Light scattering by arbitrarily oriented rotationally symmetric particles

We use the T-matrix approach and the analytical orientation-averaging technique to formulate the problem of light scattering by an ensemble of rotationally symmetric particles in arbitrary orientation. The mathematical formulation yields analytical expressions for the elements of the ensemble-averaged scattering matrix that involve no more than four nested summations. An expansion into generalized spherical functions is used in the particular case where the scatterers are partially aligned along the direction of incidence. A computer code that implements the analytical expressions derived is publicly available on the World Wide Web at http://irctr.et.tudelft.nl/ -Skaropoulos/T-matrix.htm.     

Point-spread function for a rotationally symmetric birefringent lens

Imaging properties of a birefringent lens, in which the fast (or the slow) axis is distributed in the radial direction whereas magnitude of birefringence varies as a quadratic function of the pupil radius, are investigated by calculating a point-spread function. It is found that the point image is analytically described by using the Lommel function as well as the zero-order Bessel function, and a localized intensity null surrounded by bright regions in all directions can be realized at a geometrical focus under certain conditions. The magnitude of birefringence that is tolerable in image formations is also discussed, assuming that the lens is applied to microlithography.     

Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence

The influence of birefringence caused by rotationally symmetric stress distribution in a high-resolution projection optical system is investigated. The general form of the pupil function is derived based on the Jones matrix calculation, expressing the wave front as a combination of the two orthogonal polarization components. Assuming a linearly polarized incident beam, it is found that the main polarization portion of the wave front exiting the projection lens has astigmatic aberration in the Seidel region and shows phase singularity at four pupil points at which the amplitude transmittance becomes zero.     

Nonnull testing of rotationally symmetric aspheres: a systematic error assessment

An optical setup for the testing of rotationally symmetric aspheres without a null optic is proposed. The optical setup is able to transfer the strongly curved wave fronts that stem from the reflection of a spherical testing wave front at a rotationally symmetric asphere. By simulation it is proved that the algorithms of the Shack-Hartmann sensor that is used can cope with the steep wave-front slopes (~110lambda/mm) in the detection plane. The systematic errors of the testing configuration are analyzed and separated. For all types of error, functionals are derived whose significance is proved by simulation. The maximum residual errors in the simulations are fewer than lambda/500 (peak to valley).     

Amplitude and phase recovery of rotationally symmetric beams

Two methods are presented for the amplitude and phase recovery of optical beams with rotational symmetry. These are the tomographic method based on the ambiguity function and the one-step wavefront recovery based on the measurement of a phase-space distribution closely related to the Wigner distribution function. The results obtained from these two methods are compared, and the appropriateness of using either one of them for specific situations is discussed.     

Parametric characterization of rotationally symmetric hard-edged diffracted beams

The truncated second-order moments and generalized M2 factor (M(G)2 factor) of two-dimensional beams in the Cartesian coordinate system are extended to the case of three-dimensional rotationally symmetric hard-edged diffracted beams in the cylindrical coordinate system. It is shown that the propagation equations of truncated second-order moments and the M(G)2 factor take forms similar to those for the nontruncated case. The closed-form expression for the M(G)2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams is derived that depends on the truncation parameter beta and beam order N. For N --> infinity, the M(G)2 factor equals 4/square root of 3 corresponding to the value of truncated plane waves, which guarantees consistency of the formalism.     

Laser direct writing of rotationally symmetric high-resolution structures

We present a laser direct writing system for the efficient fabrication of high-resolution axicon structures. The setup makes use of scanning beam interference lithography incorporated with a fringe locking scheme for tight fringe phase control and allows us to fabricate large area structures with a period down to 450 nm.     

Exact calculation of the circle of least confusion of a rotationally symmetric mirror

The position and dimensions of the circle of least confusion (CLC) on axis for a lensless Schmidt camera telescope operating at F(0.82) are calculated. The camera is to be used in the fluorescence detector of the Pierre Auger Observatory. Our analysis was developed for an aspherical mirror for any on-axis position of the point light source. Our technique uses the intersection of the marginal ray from one side of the aperture with the caustic produced by the intermediate rays from the opposite side of the aperture to locate the CLC.     

Focusing and the optical transfer function in a rotationally symmetric optical system

Two criteria of focusing in a rotationally symmetric optical system, the focal-amplification ratio and the encircled-energy factor, are expressed by the integrals of the optical transfer function, thus providing a simple relation between these two types of characteristics. The approximation of the optical transfer function of diffractive lenses is made possible on the basis of this relation, as is an estimation of the effect of certain apodizers on the image quality.     

一种微型转子的激光加工和光致旋转

利用单束强聚焦激光产生的光学力可以驱动微型器件,具有无机械接触和无需导线等优点,为微型机电系统提供了一种新型的驱动方式。在自行研制的飞秒激光微细加工系统中,采用一种新型的丙烯酸酯紫外光固化树脂,通过双光子聚合加工出直径6μm的万字形微转子。利用光镊装置实现了微转子的俘获,并在激光功率50mW时实现了转速为200rpm的光致旋转。微型转子的光致旋转为实现微机械马达提供了一种有效手段。     

Visual instrument image-quality assessment with rotationally symmetric difference of Gaussians

We performed contrast-sensitivity measurements using rotationally symmetric, variable contrast difference-of-Gaussians targets, viewed through specially designed telescopes that presented various amounts of monochromatic aberrations. The contrast-sensitivity ratios between aberrated and unaberrated cases were correlated with instrument-based measures of image quality. The radius that encircles 84% of the energy of the point-spread function was found to give the best correlation with the subjective data.     

Casting methods for the production of rotationally symmetric copper bimetals

ABSTRACT

Multiple-material products are characterised by a complex property profile which is achieved by combining the particular advantages of at least two different materials. Bimetal casting is an energy- and material-efficient technology for the production of multi-metallic objects. This paper describes the development of a semi-continuous casting process for the formation of a rotationally symmetric bimetal with a cohesive bonding character at the interface of a copper–tin alloy (CuSn6) and pure copper (Cu99.5). Initial experiments are conducted by static casting to evaluate the thermal process window. Based on the results of the initial experiments, a vertical semi-continuous compound casting process is developed. A stable cohesive bond between the joining partners is accomplished by forming a solid solution at the interface.

This paper is part of a Thematic Issue on Copper and its Alloys.     

Computer simulation of schlieren images of rotationally symmetric plasma systems: a simple method

Schlieren techniques are commonly used methods for quantitative analysis of cylindrical or spherical index of refraction profiles. Many schlieren objects, however, are characterized by more complex geometries, so we have investigated the more general case of noncylindrical, rotationally symmetric distributions of index of refraction n(r,z). Assuming straight ray paths in the schlieren object we have calculated 2-D beam deviation profiles. It is shown that experimental schlieren images of the noncylindrical plasma generated by a plasma focus device can be simulated with these deviation profiles. The computer simulation allows a quantitative analysis of these schlieren images, which yields, for example, the plasma parameters, electron density, and electron density gradients.     

Multiwell laser heterostructures fabricated by liquid-phase epitaxy

A methodology has been developed for growing InGaAsP/InP multiwell laser heterostructures by liquid-phase epitaxy. Depth profiling using a secondary ion mass spectrometer was used to investigate the distribution profiles of the composition of multiwell laser heterostructures. Liquid-phase epitaxy was used to fabricate InGaAsP/InP multiwell laser heterostructures with active regions having emission wavelengths of 1.3 and 1.55 μm and their radiative characteristics were studied. Pis’ma Zh. Tekh. Fiz. 24, 61–67 (November 12, 1998)     

Diffraction analysis of rotationally symmetric optical systems using computer-generated aberration polynomials

A ray trace scheme for the automatic generation of optical aberration polynomials to arbitrary orders pioneered by T. B. Andersen is successfully applied to the diffraction analysis of rotationally symmetric optical systems on a desk-top computer. The diffraction-based optical transfer functions at various field positions are computed using the relatively new Winograd Fourier transform algorithm. The coding includes aspherical and reflective surfaces.     

Refractive power of a multilayer rotationally symmetric model of the human cornea and tear film

Optical models of the human cornea and tear film typically employ a single homogeneous cornea with an average refractive index. I propose to use a more realistic multilayer model based on morphological data from the literature. The mathematical methodology to derive the refractive power equation of this model is presented. Special attention is given to the axial gradient index of the refraction structure of the stroma layer because of its optical implications. The importance of considering this multilayer model is quantified in a specific example (orthokeratology) with the help of the derived power equation.