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Colin J R Sheppard

Publications and source records attributed to Colin J R Sheppard.

14 recordsLinked to original sources
PubMed2007

Fractal model of light scattering in biological tissue and cells.

The K-distribution, widely used for investigation of fractal scattering in the atmosphere and from surfaces, is applied as a model for light propagation in biological tissue and cells. This leads to simple expressions for the scattering function, anisotropy function, phase function, reduced scattering coefficient, and scattering power. Compared with an alternative previously published model [Opt. Lett.30, 3051 (2005)], the range of allowable power laws is extended into the subfractal regime.

Animals↗
PubMed2006

The sampling limit in fluorescence microscopy.

Sampling in fluorescence microscopy is treated using the concept of the three-dimensional (3D) optical transfer function (OTF). The border of the OTF frequency surface defines the required minimum sampling. The shape of the OTF is derived from simple considerations and valid for far-field high numerical aperture, vector theory. Optimal regular sampling is achieved by a hexagonal grid in 2D, and corresponding hexagonal structures, body-centered cubic (bcc) and hexagonal close-packed (hcp) structures, in 3D. As compared to standard (rectilinear grid) sampling a reduction of 13.4% in 2D and 29.3% in 3D can be achieved with optimized sampling. This reduction in data size is also accompanied by an imaging speed improvement, a reduction of sample bleaching, and can lead to imaging with better signal to noise ratio.

Journal Article↗
PubMed2006

Fundamentals of superresolution.

The fundamental principles behind superresolution are discussed, and different schemes classified. Different definitions for localization of a wave are discussed.

Journal Article↗
PubMed2004

Annular pupils, radial polarization, and superresolution.

An annular pupil, which can be used to produce a Bessel beam, when combined with radially polarized illumination promises improvements in microscope resolution, increased packing density for optical storage, and finer optical lithography. When combined with a circular detection pupil in confocal microscopy a point-spread function 112 nm wide results (lambda = 488 nm). Radially polarized annular illumination of a solid-immersion lens can yield a focal spot smaller than 100 nm for lambda = 488 nm. Use of radially polarized illumination with pupil masks is discussed.

Journal Article↗
PubMed2004

Zernike expansion of separable functions of cartesian coordinates.

A Zernike expansion over a circle is given for an arbitrary function of a single linear spatial coordinate. The example of a half-plane mask (Hilbert filter) is considered. The expansion can also be applied to cylindrical aberrations over a circular pupil. A product of two such series can thus be used to expand an arbitrary separable function of two Cartesian coordinates.

Journal Article↗
PubMed2004

Image formation in low-coherence and confocal interference microscopes.

Image formation in the coherence probe microscope (CPM) and in optical coherence tomography (OCT) are compared. These systems differ in that CPM is a conventional interference microscope, but OCT is a confocal interference microscope. A major disadvantage of CPM for imaging through thick object structures is that there is no optical sectioning for the background image, which can saturate the detector. The behavior of the interference term in the presence of aberrations also exhibits some differences: Aberrations can be compensated in CPM, but not in OCT.

Equipment Design↗
PubMed2004

Practical limits of resolution in confocal and non-linear microscopy.

Calculated and measured resolution figures are presented for confocal microscopes with different pinhole sizes and for nonlinear (2-photon and second harmonic) microscopes. A modest degree of super-resolution is predicted for a confocal microscope but in practice this is not achievable and confocal fluorescence gives little resolution improvement over widefield. However, practical non-linear microscopes do approach their theoretical resolution and therefore show no resolution disadvantage relative to confocal microscopes in spite of the longer excitation wavelength.

Animals↗
PubMed2004

Fresnel diffraction by a circular aperture with off-axis illumination and its use in deconvolution of microscope images.

The Fresnel approximation for off-axis illumination of a circular aperture is reexamined. The point-spread function for an aberration-free system can be expressed in terms of redefined optical coordinates. An improved expression is given for contours of constant intensity in the focal plane. The variation in axial width of the focal spot with angle of offset is discussed. The predictions are compared with exact calculations of the Rayleigh-Sommerfeld diffraction integral. Limitations for application in deconvolution of microscope images formed with objectives of finite tube length are discussed.

Journal Article↗
PubMed2004

Orthogonal aberration functions for high-aperture optical systems.

Aberration functions that are a complete, orthogonal, and normalized set over a weighted spherical pupil are developed. A general weighting is considered, for which special cases are applicable to systems satisfying the Abbe sine condition and the Herschel condition. Paraboloidal mirrors are also considered. This weighting can also be used to account empirically for Fresnel reflection losses in the optical system. The functions can be expressed in an analytic form. Expressions are given for 24 low-order aberrations.

Journal Article↗
PubMed2003

Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number.

Analytic expressions are given for the on-axis intensity predicted by the Rayleigh-Sommerfeld and Kirchhoff diffraction integrals for a scalar optical system of high numerical aperture and finite value of Fresnel number. A definition of the axial optical coordinate is introduced that is valid for finite values of Fresnel number, for high-aperture systems, and for observation points distant from the focus. The focal shift effect is reexamined. For the case when the focal shift is small, explicit expressions are given for the focal shift and the axial peak in intensity.

Journal Article↗
PubMed2002

Three-dimensional phase imaging with the intensity transport equation.

Phase can be retrieved from intensity measurements with the intensity transport equation. Three-dimensional image formation of weak phase objects based on this method is investigated. It is shown that, although the refractive index of a thin object can be measured, the three-dimensional variation of refractive index of an arbitrary object cannot, in general, be reconstructed, as spatial frequencies with a zero-axial component are not detected. However, this may not be a problem if regions with known refractive index are present in the sample.

Journal Article↗
PubMed2002

Straightness measurements with a reflection confocal optical system-an experimental study.

Straightness measurement is an important technique in the field of mechanical engineering. We previously proposed a novel optical method for measuring straightness of motion using reflection confocal optics. The advantage of this method in comparison with the transmission optical systems of others [Opt. Laser Technol. 6, 166 (1974)] is that the lateral displacements in the two axes perpendicular to the optical axis and the rotation angles around all three axes can be measured simultaneously. We demonstrate straightness measurements using reflection confocal optics and show these measurements to be in good agreement with the theory.

Journal Article↗
PubMed2002

Generalized Bessel pulse beams.

A generalization of type 3 ultrashort pulses (also known as pulse beams or isodiffracting pulses) is introduced. The Bessel beam form of this generalized beam consists of pulses that propagate in free space, without spreading, with a velocity that can be less than that of light. A model spectral distribution that is zero outside a finite range is investigated.

Journal Article↗