Parameterization of the deterministic Mueller matrix: application to a uniform medium.

The extraction of the elementary polarization properties of a uniform medium from a deterministic Mueller matrix has been considered by several researchers. The relationship between a parameterization of the deterministic Mueller matrix that we described recently and the elementary polarization properties for a uniform medium is investigated. The elementary polarization properties can be calculated exactly from the Mueller matrix parameters.

Interpretation of the optical transfer function: Significance for image scanning microscopy.

The optical transfer function (OTF) is widely used to compare the performance of different optical systems. Conventionally, the OTF is normalized to unity for zero spatial frequency, but in some cases it is better to consider the unnormalized OTF, which gives the absolute value of the image signal. Examples are in confocal microscopy and image scanning microscopy, where the signal level increases with pinhole or array size.

Parameterization of the Mueller matrix.

A deterministic Mueller matrix (Mueller-Jones matrix) contains seven independent parameters. By writing the so-called coherence vector in parametric form, the Mueller matrix can also be written in parametric form, where the matrix elements automatically satisfy the known relationships between each other. Three of these parameters are also related to the so-called anisotropy coefficients.

Geometry of the Mueller matrix spectral decomposition.

An arbitrary Mueller matrix can be decomposed into a sum of up to four deterministic Mueller-Jones matrices, with strengths given by the eigenvalues of an associated Hermitian matrix. A geometrical representation of the eigenvalues in terms of the matrix invariants, using a barycentric (quaternary) plot, is presented. Different polarization purity measures can be expressed in terms of the barycentric coordinates.

Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement.

We propose and demonstrate a novel subtraction microscopy algorithm, exploiting fluorescence emission difference or switching laser mode and their derivatives for image enhancement. The key novelty of the proposed approach lies in the weighted subtraction coefficient, adjusted pixel-by-pixel with respect to the intensity distributions of initial images. This method produces significant resolution enhancement and minimizes image distortions.

Expressions for parallel decomposition of the Mueller matrix.

It is useful to convert between the Mueller matrix and two different Hermitian matrices, representing an optical material or system. We introduce forms for the matrices for transforming between the column vector forms of these different matrices. A review of matrix algebra is presented.

Superconcentration of light: circumventing the classical limit to achievable irradiance.

Concentration of light is limited by a fundamental physical principle, which ensures that étendue, the product of area and solid angle, can never decrease in an optical system. In microscopy, many superresolving methods, which can overcome the classical resolution limit, have recently emerged. We propose, and demonstrate experimentally, that it is also possible to circumvent the classical light concentration limit.

Pupil filters for extending the field-of-view in light-sheet microscopy.

Pupil filters, represented by binary phase modulation, have been applied to extend the field of view of a light-sheet fluorescence microscope. Optimization has been used, first numerically to calculate the optimum filter structure and then experimentally, to scale and align the numerically synthesized filter in the microscope. A significant practical extension of the field of view has been observed, making the reported approach a valuable tool on the path to wide-field light-sheet microscopy.

Image scanning microscopy with a quadrant detector.

Confocal scanning microscopy (CSM) is the most widely used modern optical microscopy technique. Theoretically, it allows the diffraction barrier to be surpassed by a factor of 2, but practically this improvement is sacrificed to obtain a good signal-to-noise ratio (SNR). Image scanning microscopy (ISM) solves this limitation but, in the current implementations, the system complexity is increased and the versatility of CSM is reduced.

Diffraction of a focused wave by an aperture: a new perspective.

A new approach for calculating the field in the focal region along lines through the focal point of a lens is presented. In particular, the method is applied to a circular aperture. It is also applied to other shaped apertures, including circular sectors or segments, such as a semicircular aperture or Hilbert mask, and to polygonal shapes.

Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale.

X-ray phase-contrast imaging (XPCI) can dramatically improve soft tissue contrast in X-ray medical imaging. Despite worldwide efforts to develop novel XPCI systems, a numerical framework to rigorously predict the performance of a clinical XPCI system at a human scale is not yet available. We have developed such a tool by combining a numerical anthropomorphic phantom defined with non-uniform rational B-splines (NURBS) and a wave optics-based simulator that can accurately capture the phase-contrast signal from a human-scaled numerical phantom.

Temporal reshaping of two-dimensional pulses.

An analytic study of complete cylindrical focusing of pulses in two dimensions is presented, and compared with the analogous three-dimensional case of focusing over a complete sphere. Such behavior is relevant for understanding the limiting performance of ultrafast, planar photonic and plasmonic devices. A particular spectral distribution is assumed that contains finite energy.

Two-dimensional complex source point solutions: application to propagationally invariant beams, optical fiber modes, planar waveguides, and plasmonic devices.

Highly convergent beam modes in two dimensions are considered based on rigorous solutions of the scalar wave (Helmholtz) equation, using the complex source point formalism. The modes are applicable to planar waveguide or surface plasmonic structures and nearly concentric microcavity resonator modes in two dimensions. A novel solution is that of a vortex beam, where the direction of propagation is in the plane of the vortex.

Polarized focused vortex beams: half-order phase vortices.

A theoretical treatment is presented for the focusing of polarized vortex beams, including the generation of Bessel beams. A combination of a phase vortex with arbitrary topological charge, and a polarization vortex of arbitrary order is considered. Results are given for both paraxial and high NA systems.

Maréchal condition and the effect of aberrations on Strehl intensity.

The effect of aberrations on the Strehl intensity is analyzed. The aberrations are assumed to be random and normally distributed. A variety of different correlation coefficients for the aberration variation are discussed, including Gaussian correlation and Kolmogorov turbulence.

Creation of a 50,000λ long needle-like field with 0.36λ width: comment.

In a recent paper, a method for the generation of a long, narrow needle of light was proposed [J. Opt. Soc.

Multipole and plane wave expansions of diverging and converging fields.

This paper presents and compares two basis systems, spherical harmonics and plane waves, for studying diverging and converging beams in an optical system. We show a similarity between a converging field and the time reversed field of a radiation field. We present and analyze the differences between the Debye-Wolf diffraction integral and the multipole theory for focusing of polarized light.

Analytic method to optimize aperture design in focal modulation microscopy.

Focal modulation microscopy (FMM) has been demonstrated more effective than confocal microscopy for imaging of thick biological tissues. To improve its penetration depth further, we propose a simple analytical method to enlarge the modulation depth, the unique property of FMM directly linked to its signal-to-noise ratio. The modulation depth increases as the excitation intensity of the binary phase aperture status is pushed further away from the focal region of the detection optics, thereby creating a dark region in the focal volume, which we call maximally flat crater (MFC).

Rigorous analytical modeling of high-aperture focusing through a spherical interface.

High-aperture focusing through a spherical interface has been employed in optical data storage, photolithography, and especially microscopy. This paper first forms an approximate model, based on geometrical optics and Fourier optics, for evaluating focal fields of the focusing systems. This approximate model helps to clarify some doubts existing in literature.

Balanced diffraction aberrations, independent of the observation point: application to a tilted dielectric plate.

Balancing of Zernike aberrations breaks down if the defocus term is large enough that the condition (z/λ)≪2/[π(NA)⁴] is not satisfied. A modified Zernike aberration expansion, based on the Zernike aberrations, is developed that accurately includes axial displacement as a low-order term, even for large displacements. This expansion can be used to analyze aberrations for on-axis illumination of a high numerical aperture system.

Calculation of the volumetric diffracted field with a three-dimensional convolution: the three-dimensional angular spectrum method.

The first Rayleigh-Sommerfeld diffraction formula is treated in an exact form as a three-dimensional (3D) convolution in the spatial domain. Therefore, a 3D Fourier transform can be employed to convert the 3D diffracted electromagnetic field to the reciprocal space without approximations, which we call the 3D angular spectrum (3D-AS) method. It is also demonstrated that if evanescent waves are neglected, the 3D-AS method can be readily implemented numerically, with the results in good agreement with theoretical predictions.

Imaging using cylindrical vector beams in a high-numerical-aperture microscopy system.

Imaging of object structures using cylindrical vector beams in an aplanatic solid immersion lens (SIL) microscope is investigated. Based on a complete optical model of an aplanatic SIL microscope, images of some object structures using radial polarization, azimuthal polarization, and azimuthal vortex beams are simulated. Some interesting imaging effects of these object structures are observed.

Full-wave approach for x-ray phase imaging.

We present a rigorous forward model for phase imaging of a 3-D object illuminated by a cone-shaped x-ray beam. Our model is based on a full-wave approach valid under the first Rytov approximation, and thus can be used with large and thick objects, e.g.

Superresolution by image scanning microscopy using pixel reassignment.

The effect of detector array size on resolution and signal collection efficiency of image scanning microscopy based on pixel reassignment is studied. It is shown how the method can also be employed if there is a Stokes shift in fluorescence emission wavelength. With no Stokes shift, the width of the point spread function can be sharpened by a factor of 1.

Improvement of axial resolution and contrast in temporally focused widefield two-photon microscopy with structured light illumination.

Although temporally focused wide-field two-photon microscopy (TFM) can perform depth resolved wide field imaging, it cannot avoid the image degradation due to scattering of excitation and emission photons when imaging in a turbid medium. Further, its axial resolution is inferior to standard point-scanning two-photon microscopy. We implemented a structured light illumination for TFM and have shown that it can effectively reject the out-of-focus scattered emission photons improving image contrast.