Calculating point spread functions: methods, pitfalls, and solutions.

The knowledge of the exact structure of the optical system point spread function (PSF) enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications. Most existing real-space-based PSF models fall into a sampling pitfall near the center position, yielding to the violation of energy conservation.

Image scanning microscopy with a doughnut beam: signal strength and integrated intensity.

We discuss the effects of image scanning microscopy using doughnut beam illumination on the properties of signal strength and integrated intensity. Doughnut beam illumination can give better optical sectioning and background rejection than Airy disk illumination. The outer pixels of a detector array give a signal from defocused regions, so digital processing of these (e.

Advancing full-field metrology: rapid 3D imaging with geometric phase ferroelectric liquid crystal technology in full-field optical coherence microscopy.

Optical coherence microscopy (OCM) is a variant of OCT in which a high-numerical aperture lens is used. Full-field OCM (FF-OCM) is an emerging non-invasive, label-free, interferometric technique for imaging of surface structures or semi-transparent biomedical subjects with micron-scale resolutions. Different approaches to three dimensional full-field optical metrology are reviewed.

Signal strength and integrated intensity in confocal and image scanning microscopy.

The properties of signal strength and integrated intensity in a scanned imaging system are reviewed. These properties are especially applied to confocal imaging systems, including image scanning microscopy. The integrated intensity, equal to the image of a uniform planar (sheet) object, rather than the peak of the point spread function, is a measure of the flux in an image.

Focus image scanning microscopy for sharp and gentle super-resolved microscopy.

To date, the feasibility of super-resolution microscopy for imaging live and thick samples is still limited. Stimulated emission depletion (STED) microscopy requires high-intensity illumination to achieve sub-diffraction resolution, potentially introducing photodamage to live specimens. Moreover, the out-of-focus background may degrade the signal stemming from the focal plane.

Purity of 3D polarization.

Measures of purity for 3D partially polarized fields, and in particular, the separation into circularly and linearly polarized contributions, are reexamined, and a new degree of total linear polarization introduced. Explicit expressions for the characteristic decomposition in terms of coherency matrix elements are presented, including the special case of an intrinsic coherency matrix. Parameterization of the coherency matrix in terms of ellipticity, and the directions of the ellipse normal and major axis are investigated.

Phasor approach of Mueller matrix optical scanning microscopy for biological tissue imaging.

Mueller matrix microscopy is an advanced imaging technique providing a full characterization of the optical polarization fingerprint of a sample. The Lu-Chipman (LC) decomposition, a method based on the modeling of elementary polarimetric arrangements and matrix inversions, is the gold standard to extract each polarimetric component separately. However, this models the optical system as a small number of discrete optical elements and requires a priori knowledge of the order in which these elements occur.

Structured illumination microscopy and image scanning microscopy: a review and comparison of imaging properties.

Structured illumination microscopy and image scanning microscopy are two microscopical tech- niques, rapidly increasing in practical application, that can result in improvement in transverse spatial resolution, and/or improvement in axial imaging performance. The history and principles of these techniques are reviewed, and the imaging properties of the two methods compared. This article is part of the Theo Murphy meeting issue 'Super-resolution structured illumination microscopy (part 1)'.

Scattering and three-dimensional imaging in surface topography measuring interference microscopy.

Surface topography measuring interference microscopy is a three-dimensional (3D) imaging technique that provides quantitative analysis of industrial and biomedical specimens. Many different instrument modalities and configurations exist, but they all share the same theoretical foundation. In this paper, we discuss a unified theoretical framework for 3D image (interferogram) formation in interference microscopy.

Polarimetric optical scanning microscopy of zebrafish embryonic development using the coherency matrix.

Many of the most important resolution improvements in optical microscopy techniques are based on the reduction of scattering effects. The main benefit of polarimetry-based imaging to this end is the discrimination between scattering phenomena originating from complex systems and the experimental noise. The determination of the coherency matrix elements from the experimental Mueller matrix can take advantage of scattering measurements to obtain additional information on the structural organization of a sample.

Private versus Shared, Automated Electric Vehicles for U.S. Personal Mobility: Energy Use, Greenhouse Gas Emissions, Grid Integration, and Cost Impacts.

Transportation is the fastest-growing source of greenhouse gas (GHG) emissions and energy consumption globally. While the convergence of shared mobility, vehicle automation, and electrification has the potential to drastically reduce transportation impacts, it requires careful integration with rapidly evolving electricity systems. Here, we examine these interactions using a U.

Analysis of numerical diffraction calculation methods: from the perspective of phase space optics and the sampling theorem.

Diffraction calculations are widely used in applications that require numerical simulation of optical wave propagation. Different numerical diffraction calculation methods have their own transform and sampling properties. In this study, we provide a unified analysis where five popular fast diffraction calculation methods are analyzed from the perspective of phase space optics and the sampling theorem: single fast Fourier transform-based Fresnel transform, Fresnel transfer function approach, Fresnel impulse response approach, angular spectrum method, and Rayleigh-Sommerfeld convolution.

Image scanning microscopy with multiphoton excitation or Bessel beam illumination.

Image scanning microscopy is a technique of confocal microscopy in which the confocal pinhole is replaced by a detector array, and the image is reconstructed most straightforwardly by pixel reassignment. In the fluorescence mode, the detector array collects most of the fluorescent light, so the signal-to-noise ratio is much improved compared with confocal microscopy with a small pinhole, while the resolution is improved compared with conventional fluorescence microscopy. Here we consider two cases in which the illumination and detection point spread functions are dissimilar: illumination with a Bessel beam and multiphoton microscopy.

Two-photon image-scanning microscopy with SPAD array and blind image reconstruction.

Two-photon excitation (2PE) laser scanning microscopy is the imaging modality of choice when one desires to work with thick biological samples. However, its spatial resolution is poor, below confocal laser scanning microscopy. Here, we propose a straightforward implementation of 2PE image scanning microscopy (2PE-ISM) that, by leveraging our recently introduced single-photon avalanche diode (SPAD) array detector and a novel blind image reconstruction method, is shown to enhance the effective resolution, as well as the overall image quality of 2PE microscopy.

Eigenvectors of polarization coherency matrices.

Calculation of the eigenvectors of two- and three-dimensional coherency matrices, and the four-dimensional coherency matrix associated with a Mueller matrix, is considered, especially for algebraic cases, in the light of recently published algorithms. The preferred approach is based on a combination of an evaluation of the characteristic polynomial and an adjugate matrix. The diagonal terms of the coherency matrix are given in terms of the characteristic polynomial of reduced matrices as functions of the eigenvalues of the coherency matrix.

Polarization in reflectance imaging.

The Sinclair and Kennaugh matrices are widely used in the remote sensing discipline for signals detected in the backward direction. The connections between the Jones matrix and the Sinclair matrix, and between the Mueller matrix and the Kennaugh matrix, are explored. Different operations on the Jones matrix and their corresponding effects on the Mueller matrix, coherency matrix, and coherence vector are derived.

Pixel reassignment in image scanning microscopy: a re-evaluation.

Image scanning microscopy is a technique based on confocal microscopy, in which the confocal pinhole is replaced by a detector array, and the resulting image is reconstructed, usually by the process of pixel reassignment. The detector array collects most of the fluorescent light, so the signal-to-noise ratio is much improved compared with confocal microscopy with a small pinhole, while the resolution is improved compared with conventional (wide-field) microscopy. In previous studies, it has usually been assumed that pixels should be reassigned by a constant factor, to a point midway between the illumination and detection spots.

Multiphoton microscopy: a personal historical review, with some future predictions.

The historical development of multiphoton microscopy is described, starting with a review of two-photon absorption, and including two- and three-photon fluorescence microscopies, and second- and third-harmonic generation microscopies. The effects of pulse length on signal strength and breakdown are considered. Different contrast mechanisms, including use of nanoparticles, are discussed.

Eigenvalues of the coherency matrix for exact backscattering.

An important approach to interpretation of the Mueller matrix is based on the eigenvalues of the coherency matrix, given by the roots of a quartic characteristic equation. For the case of backscattering, one eigenvalue is zero from reciprocity arguments, and the characteristic equation reduces to a cubic. These two approaches (quartic and cubic) to calculation of the eigenvalues for exact backscattering are analytically considered and compared.

Coherency and differential Mueller matrices for polarizing media.

The elements of the coherency matrix give the strength of the components of a Mueller matrix in the coherency basis. The Z-matrix (called the polarization-coupling matrix or state-generating matrix) represents a partial sum of the coherency expansion. For transmission through a deterministic medium, the coherency elements can be used directly as generators to calculate the development of polarization upon propagation.

A robust and versatile platform for image scanning microscopy enabling super-resolution FLIM.

Image scanning microscopy (ISM) can improve the effective spatial resolution of confocal microscopy to its theoretical limit. However, current implementations are not robust or versatile, and are incompatible with fluorescence lifetime imaging (FLIM). We describe an implementation of ISM based on a single-photon detector array that enables super-resolution FLIM and improves multicolor, live-cell and in-depth imaging, thereby paving the way for a massive transition from confocal microscopy to ISM.

Pixellated circle.

For applications in optical systems it is often necessary to represent a circular aperture in a pixellated form. An objective parameter is introduced that is a measure of how well an approximate circle can be generated from a small array of square pixels. Both filled circles (disks) and rings are considered.

Partially coherent microscope imaging system in phase space: effect of defocus and phase reconstruction.

Explicit relationships between the defocused partially coherent cross-coefficient and phase space representations in the image plane are derived. Measurement of a phase space representation in the image plane in principle allows the complex image to be extracted. Implications for phase retrieval using the weak object transfer function or the transport of intensity equation are considered.

Two-photon focal modulation microscopy for high-resolution imaging in deep tissue.

Two-photon microscopy (2PM) is one of the most widely used tools for in vivo deep tissue imaging. However, the spatial resolution and penetration depth are still limited due to the strong scattering background. Here we demonstrate a two-photon focal modulation microscopy.