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.g., by simple subtraction) can further improve optical sectioning and background rejection from a single in-focus scan.

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. The usual method for the phase-shifting technique in FF-OCM involves mechanically moving a mirror to change the optical path difference for obtaining en-face OCM images. However, with the use of a broadband source in FF-OCM, the phase shifts of different spectral components are not the same, resulting in the ambiguities in 3D image reconstruction. In this study, we demonstrate, by imaging tissues and cells, a unique geometric phase-shifter based on ferroelectric liquid crystal technology, to realize achromatic phase-shifting for rapid three-dimensional imaging in a FF-OCM system.

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. Analytic expressions are presented for the intensity in the detector plane for a uniform volume object, and for the resulting background. The variation in the integrated intensity with defocus for an offset point detector is presented. This axial fingerprint is independent of any pixel reassignment. The intensity in the detector plane is shown to contain the defocus information, and simple processing of the recorded data can improve optical sectioning and background rejection.

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. Here, we propose a new method to mitigate these limitations without drawbacks. First, we enhance a STED microscope with a detector array, enabling image scanning microscopy (ISM). Therefore, we implement STED-ISM, a method that exploits the working principle of ISM to reduce the depletion intensity and achieve a target resolution. Later, we develop Focus-ISM, a strategy to improve the optical sectioning and remove the background of any ISM-based imaging technique, with or without a STED beam. The proposed approach requires minimal architectural changes to a conventional microscope but provides substantial advantages for live and thick sample imaging.

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. Phase consistency is discussed. A comprehensive collection of results regarding intrinsic polarization properties is presented.

Pixel reassignment in image scanning microscopy with a doughnut beam: example of maximum likelihood restoration.

In image scanning microscopy, the pinhole of a confocal microscope is replaced by a detector array. The point spread function for each detector element can be interpreted as the probability density function of the signal, the peak giving the most likely origin. This thus allows a form of maximum likelihood restoration, and compensation for aberrations, with similarities to adaptive optics. As an example of an aberration, we investigate theoretically and experimentally illumination with a vortex doughnut beam. After reassignment and summation over the detector array, the point spread function is compact, and the resolution and signal level higher than in a conventional microscope.

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)'.

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. We analyze the contrast mechanisms extracted from (a) the coherency matrix elements, (b) its eigenvalues and (c) the indices of polarimetric purity at different stages of zebrafish embryos, based on previous work using Mueller matrix optical scanning microscopy. We show that the use of the coherency matrix and related decompositions leads to an improvement in the imaging contrast, without requiring any complicated algebraic operations or any a priori knowledge of the sample, in contrast to standard polarimetric methods.

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.S.-wide simulation framework encompassing private electric vehicles (EVs), shared automated EVs (SAEVs), charging infrastructure, controlled EV charging, and a grid economic dispatch model to simulate personal mobility exclusively using EVs. We find that private EVs with uncontrolled charging would reduce GHG emissions by 46% compared to gasoline vehicles. Private EVs with fleetwide controlled charging would achieve a 49% reduction in emissions from baseline and reduce peak charging demand by 53% from the uncontrolled scenario. We also find that an SAEV fleet 9% the size of today's active vehicle fleet can satisfy trip demand with only 2.6 million chargers (0.2 per EV). Such an SAEV fleet would achieve a 70% reduction in GHG emissions at 41% of the lifecycle cost as a private EV fleet with controlled charging. The emissions and cost advantage of SAEVs is primarily due to reduced vehicle manufacturing compared with private EVs.

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. The evolutions of an input signal's space-bandwidth product (SBP) during wave propagation are illustrated with the help of a phase space diagram (PSD) and an ABCD matrix. It is demonstrated that all of the above methods cannot make full use of the SBP of the input signal after diffraction; and some transform properties have been ignored. Each method has its own restrictions and applicable range. The reason why different methods have different applicable ranges is explained with physical models. After comprehensively studying and comparing the effect on the SBP and sampling properties of these methods, suggestions are given for choosing the proper method for different applications and overcoming the restrictions of corresponding methods. The PSD and ABCD matrix are used to illustrate the properties of these methods intuitively. Numerical results are presented to verify the analysis, and potential ways to develop new diffraction calculation methods are also discussed.

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. It has been shown previously that for Bessel beam illumination in image scanning microscopy with a large array, the imaging performance is degraded. On the other hand, it is also known that the resolution of confocal microscopy is improved by Bessel beam illumination. Here we analyze image scanning microscopy with Bessel beam illumination together with a small array and show that an improvement in transverse resolution (width of the point spread function) by a factor of 1.78 compared with a conventional fluorescence microscope can be obtained. We also examine the behavior of image scanning microscopy in two- or three-photon fluorescence and for two-photon excitation also with Bessel beam illumination. The combination of the optical sectioning effect of image scanning microscopy with multiphoton microscopy reduces background from the sample surface, which can increase penetration depth. For a detector array size of two Airy units, the resolution of two-photon image scanning microscopy is a factor 1.85 better and the peak of the point spread function 2.84 times higher than in nonconfocal two-photon fluorescence. The resolution of three-photon image scanning microscopy is a factor 2.10 better, and the peak of the point spread function is 3.77 times higher than in nonconfocal three-photon fluorescence. The resolution of two-photon image scanning microscopy with Bessel beam illumination is a factor 2.13 better than in standard two-photon fluorescence. Axial resolution and optical sectioning in two-photon or three-photon fluorescence are also improved by using the image scanning modality.

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. With our adaptive pixel reassignment procedure ∼1.6 times resolution increase is maintained deep into thick semi-transparent samples. The integration of Fourier ring correlation based semi-blind deconvolution is shown to further enhance the effective resolution by a factor of ∼2 - and automatic background correction is shown to boost the image quality especially in noisy images. Most importantly, our 2PE-ISM implementation requires no calibration measurements or other input from the user, which is an important aspect in terms of day-to-day usability of the technique.

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. The analogous polynomial form for the off-diagonal elements of the coherency matrix is also presented. Simple expressions are given for the pure component in the characteristic decomposition.

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. Here it is shown that the peak intensity of the effective point spread function (PSF) can be further increased by 4% by a new choice of the pixel reassignment factor. For an array of two Airy units, the peak of the effective PSF is 1.90 times that of a conventional microscope, and the transverse resolution is 1.53 times better. It is confirmed that image scanning microscopy gives optical sectioning strength identical to that of a confocal microscope with a pinhole equal to the size of the detector array. However, it is shown that image scanning microscopy exhibits axial resolution superior to a confocal microscope with a pinhole the same size as the detector array. For a two-Airy-unit array, the axial resolution is 1.34 times better than in a conventional microscope for the standard reassignment factor, and 1.28 times better for the new reassignment factor. The axial resolution of a confocal microscope with a two-Airy-unit pinhole is only 1.04 times better than conventional microscopy. We also examine the signal-to-noise ratio of a point object in a uniform background (called the detectability), and show that it is 1.6 times higher than in a confocal microscope.

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. As an example, the Sinclair matrix leads to a Mueller-Sinclair matrix, and a transformed coherence vector. The Kennaugh matrix is not, however, a Mueller matrix, but can be determined from the Mueller or Mueller-Sinclair matrices. We consider backscattering through a medium on a perfect mirror. We propose that backscattering from a uniform medium can be modeled as an effective uniform medium situated on a perfectly reflective substrate, and the elementary polarization properties derived. In this way, the concept of a uniform polarizing medium can be extended to the reflectance geometry. An experimental Mueller matrix from the literature is considered as an example.

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. Two new promising techniques that can be applied to multiphoton microscopy are described.

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. As expected, the cubic approach is usually simpler, but for the special case of two zero eigenvalues, either approach reduces to the predictions of the simple quadratic characteristic equation. Either approach can be used for numerical calculation of the eigenvalues. The variation in different purity measures with the values of the Mueller matrix elements is presented. An experimental Mueller matrix for backscattering from a turbid chiral medium is investigated.

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.

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. By utilizing the modulation and demodulation techniques, background rejection capability is enhanced, thus spatial resolution and imaging penetration depth are improved. Compared with 2PM, the transverse resolution is increased by 70%, while the axial resolution is increased to 2-fold. Furthermore, when applied in conventional 2PM mode, it can achieve inertial-free scanning in either transverse or axial direction with in principle unlimited scanning speed. Finally, we applied 2PFMM in thick scattering samples to further examine the imaging performance. The results show that the signal-to-background ratio of 2PFMM can be improved up to five times of 2PM at the depth of 500 µm. Fluorescent imaging in the mouse brain tissue. 3D Thy1-GFP hippocampal neurons imaged by (A) 2PM compared with (B) 2PFMM; (C-H) xy maximum-intensity projection imaged by 2PM compared with 2PFMM. Scale bar 50 µm.

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. The phase gradient transfer function, which determines the image for an object exhibiting a slowly varying phase gradient for a partially coherent microscope system, is derived. The effect of the effective source size and geometry on phase imaging with the transport of intensity equation is investigated. The primary consequence of source shape is a rescaling of the phase reconstruction. An annular source is found to give close to a linear response, while at the same time providing improved transverse resolution and an improved response to low spatial frequencies.