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. For example, counterintuitively, it is found that, compared to linear and circular polarizations, radial polarization requires a larger pinhole to acquire a good image and resolution. Similarly, it is shown that an azimuthal vortex beam provides good images for a variety of object structures and pinhole sizes. Theories and explanations are provided to justify the observed effects. The presented results play an important role in high-numerical-aperture optical imaging.

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 1.53, and its peak intensity increased by a factor of 1.84.

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., luggage and human patients. We unify light-matter interaction and free-space propagation into an integrated wave optics framework. Therefore, our model can accurately calculate x-ray phase images formed with sources of arbitrary shape, and it can be effectively incorporated into x-ray phase tomography as a forward model. Within the best of our knowledge, this is the first non-paraxial, full-wave model for X-ray phase imaging.

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. Further, the depth resolution of the improved system is dictated by the spatial frequency of the structure light with the potential of attaining depth resolution better than point-scanning two-photon microscopy.

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. We then propose a rigorous model that is applicable to more general systems. Our model is based on multipole theory, which expands the electromagnetic fields into spherical harmonics.

A complete and computationally efficient numerical model of aplanatic solid immersion lens scanning microscope

This paper presents a computational model for modeling an aplanatic solid immersion lens scanning microscope. The scanning microscope model consists of three subsystems, each of which can be computed as a separate system, connected to the preceding or succeeding subsystem through the input/output only. Numerical techniques are used to enhance the computational efficiency of each subsystem. A distinct merit of the proposed model is that it can be used to simulate imaging results for diverse setups of the scanning microscope, like various polarizations, numerical aperture, and different detector pinhole sizes. It allows the study and analysis of both theoretical aspects like achievable resolution, and practical aspects like expected images for different object patterns and experimental setups. Further, due to its computational efficiency, diverse large scale structures can be easily simulated in scanning microscope and good experimental approaches determined before indulging into the time consuming and costly process of experimentation.

Rayleigh-Sommerfeld diffraction formula in k space

An angular spectrum representation in three dimensions is used to develop three-dimensional Fourier forms of the first and second Rayleigh-Sommerfeld diffraction formulae and the Kirchhoff diffraction formula. For forward-propagating waves, these reduce to three-dimensional Fourier representations for diffraction in the forward half-space.

Temporally focused wide-field two-photon microscopy: paraxial to vectorial

Temporal focusing allows for optically sectioned wide-field microscopy. The optical sectioning arises because this method takes a pulsed input beam, stretches the pulses by diffracting off a grating, and focuses the stretched pulses such that only at the focal plane are the pulses re-compressed. This approach generates nonlinear optical processes at the focal plane and results in depth discrimination. Prior theoretical models of temporal focusing processes approximate the contributions of the different spectral components by their mean. This is valid for longer pulses that have narrower spectral bandwidth but results in a systematic deviation when broad spectrum, femtosecond pulses are used. Further, prior model takes the paraxial approximation but since these pulses are focused with high numerical aperture (NA) objectives, the effects of the vectorial nature of light should be considered. In this paper we present a paraxial and a vector theory of temporal focusing that takes into account the finite spread of the spectrum. Using paraxial theory we arrive at an analytical solution to the electric field at the focus for temporally focused wide-field two-photon (TF2p) microscopy as well as in the case of a spectrally chirped input beam. We find that using paraxial theory while accounting for the broad spectral spread gives results almost twice vector theory. Experiment results agree with predictions of the vector theory giving an axial full-width half maximum (FWHM) of 2.1 μmand1.8 μmrespectively as long as spectral spread is taken into account. Using our system parameters, the optical sectioning of the TF2p microscope is found to be 8 μm. The optical transfer function (OTF) of a TF2p microscope is also derived and is found to pass a significantly more limited band of axial frequencies than a point scanning two-photon (2p) microscope or a single photon (1p) confocal microscope.

Limitations of the paraxial Debye approximation

In the paraxial form of the Debye integral for focusing, higher order defocus terms are ignored, which can result in errors in dealing with aberrations, even for low numerical aperture. These errors can be avoided by using a different integration variable. The aberrations of a glass slab, such as a coverslip, are expanded in terms of the new variable, and expressed in terms of Zernike polynomials to assist with aberration balancing. Tube length error is also discussed.

Pupil filters for generation of light sheets

Pupil filters for cylindrical (two-dimensional) focusing with extended depth of field are investigated. An important application is in generating light sheets with uniform intensity. Filters for spherical (three-dimensional) focusing with a flat axial intensity, coupled with weak side lobes are also discussed.

Complex source point theory of paraxial and nonparaxial cosine-Gauss and Bessel-Gauss beams

It shown how cosine-Gauss and Bessel-Gauss beams can be generated using the complex source point theory. Paraxial beams are treated first. An analytic expression is derived for the nonparaxial cosine-Gaussian beam, based on the complex source point approach, and numerical results are presented to illustrate its behavior. A way to generate nonparaxial Bessel-Gauss beams is also indicated.

Cylindrical lenses--focusing and imaging: a review [Invited]

Focusing by an aberration-free cylindrical lens is analyzed in the paraxial Fresnel and Debye approximations, and expressions are given. Plots are given for the intensity in the focal region, the defocused optical transfer function (OTF), the generalized OTF, and the ambiguity function and are compared with the case of an aberration-free spherical lens. Nonparaxial lenses are also discussed.

Three-level filter for increased depth of focus and Bessel beam generation

A novel axially-symmetric filter for increasing focal depth and generating an approximation to a Bessel beam is proposed. It consists of an array of rings of strength -1,0 and 1. The design is based on an analytic solution, and combines high resolution in the transverse direction with good efficiency. One presented design increases the depth of focus compared with a standard lens by more than 30 times, with a very flat axial intensity distribution over this range. Effects of discretization are discussed. Various different approaches to increasing depth of focus are compared, to put the new design into perspective.

Coupled and uncoupled dipole models of nonlinear scattering

Dipole models are one of the simplest numerical models to understand nonlinear scattering. Existing dipole model for second harmonic generation, third harmonic generation and coherent anti-Stokes Raman scattering assume that the dipoles which make up a scatterer do not interact with one another. Thus, this dipole model can be called the uncoupled dipole model. This dipole model is not sufficient to describe the effects of refractive index of a scatterer or to describe scattering at the edges of a scatterer. Taking into account the interaction between dipoles overcomes these short comings of the uncoupled dipole model. Coupled dipole model has been primarily used for linear scattering studies but it can be extended to predict nonlinear scattering. The coupled and uncoupled dipole models have been compared to highlight their differences. Results of nonlinear scattering predicted by coupled dipole model agree well with previously reported experimental results.

Geometric representation for partial polarization in three dimensions

Recently, we described a geometric construction for determining the eigenvalues of the coherency matrix in three dimensions. We show that this leads directly to a representation of the three-dimensional degree of polarization in terms of a triangular composition plot, in which different polarization measures have simple properties and can be expressed in terms of the matrix invariants. This composition plot is an alternative to the spherical plot recently used to illustrate the degree of polarization in terms of entanglement.

Resolution of aplanatic solid immersion lens based microscopy

We study the resolution of a subsurface microscopy system based on the use of an aplanatic solid immersion lens. Resolution limits under various criteria are calculated theoretically as well as numerically. Images of combinations of dipoles of various orientations are considered. Both lateral and longitudinal resolutions are studied. The theoretical criteria are compared against the visually resolvable simulated images of the dipoles. The observations are explained explicitly through a detailed analysis of the dyadic Green's function. A new resolution criterion is also proposed, which provides a very accurate estimate of the resolution limits.

Subtractive imaging in confocal scanning microscopy using a CCD camera as a detector

We report a scheme for the detector system of confocal microscopes in which the pinhole and a large-area detector are substituted by a CCD camera. The numerical integration of the intensities acquired by the active pixels emulates the signal passing through the pinhole. We demonstrate the imaging capability and the optical sectioning of the system. Subtractive-imaging confocal microscopy can be implemented in a simple manner, providing superresolution and improving optical sectioning.

Limitations of superoscillation filters in microscopy applications

The idea of superresolving pupil filters comes from the concept of superoscillations that may occur in regions of a band-limited signal with small amplitude having oscillations faster than the fastest Fourier component of the signal. In optical microscopy, superresolution can be achieved by appropriate design of pupil functions where the angular aperture determines the ultimate focal spot smaller than the Abbe diffraction limit outside the evanescent field region. The angular aperture cannot be increased indefinitely and the huge sidelobes cannot be avoided that are present in superresolving filters. The limitations of using such kind of filters in microscopy applications are discussed through computational examples.

Reconstruction in interferometric synthetic aperture microscopy: comparison with optical coherence tomography and digital holographic microscopy

It is shown that the spatial frequencies recorded in interferometric synthetic aperture microscopy do not correspond to exact backscattering [as they do in unistatic synthetic aperture radar (SAR)] and that the reconstruction process based on SAR is therefore based on an approximation. The spatial frequency response is developed based on the three-dimensional coherent transfer function approach and compared with that in optical coherence tomography and digital holographic microscopy.

Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain

We propose a new method using coherent diffractive imaging for optical color-image encryption and synthesis in the Fresnel domain. An optical multiple-random-phase-mask encryption system is applied, and a strategy based on lateral translations of a phase-only mask is employed during image encryption. For the decryption, an iterative phase retrieval algorithm is applied to extract high-quality decrypted color images from diffraction intensity maps (i.e., ciphertexts). In addition, optical color-image synthesis is also investigated based on coherent diffractive imaging. Numerical results are presented to demonstrate feasibility and effectiveness of the proposed method. Compared with conventional interference methods, coherent diffractive imaging approach may open up a new research perspective or can provide an effective alternative for optical color-image encryption and synthesis.

Multipole theory for tight focusing of polarized light, including radially polarized and other special cases

A multipole expansion, based on spherical harmonics, provides an efficient method for calculating the field in the focal region of a lens for radially polarized illumination, or other illumination polarization and phase distributions, including vortex beams. The multipole approach also has the benefit of providing a simple measure of the purity of the longitudinal field mode. The method is also convenient for calculation of fields scattered by particles and calculation of optical trapping forces.

Improving signal-to-noise ratio of structured light microscopy based on photon reassignment

In this paper, we report a method for 3D visualization of a biological specimen utilizing a structured light wide-field microscopic imaging system. This method improves on existing structured light imaging modalities by reassigning fluorescence photons generated from off-focal plane excitation, improving in-focus signal strength. Utilizing a maximum likelihood approach, we identify the most likely fluorophore distribution in 3D that will produce the observed image stacks under structured and uniform illumination using an iterative maximization algorithm. Our results show the optical sectioning capability of tissue specimens while mostly preserving image stack photon count, which is usually not achievable with other existing structured light imaging methods.

Partial polarization in three dimensions

Various different parameters have been introduced to describe the degree of polarization of a partially polarized electromagnetic field in three dimensions. Of these, parameters based on the eigenvalues of the coherency matrix are invariant under a unitary transformation. Here, explicit expressions are presented for the eigenvalues, thus providing a geometrical interpretation of the behavior. These expressions are applied to the Huynen decomposition and allow interrelations between different parameters to be developed.

Optical double-image cryptography based on diffractive imaging with a laterally-translated phase grating

In this paper, we propose a method using structured-illumination-based diffractive imaging with a laterally-translated phase grating for optical double-image cryptography. An optical cryptosystem is designed, and multiple random phase-only masks are placed in the optical path. When a phase grating is laterally translated just before the plaintexts, several diffraction intensity patterns (i.e., ciphertexts) can be correspondingly obtained. During image decryption, an iterative retrieval algorithm is developed to extract plaintexts from the ciphertexts. In addition, security and advantages of the proposed method are analyzed. Feasibility and effectiveness of the proposed method are demonstrated by numerical simulation results.

Dyadic Green's function for aplanatic solid immersion lens based sub-surface microscopy

We present the derivation of the dyadic Green's function for the aplanatic solid immersion lens based microscopy system. The presented dyadic Green's function is general and is applicable at non-aplanatic points as well in the object plane. Thus, the electromagnetic wave formulation is used to describe the optical system without paraxial assumptions. Various important and useful properties of SIL based microscopy system are also presented. The effect of the numerical aperture of the objective on the peak intensities, resolutions and the depth of field are also reported. Some interesting longitudinal effects are also reported.