Oil-immersion microscope objective lenses have been designed and optimized for the study of thin, two-dimensional object sections that are mounted immediately below the coverslip in a medium that is index matched to the immersion oil. It has been demonstrated both experimentally and through geometrical- and physical-optics theory that, when the microscope is not used with the correct coverslip or immersion oil, when the detector is not located at the optimal plane in image space, or when the object does not satisfy specific conditions, aberration will degrade both the contrast and the resolution of the image. In biology the most severe aberration is introduced when an oil-immersion objective lens is used to study thick specimens, such as living cells and tissues, whose refractive indices are significantly different from that of the immersion oil. We present a model of the three-dimensional imaging properties of a fluorescence light microscope subject to such aberration and compare the imaging properties predicted by the model with those measured experimentally. The model can be used to understand and compensate for aberration introduced to a microscope system under nondesign optical conditions so that both confocal laser scanning microscopy and optical serial sectioning microscopy can be optimized.

Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy.

Closed-form nonparaxial expressions for optical beams are useful to calculate the fields produced by tightly focused laser beams. Such expressions for elegant Laguerre-Gaussian (eLG) beams that are exact solutions of the Helmholtz equation are introduced. These solutions are expressed as linear combinations of a finite number of analytic functions that involve spherical Bessel functions and associated Legendre functions of complex arguments. In the paraxial limit, the expressions proposed have the property to reduce to the well-known eLG beams.

Nonparaxial elegant Laguerre-Gaussian beams.

Contemporary optics for scientists and engineers

Dual mode horns employed commonly as feeds for parabolic reflector antennas generate a radiation pattern that can be well-approximated by a Gaussian beam. To determine the far field of the antenna, it has been customary to perform integrations either of the physical optics currents on the reflector surfaces or of the ray optically determined field in the antenna aperture. These time-consuming integrations may be avoided if the Gaussian beam is tracked directly from the feed horn via subreflectors, if any, to the main reflector and then to the far zone. The tracking of such fields may be accomplished either by the complex-source point method or, in principle, by evanescent wave tracking. The former utilizes a complex coordinate space while the latter tracks fields entirely in the physical (real) coordinate space. For a parabolic antenna with an offset beam feed centered at the focus, both methods are examined here and an assessment is made of how the one can best complement the other. Numerical comparisons with results deduced elsewhere by a semi-heuristic procedure, and with experimental data, reveal the accuracy and versatility of the complex ray procedure.

Asymptotic analysis of parabolic reflector antennas

Acoustic forces arising from high-frequency surface acoustic waves (SAW) underpin an exciting range of promising techniques for non-contact manipulation of fluid and objects at micron scale. Despite increasing significance of SAW-driven technologies in microfluidics, the understanding of a broad range of phenomena occurring within an individual SAW system is limited. Acoustic effects including streaming and radiation force fields are often assumed to result from wave propagation in a simple planar fashion. The propagation patterns of a single SAW emanating from a finite-width source, however, cause a far richer range of physical effects. In this work, we seek a better understanding of the various effects arising from the incidence of a finite-width SAW beam propagating into a quiescent fluid. Through numerical and experimental verification, we present five distinct mechanisms within an individual system. These cause fluid swirling in two orthogonal planes, and particle trapping in two directions, as well as migration of particles in the direction of wave propagation. For a range of IDT aperture and channel dimensions, the relative importance of these mechanisms is evaluated.

Surface acoustic wave diffraction driven mechanisms in microfluidic systems

The Huygens–Fresnel diffraction integral has been formulated for incident spherical waves with use of the Kirchhoff obliquity factor and the wave front as the surface of integration instead of the aperture plane. Accurate numerical integration calculations were used to investigate very-near-field (a few aperture diameters or less) diffraction for the well-established case of a circular aperture. It is shown that the classical aperture-plane formulation degenerates when the wave front, as truncated at the aperture, has any degree of curvature to it, whereas the wave-front formulation produces accurate results from ∞ up to one aperture diameter behind the aperture plane. It is also shown that the Huygens–Fresnel–Kirchhoff incident-plane-wave-aperture-plane-integration and incident-spherical-wave-wave-front-integration formulations produce equally accurate results for apertures with exit f-numbers as small as 1.

Huygens-Fresnel-Kirchhoff wave-front diffraction formulation: spherical waves

The Huygens–Fresnel diffraction integral has been formulated for incident Gaussian laser beams by using the Kirchhoff obliquity factor with the wave front instead of the aperture plane as the surface of integration. Accurate numerical-integration calculations were used to investigate the Fresnel field diffraction region for the much-studied case of a circular aperture. It is shown that the classical aperture-plane formulation becomes inaccurate when the wave front, as truncated at the aperture, has any degree of curvature to it, whereas the newly developed wave-front formulation produces accurate results for as much as one aperture diameter behind the aperture plane. The wave-front diffraction integral was developed for both the classical paraxial and the recently developed exact solutions to the scalar wave equation for a Gaussian beam. Detailed comparisons of these two diffraction solutions show that they are essentially identical for the typical laboratory laser. The typical laboratory laser is defined as having a wavelength in the near-infrared-through-visible range, a beam diameter as large as several millimeters, and a beam divergence angle as large as several milliradians.

Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: paraxial and exact Gaussian laser beams

Kirchhoff diffraction formulations that use the wave front and the aperture plane for the surfaces of integration were compared. The full Kirchhoff obliquity factor terms distinguishing these two formulations are presented for spherical waves and for Gaussian laser beams. When they are used, identical results are obtained for the two formulations in both the spherical-wave and the Gaussian laser-beam cases. The reason that this must be true for any diffracted wave is explained. Simplified versions of these obliquity factor terms are used to place two previous papers by this author [ J. Opt. Soc. Am. A6, 1196 ( 1989); J. Opt. Soc. Am. A7, 47 ( 1990)] into the proper context. This in turn provides the basis for errata to these articles.

Hal G. Kraus

Papers

Huygens-Fresnel-Kirchhoff wave-front diffraction formulation: spherical waves

Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: paraxial and exact Gaussian laser beams

Huygens–Fresnel–Kirchhoff wave-front diffraction formulations for spherical waves and Gaussian laser beams: discussion and errata