical aberration in the cornea. A literature review of recent studies indicated a fairly high amount of spherical aberration in human corneas. Two model eyes are proposed. One is a modification of the present ISO standard, replacing the current achromat doublet with an aspheric singlet cut in poly(methyl methacrylate) (PMMA). The other also has an aspheric singlet cut in PMMA, but the dimensions of it and the entire model eye are close to the physiological dimensions of the eye. They give equivalent results when the object is at infinity, but for finite object distances only the latter is correct. The two models are analyzed by calculation assuming IOLs with different degrees of asphericity to elucidate their sensitivity to variation and propose tolerances. Measured results in a variant of the modified ISO model eye are presented.     

Millimeter-wave antireflection coating for cryogenic silicon lenses

We have developed and tested an antireflection (AR) coating method for silicon lenses used at cryogenic temperatures and millimeter wavelengths. Our particular application is a measurement of the cosmic microwave background. The coating consists of machined pieces of Cirlex glued to the silicon. The measured reflection from an AR-coated flat piece is less than 1.5% at the design wavelength. The coating has been applied to flats and lenses and has survived multiple thermal cycles from 300 to 4 K. We present the manufacturing method, the material properties, the tests performed, and estimates of the loss that can be achieved in practical lenses.     

Variable frequency field conjugate lenses for ultrasoundhyperthermia

This paper describes variable frequency focusing with field conjugate lenses designed to mimic the multiple-focusing capabilities of large two-dimensional phased arrays. Simulations, experiments, and Fresnel diffraction analysis are used to show that both the size and the depth of a field conjugate lens focus may vary with frequency. Examples are given for field conjugate lens focusing with planar transducers, focused transducers, and ordinary refracting lenses     

Future lenses for 16-mm cinematograph projectors

Designs of two-lens systems for use as 16-mm cinematograph projector objectives have been developed at a focal length of 50 mm and relative apertures of f/1.4 and f/1.2, respectively. The 50-mm f/1.4 system is comprised of five elements, and the 50-mm f/1.2 system is comprised of six elements. The proposed designs are not based on any known configuration, but their forms are arrived at from a hybrid approach combining the good points of some of the better known systems. The proposed systems are capable of giving extremely good performance, which has not been possible so far in the lenses of the same complexity in current use.     

Field conjugate acoustic lenses for ultrasound hyperthermia

Multipoint foci have been synthesized by applying the pseudoinverse field conjugation method to a single ultrasonic transducer coupled to a polystyrene lens. The lens design is based on phased array calculations are then fabricated on a computer-controlled milling machine. The measured beam patterns from the lenses agree closely with the beam patterns predicted by theory for the equivalent phased arrays. Temperature distributions from thermal modeling and those measured in tissue equivalent phantoms show that the lens system is capable of generating strongly localized, controlled temperature fields for hyperthermia.     

Modified phase function model for kinoform lenses

A more computationally tractable model of the kinoform lenses in hybrid refractive-diffractive systems is proposed by taking into consideration the actual phase function of the kinoform lenses for every wavelength. The principle and outline of this modified model are explained. We compare the results of this approach with the more conventional single order calculation and with the standard diffraction-order expansion by using a practical hybrid optical system example.