P. Török

Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I

We consider the electromagnetic diffraction occurring when light is focused by a lens without spherical aberration through a planar interface between materials of mismatched refractive indices, which focusing produces spherical aberration. By means of a rigorous vectorial electromagnetic treatment developed previously for this problem by Torok et al. [ J. Opt. Soc. Am. A12, 325 ( 1995)], the time-averaged electric energy density distributions in the region of the focused probe are numerically evaluated for air–glass and air–silicon interfaces as functions of lens numerical aperture and probe depth. Strehl intensity, lateral and axial sizes, and axial location of the probe are shown to be regular functions for low numerical apertures and probe depths but irregular functions for high numerical apertures and probe depths. An explanation to account for these occurrences is presented that also explains some previous experimental results of confocal microscopy.

Effects of specimen refractive index on confocal imaging

The aberrations introduced when focusing within a specimen with a refractive index equal to that of water using an oil‐immersion objective are investigated theoretically. The peak intensity in the confocal point spread function drops by a factor of two for focusing less than 10 μm into the specimen. The effects on scaling of dimensions in the resulting images are discussed. The image exhibits an axial stretching by a factor of about 1.12.

Analytical solution of the diffraction integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices

The treatment of the diffraction of electromagnetic waves for light focused by a high numerical aperture lens from a first medium into a second medium [ J. Opt. Soc. Am. A12, 325 ( 1995)] is extended so as to provide an analytical solution for the diffraction integrals by means of polynomial expansion. Methods are proposed and used to eliminate strong oscillations from the diffraction integrals. The aberration function is analyzed and expanded in terms of Zernike polynomials. The Zernike coefficients are obtained, and the error of the expansion is determined. It is shown that when the relative refractive index of the second and first media is larger than unity, the higher-order Zernike coefficients are independent of the refractive index of the second medium. A physical interpretation is given to explain this behavior. Pictorial representation of the first 25 Zernike polynomials is also presented.

On the general properties of polarised light conventional and confocal microscopes

This paper considers the general properties of polarising microscopes and, in particular, light polarisation changes produced by high aperture lenses. A method is suggested for vectorial ray tracing of complex optical systems and to model high aperture lenses. The two principal arrangements of polarising microscopes (linearly and circularly polarised) are also considered. We discuss the effect of pinhole size on the detected intensity. A theory for point resolution of these microscopes is also presented and results are analysed. We support our theoretical predictions with experimental data.

The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation

Abstract We present an exact solution of Maxwells equations for a non-paraxial Gaussian wave. Paraxial vectorial and paraxial scalar approximations of the exact solution are also obtained. We examine in detail, via several numerical examples, the validity conditions for the paraxial scalar and paraxial vectorial approximations when compared to the exact solution. Our findings show that when the half width of the beam waist is greater than 10 λ the paraxial scalar approximation yields accurate results. When, however, the half width of the beam waist is comparable to the wavelength the exact solution predicts significant deviations from the paraxial scalar approximation. These results might prove important in semiconductor laser research.

The role of specimen‐induced spherical aberration in confocal microscopy

We present an overview of recent theories for describing specimen‐induced spherical aberration in confocal microscopy. One of these theories is used to compute numerically the role of spherical aberration in general confocal, and especially in biological confocal, microscopy for a variety of three‐layer specimen structures. In particular, we study the effect of specimen‐induced spherical aberration on the maximum value of the overall confocal point spread function, the accompanying focal shift and the size of the optical probe in both fluorescence and brightfield confocal microscopy.

Theory for confocal and conventional microscopes imaging small dielectric scatterers

Abstract In this paper we develop the theory of confocal microscopes imaging small scatterers. Since scattering is a polarization dependent phenomenon we employ a full vectorial theory to treat this problem. This approach permits us to consider both imaging in high aperture systems as well as image formation in polarized light microscopy. We extend previous theories by including effects of the finite sized detector apertures. Numerical examples are presented for the most important cases. The results of the full vectorial theory are compared with those obtained from low aperture paraxial theory.

Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion

The field distribution in the focal region of a high-aperture optical system is calculated using an expansion into multipole components. For any angular illumination distribution and numerical aperture, the incident field is expanded into spherical harmonics and the field in the focal region is then determined by a sum of multipole fields. These are expressed as analytic expressions in terms of associated Legendre functions and spherical Bessel functions, thus avoiding computational problems in evaluation of diffraction integrals. As a result, focal distributions can be calculated much more efficiently than by using direct quadrature.

Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes

A theory for multiphoton fluorescence imaging in high aperture scanning optical microscopes employing finite sized detectors is presented. The effect of polarisation of the fluorescent emission on the imaging properties of such microscopes is investigated. The lateral and axial resolutions are calculated for one‐, two‐ and three‐photon excitation of p‐quaterphenyl for high and low aperture optical systems. Significant improvement in lateral resolution is found to be achieved by employing a confocal pinhole. This improvement increases with the order of the multiphoton process. Simultaneously, it is found that, when the size of the pinhole is reduced to achieve the best possible resolution, the signal‐to‐noise ratio is not degraded by more than 30%. The degree of optical sectioning achieved is found to improve dramatically with the use of confocal detection. For two‐ and three‐photon excitation axial full width half‐maximum improvement of 30% is predicted.

High numerical aperture vectorial imaging in coherent optical microscopes

Imaging systems are typically partitioned into three components: focusing of incident light, scattering of incident light by an object and imaging of scattered light. We present a model of high Numerical Aperture (NA) imaging systems which differs from prior models as it treats each of the three components of the imaging system rigorously. It is well known that when high NA lenses are used the imaging system must be treated with vectorial analysis. This in turn requires that the scattering of light by the object be calculated rigorously according to Maxwells equations. Maxwells equations are solvable analytically for only a small class of scattering objects necessitating the use of rigorous numerical methods for the general case. Finally, rigorous vectorial diffraction theory and focusing theory are combined to calculate the image of the scattered light. We demonstrate the usefulness of the model through examples.