Theory for confocal and conventional microscopes imaging small dielectric scatterers

Abstract

In this paper we develop the theory of confocal microscopes imaging small scatterers. Since scattering is a polarization dependent phenomenon we employ a full vectorial theory to treat this problem. This approach permits us to consider both imaging in high aperture systems as well as image formation in polarized light microscopy. We extend previous theories by including effects of the finite sized detector apertures. Numerical examples are presented for the most important cases. The results of the full vectorial theory are compared with those obtained from low aperture paraxial theory.     

Effect of half-stop lateral misalignment on imaging of dark-field and stereoscopic confocal microscopes

There are several ways to realize dark-field imaging in confocal microscopy. In a recent paper [J. Microsc. 181 260-268 (1996)] we suggested a simple modification of a commercial confocal microscope to incorporate dark-field imaging. This modification involved an aperture stop covering half of the entrance pupil of the objective lens. Now we investigate the lateral misalignment of the aperture stop for dark-field and stereoscopic confocal microscopes. We show the effect of lateral alignment of the half-stop on the point-spread and transfer functions and also examine the detected signal from a sloping plane reflector. Lateral and axial resolution values are given from theoretical data.     

Polarization microscopy of magnetic domains for magneto-optical disks.

Polarization microscopes are widely used to image the magnetic domains of a magneto-optical disk and to characterize the birefringence of the disk substrate. For high-resolution imaging, unfortunately, the coupling of the polarization rotation from the Kerr signal, the effect of Fresnel's reflection coefficients, and the substrate birefringence severely deteriorate the image contrast obtained from conventional observations. Here we present the technique of differential polarization microscopy, which replaces the analyzer with a Wollaston prism, for providing better image contrast. Images of a magnetic pattern obtained with both conventional and differential methods are observed for objective lenses that have different numerical apertures and magneto-optical disks with and without a birefringent substrate. The computer simulations and experimental results show that the use of this differential method improves the image contrast and provides excellent tolerance for defects of the optical system.     

Field localization in very small aperture lasers studied by apertureless near-field microscopy

Localized surface plasmon polaritons (SSPs) have been observed on very small aperture lasers using apertureless near-field microscopy. Fields around multiple apertures are shown to result from interferences of SPP point sources at each aperture and optical fields. The near-field optical pattern around a single aperture indicates the interference of SPPs with their scattered counterparts. Near-field measurements also confirmed a preferred orientation of the rectangular aperture waveguide for the signal localization in very small aperture lasers.     

New method for determining the depth of field of microscope systems

This paper presents new formulas to determine the depth of field (DOF) of optical and digital microscope systems. Unlike the conventional DOF formula, the new methods consider the interplay of geometric and diffraction optics for infinite and finite optical microscopes and for corresponding digital microscope systems. It is shown that in addition to the well understood parameters such as numerical apertures, focal length, and light wavelength, system components such as aperture stops also affect the DOF. For the same objective lens, the DOF is inversely proportional to the size of the aperture stop, and it is proportional to the focal length of the ocular lens. It is also shown that under optimal viewing and operating conditions, the visual accommodation of human observers has no meaningful impact on DOF. The new formulas reported are useful for accurately calculating the DOF of microscopes.     

Effect of etchant diffusion on tip profiles of glass fiber probes

The tips of the probes are the key components in scanning probe microscopes and their applications in nano-scale imaging and nanofabrications. We investigated first the change of near-field scanning optical microscopy probe tips from optical fiber against time by chemical static etching. Several coverlayer-hydrofluoric acid aqueous solution systems and their possible factors affecting the tips' profile were studied. Tips with shorter tapers, larger conical aperture angles, and reproducible shapes were successfully obtained in high yields. It was found that the taper profiles were affected to a great extent by the one-dimensional linear diffusion of etchants in the coverlayer caused by concentration gradients and convection.     

Vectorial, high-numerical-aperture study of phase-contrast microscopes

We describe, using a high-numerical-aperture vectorial model, the image formation of phase-contrast microscopes. In particular, imaging of a weak phase object is considered. We show that, partly owing to the fact that phase-contrast microscopes are interference microscopes, their image formation is fundamentally different from that of conventional transmission optical microscopes. Our detailed analysis reveals a number of yet undocumented properties of these microscopes, including that depending on the given configuration, they can exhibit an improved lateral resolution when larger detectors are used in comparison with that obtained for a small detector size. We present numerical examples to explain this phenomenon and discuss our analysis in detail.     

Optimizing the radiation pattern of sparse periodic linear arrays

We have developed a method for designing sparse periodic arrays. Grating lobes in the two-way radiation pattern are avoided by using different element spacings on transmission and reception. The transmit and receive aperture functions are selected such that the convolution of the aperture functions produces a desired effective aperture. A desired effective aperture is simply an aperture with an appropriate width, element spacing, and shape such that the Fourier transform of this function gives the desired two-way radiation pattern. If a synthetic aperture approach is used, an exact solution to the problem is possible. However, for conventional imaging, often only an approximation of the desired effective aperture can be found. Different strategies for obtaining these approximate solutions are described. The radiation pattern of a sparse array designed using the effective aperture concept is compared experimentally with the radiation patterns of a dense array, and sparse arrays with periodic and random element spacing. We show that the number of elements in a 128-element linear array can be reduced by at least four times with little degradation of the beam forming properties of the array     

焊接微缺陷磁光成像检测有限元分析

目的 研究铁磁材料焊接微缺陷的磁光成像规律.方法 运用漏磁检测原理和法拉第磁致旋光效应,建立微缺陷三维有限元模型,分析微缺陷磁光成像过程与磁场之间的关联,研究不同提离值、励磁电流、缺陷宽度、缺陷深度下的磁光成像,以及探索这些因素对磁光图像特征的影响.在此基础上,对最小宽度为0.05 mm的微缺陷进行磁光成像检测实验,并...     

Calibration of subnanometer motion with picometer accuracy

We have developed a method for calibrating subnanometer movements of a piezoelectric actuator with picometer accuracy and for a wide range of frequencies. This range make this calibration useful for scanning probe microscopes, particularly for an apertureless scanning near-field optical microscope in which the tip is dithered to modulate the optical signal. The setup consists of a Michelson interferometer that has a mobile arm capable of moving more than one fringe. The piezoelectric actuator to be calibrated vibrates at the desired frequency in the other arm. Net displacement can be calculated by simultaneous measurement of an interferometric signal and its derivative. Hysteresis of the system can be also measured. It will be shown that the actuator response is linear only for the low-frequency region (in our case as much as approximately 10 kHz). Above that frequency range, higher harmonics appear and cannot be neglected to obtain real displacement. Finally, it will be shown that the use of higher harmonics in calibration or detection schemes (that rely on the linearity of the response) must be validated, and this technique has proved adequate for that purpose.     

Apertureless near-field/far-field CW two-photon microscope for biological and material imaging and spectroscopic applications

We present the development of a versatile spectroscopic imaging tool to allow for imaging with single-molecule sensitivity and high spatial resolution. The microscope allows for near-field and subdiffraction-limited far-field imaging by integrating a shear-force microscope on top of a custom inverted microscope design. The instrument has the ability to image in ambient conditions with optical resolutions on the order of tens of nanometers in the near field. A single low-cost computer controls the microscope with a field programmable gate array data acquisition card. High spatial resolution imaging is achieved with an inexpensive CW multiphoton excitation source, using an apertureless probe and simplified optical pathways. The high-resolution, combined with high collection efficiency and single-molecule sensitive optical capabilities of the microscope, are demonstrated with a low-cost CW laser source as well as a mode-locked laser source.     

Amplitude and phase microscopy for sizing of spherical particles

We describe a numerical vector diffraction model based on Mie theory that describes the imaging of spherical particles by bright-field, confocal, and interferometric microscopes. The model correctly scales the amplitude-scattered field relative to the incident field so that the forward-scattered and incident light can be interfered to correctly model imaging with copolarization transmission microscopes for the first time to our knowledge. The model is used to demonstrate that amplitude and phase imaging with an interferometric microscope allows subwavelength particle sizing. Furthermore, we show that the phase channel allows much smaller particles to be sized than amplitude-only measurements. The model is validated by experimental measurements.     

Efficient three-dimensional imaging from a small cylindrical aperture

Small-diameter cylindrical imaging platforms, such as those being considered in the development of in vivo ultrasonic microprobes, pose unique image formation challenges. The curved apertures they provide are incompatible with many of the commonly used frequency-domain synthetic aperture imaging algorithms. At the same time, their frequently small diameters place limits on the available aperture and the angular resolution that may be achieved. We obtain a three-dimensional, frequency-domain imaging algorithm for this geometry by making suitable approximations to the point spread function for wave propagation in cylindrical coordinates and obtaining its Fourier transform by analogy with the equivalent problem in Cartesian coordinates. For the most effective use of aperture, we propose using a focused transducer to place a virtual source a short distance from the probe. The focus is treated as a diverging source by the imaging algorithm, which then forms images on deeper cylindrical shells. This approach retains the simplicity and potential angular resolution of a single element, yet permits full use of the available probe aperture and a higher energy output. Computer simulations and experimental results using wire targets show that this imaging technique attains the resolution limit dictated by the operating wavelength and the transducer characteristics     

Effects of source coherence and aperture array geometry on optical sectioning strength in direct-view microscopy

Laser sources offer a possible solution to the problem of low light throughput in direct-view microscopes (DVMs). However, coherent source DVMs have been shown to suffer from problems such as increased sidelobes in the depth response because of coherent cross talk between neighboring apertures. We explore theoretically how source coherence affects the depth responses of DVMs by employing various aperture spacings and number of apertures. We show that, contrary to expectation, closely spaced apertures can result in decreased full width at half-maximum of the depth response curve. We explain this as an effect of destructive interference when cross talk between neighboring apertures occurs. Using apertures arranged in a square grid as an example, we move on to show that the use of aperture arrays that consist of regularly arranged apertures can accentuate the problematic sidelobes of the depth response. We show that arranging pinholes in a rectangular grid rather than a square grid can improve the optical sectioning strength significantly. Finally, by examination of the depth responses corresponding to the infinite-pinhole-array limit, we make some general statements about source coherence and the characteristics of arrays that are likely to perform well.     

Improved emission uniformity from a liquid-jet laser-plasma extreme-ultraviolet source

Many modern compact soft-x-ray and extreme-ultraviolet (EUV) imaging systems operate with small fields of view and therefore benefit from the use of small high-brightness sources. Such systems include water-window microscopes and EUV lithography tools. We show that the photon losses in such systems can be minimized while uniformity of object-plane illumination is maintained by controlled scanning of the source. The improved collection efficiency is demonstrated both theoretically and experimentally for a scanned laser-plasma source compared with static sources. A prospective aerial image microscope and a liquid-xenon-jet laser-plasma source are offered as examples of modern imaging tools that may benefit from such scanning of the source.     

A novel beamformer design method for medical ultrasound. Part I: Theory

The design of transmit and receive aperture weightings is a critical step in the development of ultrasound imaging systems. Current design methods are generally iterative, and consequently time consuming and inexact. We describe a new and general ultrasound beamformer design method, the minimum sum squared error (MSSE) technique. The MSSE technique enables aperture design for arbitrary beam patterns (within fundamental limitations imposed by diffraction). It uses a linear algebra formulation to describe the system point spread function (psf) as a function of the aperture weightings. The sum squared error (SSE) between the system psf and the desired or goal psf is minimized, yielding the optimal aperture weightings. We present detailed analysis for continuous wave (CW) and broadband systems. We also discuss several possible applications of the technique, such as the design of aperture weightings that improve the system depth of field, generate limited diffraction transmit beams, and improve the correlation depth of field in translated aperture system geometries. Simulation results are presented in an accompanying paper.     

Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene

We show that in graphene epitaxially grown on SiC the Drude absorption is transformed into a strong terahertz plasmonic peak due to natural nanoscale inhomogeneities, such as substrate terraces and wrinkles. The excitation of the plasmon modifies dramatically the magneto-optical response and in particular the Faraday rotation. This makes graphene a unique playground for plasmon-controlled magneto-optical phenomena thanks to a cyclotron mass 2 orders of magnitude smaller than in conventional plasmonic materials such as noble metals.     

High-aperture diffraction of a scalar, off-axis Gaussian beam

A scalar treatment for Gaussian beams offset from the optic axis and then focused by a high-numerical-aperture lens is presented. Such a theory is required for describing certain types of Doppler microscopes, i.e., when the measurement is simultaneously performed by more than a single beam axially offset and then focused by a lens. Analytic expressions for the intensity in the focal region of the high-aperture lens are derived. From these expressions we calculate the intensity in the focal region with parameters of beam size, beam offset, and the numerical aperture of the lens. The relative location and variation of the intensity around the focal region are discussed in detail. We show that for small-diameter Gaussian beams the Strehl ratio increases above unity as the beam is offset from the optic axis. This is explained by the increase in the effective numerical aperture of the offset beam compared with the one collinear with the optic axis. From examining the focal distribution, we conclude that it rotates for small beam size and that increasing beam diameter causes the focused distribution to rotate and shear, i.e., to distort. We also show that the distortion of the distribution increases with increasing numerical aperture.     

Surface Plasmon Resonance Magneto-Optical Kerr Effect in Au/Co/Au Magneto-Plasmonic Multilayer

Surface plasmon resonance magneto-optical Kerr effect is studied in magneto-plasmonic multilayer as Au (11 nm)/Co (11 nm)/Au (11 nm). Our experimental setup is consists of spectral magneto-optical rotation in Kretschmann-based attenuated total reflection condition as surface plasmon resonance magneto-optical Kerr effect. Based on this new experimental setup, the sample exposed under external magnetic filed at surface plasmon resonance angle. Our results show sufficient surface plasmon resonance magneto-optical Kerr effect in visible region, thanks to the resonant excitation of surface plasmons which is very suitable for miniaturized and controllable magneto-optical imaging systems, memory, and also magneto-optical isolators.     

Near-field microscopy: throwing light on the nanoworld

Optical microscopy with nanoscale resolution, beyond that which is possible with conventional diffraction-limited microscopy, may be achieved by scanning a nanoantenna in close proximity to a sample surface. This review will first aim to provide an overview of the basic principles of this technique of scanning near-field optical microscopy (SNOM), before moving on to consider the most widely implemented form of this microscopy, in which the sample is illuminated through a small aperture held less than 10 nm from the sample surface for optical imaging with a resolution of ca. 50 nm. As an example of the application of this microscopy, the results of SNOM measurements of light-emitting polymer nanostructures are presented. In particular, SNOM enables the unambiguous identification of the different phases present in the nanostructures, through the local analysis of the fluorescence from the polymers. The exciting new possibilities for high-resolution optical microscopy and spectroscopy promised by apertureless SNOM techniques are also considered. Apertureless SNOM may involve local scattering of light from a sample surface by a tip, local enhancement of an optical signal by a metal tip, or the use of a fluorescent molecule or nanoparticle attached to a tip as a local optical probe of a surface. These new optical nanoprobes offer the promise of optical microscopy with true nanometre spatial resolution.