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We describe a phase plate for transmission electron microscopy taking advantage of a hitherto-unknown phenomenon, namely a beam-induced Volta potential on the surface of a continuous thin film. The Volta potential is negative, indicating that it is not caused by beam-induced electrostatic charging. The film must be heated to ∼200°C to prevent contamination and enable the Volta potential effect. The phase shift is created "on the fly" by the central diffraction beam eliminating the need for precise phase plate alignment. Images acquired with the Volta phase plate (VPP) show higher contrast and unlike Zernike phase plate images no fringing artifacts. Following installation into the microscope, the VPP has an initial settling time of about a week after which the phase shift behavior becomes stable. The VPP has a long service life and has been used for more than 6 mo without noticeable degradation in performance. The mechanism underlying the VPP is the same as the one responsible for the degradation over time of the performance of thin-film Zernike phase plates, but in the VPP it is used in a constructive way. The exact physics and/or chemistry behind the process causing the Volta potential are not fully understood, but experimental evidence suggests that radiation-induced surface modification combined with a chemical equilibrium between the surface and residual gases in the vacuum play an important role. [ABSTRACT FROM AUTHOR]

A new fabrication method of carbon based phase plates for phase-contrast transmission electron microscopy is presented. This method utilizes colloidal masks to produce pores as well as disks on thin carbon membranes for phase modulation. Since no serial process is involved, carbon phase plate membranes containing hundreds of pores can be mass-produced on a large scale, which allows “disposal” of contaminated or degraded phase modulating objects after use. Due to the spherical shape of the mask colloid particles, the produced pores are perfectly circular. The pore size and distribution can be easily tuned by the mask colloid size and deposition condition. By using the stencil method, disk type phase plates can also be fabricated on a pore type phase plate. Both pore and disk type phase plates were tested by measuring amorphous samples and confirmed to convert the sinus phase contrast transfer function to the cosine shape. [ABSTRACT FROM AUTHOR]

Based on the diffraction theory, the focusing properties of a radially polarized quadratic Bessel--Gaussian beam (QBG) with on-axis radial phase variance wavefront are investigated theoretically in the focal region of a high numerical aperture (NA) objective lens. The phase wavefront C and pupil beam parameter μ of QBG are the functions of the radial coordinate. The detailed numerical calculation of the focusing property of a QBG beam is presented. The numerical calculation shows that the beam parameter μ and phase parameter C have greater effect on the total electric field intensity distribution. It is observed that under the condition of different μ, evolution principle of focal pattern differs very remarkably on increasing C. Also, some different focal shapes may appear, including rhombic shape, quadrangular shape, two-spherical crust focus shape, two-peak shape, one dark hollow focus, two dark hollow focuses pattern, and triangle dark hollow focus, which find wide optical applications such as optical trapping and nanopatterning. [ABSTRACT FROM AUTHOR]

A new method to control lattice-fringe contrast in high-resolution transmission electron microscopy (HRTEM) images by the implementation of a physical phase plate (PP) is proposed. PPs are commonly used in analogy to Zernike PPs in light microscopy to enhance the phase contrast of weak-phase objects with nm-sized features, which often occur in life science applications. Such objects otherwise require strong defocusing, which leads to a degradation of the instrumental resolution and impedes intuitive image interpretation. The successful application of an electrostatic Zach PP in HRTEM is demonstrated by the investigation of single crystalline Si and Ge samples. The influence of the Zach PP on the image formation process is assessed by analyzing the amplitudes of (111) reflections in power spectra which show a cosine-type dependence on the induced phase shift under certain conditions as predicted by theory.

Abstract: Analysis of the imaging of some simple distributions of object phase by a phase plate of Zernike type shows that sharp transitions in the object phase are well transmitted. The low-frequency components of the complete object function are attenuated by the plate. The behaviour can be characterised by a cut-on parameter defined as the product of the cut-on frequency of the plate and a characteristic dimension of the object. When this parameter exceeds a value of the order of unity, a sharp boundary in the object is imaged by a Zernike plate as a dark lining inside the boundary with a white outline or halo outside the boundary, in agreement with reported observations. The maximum diameter of objects that can be imaged accurately is inversely proportional to the diameter of the hole for beam transmission in the phase plate. [Copyright &y& Elsevier]

Abstract: Electron vortex beam probes offer the possibility of mapping magnetic moments with atomic resolution. In this work we consider using the stray magnetic field produced from a narrow ferromagnetic rod magnetised along its long axis to produce a vortex beam probe, as an alternative to the currently used holographic apertures or gratings. We show through numerical modelling, electron holography observations and direct imaging of the electron probe, that a long narrow ferromagnetic rod induces a phase shift in the wave-function of passing electrons that approximately describes a helix in the regions near its ends. Directing this rod towards the optical axis of a charged-particle beam probe forming system at a limiting aperture position, with the free-end sufficiently close to the axis, is shown to offer a point spread function composed of vortex modes, with evidence of this appearing in observations of the electron probe formed from inserting a micro-fabricated CoFe rod into the beam path of a 300keV transmission electron microscope (TEM). If the rod is arranged to contain the magnetic flux of h/e, thus producing a maximum phase shift of 2π, it produces a simple spiral-like phase contrast transfer function for weak phase objects. In this arrangement the ferromagnetic rod can be used as a phase plate, positioned at the objective aperture position of a TEM, yielding enhanced image contrast which is simulated to be intermediate between comparable Zernike and Hilbert phase plates. Though this aspect of the phase plate performance is not demonstrated here, agreement between our observations and models for the probe formed from an example rod containing a magnetic flux of ~2.35h/e, indicate this phase plate arrangement could be a simple means of enhancing contrast and gaining additional information from TEM imaged weak phase samples, while also offering the capability to produce vortex beam probes. However, steps still need to be taken to either remove or improve the support membrane for the rod in our experiments to reduce any effects from charging in the phase plate. [Copyright &y& Elsevier]

Electromagnetic waves bearing orbital angular momentum in the radio frequency range is a growing subject of study. The design of systems able to produce and/or to receive such waves is then of crucial importance. The aim of this letter is to characterize, in an anechoic chamber, a new type of antenna in the millimeter frequency band. The index-varying flat plate generates an electromagnetic wave carrying orbital angular momentum. We then extract the various modes from the radiated field. [ABSTRACT FROM AUTHOR]

Abstract: The pure phase plate was introduced to alter the half-space phase value of the incident linearly polarized hyperolic-cosine-Gaussian (cosh-Gaussian) beams with sine-azimuthal variation wavefront, and focusing properties of the cosh-Gaussian beams by half space phase plate were investigated in detail. Simulation results show that focal pattern can be altered very considerably by the phase plate under condition of different beam parameters, numerical aperture, and phase parameter that indicates the phase change frequency on increasing azimuthal angle. Symmetry of the whole focal pattern can be altered remarkably, polysymmetrical focal patterns evolve into nonsymmetrical focal patterns. And some novel focal shape may appear, including cross-shape, multiple-peak focal pattern, multiple intensity lines, wheel focal pattern, swallowtail focal pattern, and dark hollow focal spots. [Copyright &y& Elsevier]

Abstract: Microfabricated devices designed to provide phase contrast in the transmission electron microscope must be free of phase distortions caused by unexpected electrostatic effects. We find that such phase distortions occur even when a device is heated to 300°C during use in order to avoid the formation of polymerized, carbonaceous contamination. Remaining factors that could cause unwanted phase distortions include patchy variations in the work function of a clean metal surface, radiation-induced formation of a localized oxide layer, and creation of a contact potential between an irradiated area and the surround due to radiation-induced structural changes. We show that coating a microfabricated device with evaporated carbon apparently eliminates the problem of patchy variation in the work function. Furthermore, we show that a carbon-coated titanium device is superior to a carbon-coated gold device, with respect to radiation-induced electrostatic effects. A carbon-coated, hybrid double-sideband/single-sideband aperture is used to record in-focus, cryo-EM images of monolayer crystals of streptavidin. Images showing no systematic phase error due to charging are achievable under conditions of low-dose data collection. The contrast in such in-focus images is sufficient that one can readily see individual streptavidin tetramer molecules. Nevertheless, these carbon-coated devices perform well for only a limited length of time, and the cause of failure is not yet understood. [Copyright &y& Elsevier]

Abstract: Imaging with Zernike phase plates is increasingly being used in cryo-TEM tomography and cryo-EM single-particle applications. However, rapid ageing of the phase plates, together with the cost and effort in producing them, present serious obstacles to widespread adoption. We are experimenting with phase plates based on silicon chips that have thin windows; such phase plates could be mass-produced and made available at moderate cost. The windows are coated with conductive layers to reduce charging, and this considerably extends the useful life of the phase plates compared to traditional pure-carbon phase plates. However, a compromise must be reached between robustness and transmission through the phase-plate film. Details are given on testing phase-plate performance by means of imaging an amorphous thin film and evaluating the power spectra of the images. [Copyright &y& Elsevier]

Abstract: Dark field TEM imaging using a stop of the central beam (DF-000) is reported. It is shown that a strong enhancement in the contrast can be obtained for graphene as example of weak phase object and endocytic multivescilar body as example of an unstained biological sample. No charging or significant contamination of the central beam stop is observed. For graphene, a resolution beyond 1Å−1 was easily obtained. DF-000 imaging can be considered as a good and easy to use alternative of a phase plate. [Copyright &y& Elsevier]

Abstract: A dark spot surrounded by light completely, no matter in two-dimensional or three-dimensional, has attracted more and more attention recently, owing to its recommendable applications such as the erase hollow spot for STED fluorescence microscope, the optical trap for cold atoms and the optical tweezers for precise manipulation. The main method to generate a dark spot is beam shaping, by modulating the phase and polarization of the given polarized beam with a proper phase plate. In this paper, most common realization methods for achieving various dark spots with circular polarization beam were summarized and simulated. And several special foci generated with cylindrical polarization beams were first designed, simulated and proposed. The feature and characteristic of dark spots are presented by intensity contour maps. Applications of each dark spot are also discussed according to its characteristic. [Copyright &y& Elsevier]

Zach phase plates (PPs) are promising devices to enhance phase contrast in transmission electron microscopy. The Zach PP shifts the phase of the zero-order beam by a strongly localized inhomogeneous electrostatic potential in the back focal plane of the objective lens. We present substantial improvements of the Zach PP, which overcome previous limitations. The implementation of a microstructured heating device significantly reduces contamination and charging of the PP structure and extends its lifetime. An improved production process allows fabricating PPs with reduced dimensions resulting in lower cut-on frequencies as revealed by simulations of the electrostatic potential. Phase contrast with inversion of PbSe nanoparticles is demonstrated in a standard transmission electron microscope with LaB6 cathode by applying different voltages. [ABSTRACT FROM AUTHOR]

Abstract: Holographic measurements on magnetised thin-film cobalt rings have demonstrated both onion and vortex states of magnetisation. For a ring in the vortex state, the difference between phases of electron paths that pass through the ring and those that travel outside it was found to agree very well with Aharonov–Bohm theory within measurement error. Thus the magnetic flux in thin-film rings of ferromagnetic material can provide the phase shift required for phase plates in transmission electron microscopy. When a ring of this type is used as a phase plate, scattered electrons will be intercepted over a radial range similar to the ring width. A cobalt ring of thickness 20nm can produce a phase difference of π/2 from a width of just under 30nm, suggesting that the range of radial interception for this type of phase plate can be correspondingly small. [Copyright &y& Elsevier]

Abstract: To achieve high lateral resolution overcoming the diffraction limit, a two-color phase plate (TPP) for generating a quasi-Laguerre–Gaussian beam was applied to super-resolution microscopy (SRM) based on fluorescence depletion. Putting the TPP into a robust optical path in a commercial laser-scanning microscope, we obtained a point spread function with a full width at half maximum three times smaller than diffraction limit. The measured contrast transfer function shows that line and space patterns finer than the diffraction limit were clearly resolved and the image contrast was improved. Since the TPP can easily improve lateral resolution in SRM without any precise adjustment, our setup provides a practical super-resolution microscope. [Copyright &y& Elsevier]

Abstract: Decrease of the irradiation dose needed to obtain a desired signal-to-noise ratio can be achieved by Zernike phase-plate imaging. Here we present results on a hole-free phase plate (HFPP) design that uses the incident electron beam to define the center of the plate, thereby eliminating the need for high precision alignment and with advantages in terms of ease of fabrication. The Zernike-like phase shift is provided by a charge distribution induced by the primary beam, rather than by a hole in the film. Compared to bright-field Fresnel-mode imaging, the hole-free phase plate (HFPP) results in two- to four-fold increase in contrast, leading to a corresponding decrease in the irradiation dose required to obtain a desired signal-to-noise ratio. A local potential distribution, developed due to electron beam-induced secondary-electron emission, is the most likely mechanism responsible for the contrast-transfer properties of the HFPP. [Copyright &y& Elsevier]

Abstract: Implementation of physical phase plates into transmission electron microscopes to achieve in-focus contrast for ice-embedded biological specimens poses several technological challenges. During the last decade several phase plates designs have been introduced and tested for electron cryo-microscopy (cryoEM), including thin film (Zernike) phase plates and electrostatic devices. Boersch phase plates (BPPs) are electrostatic einzel lenses shifting the phase of the unscattered beam by an arbitrary angle. Adjusting the phase shift to 90° achieves the maximum contrast transfer for phase objects such as biomolecules. Recently, we reported the implementation of a BPP into a dedicated phase contrast aberration-corrected electron microscope (PACEM) and demonstrated its use to generate in-focus contrast of frozen–hydrated specimens. However, a number of obstacles need to be overcome before BPPs can be used routinely, mostly related to the phase plate devices themselves. CryoEM with a physical phase plate is affected by electrostatic charging, obliteration of low spatial frequencies, and mechanical drift. Furthermore, BPPs introduce single sideband contrast (SSB), due to the obstruction of Friedel mates in the diffraction pattern. In this study we address the technical obstacles in detail and show how they may be overcome. We use X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) to identify contaminants responsible for electrostatic charging, which occurs with most phase plates. We demonstrate that obstruction of low-resolution features is significantly reduced by lowering the acceleration voltage of the microscope. Finally, we present computational approaches to correct BPP images for SSB contrast and to compensate for mechanical drift of the BPP. [Copyright &y& Elsevier]

Abstract: We report the implementation of an electrostatic Einzel lens (Boersch) phase plate in a prototype transmission electron microscope dedicated to aberration-corrected cryo-EM. The combination of phase plate, C s corrector and Diffraction Magnification Unit (DMU) as a new electron-optical element ensures minimal information loss due to obstruction by the phase plate and enables in-focus phase contrast imaging of large macromolecular assemblies. As no defocussing is necessary and the spherical aberration is corrected, maximal, non-oscillating phase contrast transfer can be achieved up to the information limit of the instrument. A microchip produced by a scalable micro-fabrication process has 10 phase plates, which are positioned in a conjugate, magnified diffraction plane generated by the DMU. Phase plates remained fully functional for weeks or months. The large distance between phase plate and the cryo sample permits the use of an effective anti-contaminator, resulting in ice contamination rates of <0.6nm/h at the specimen. Maximal in-focus phase contrast was obtained by applying voltages between 80 and 700mV to the phase plate electrode. The phase plate allows for in-focus imaging of biological objects with a signal-to-noise of 5–10 at a resolution of 2–3nm, as demonstrated for frozen-hydrated virus particles and purple membrane at liquid-nitrogen temperature. [Copyright &y& Elsevier]

A promising alternative to the widespread Z-scan technique has been recently proposed. This technique, named Baryscan, is based upon the use of a Position Sensitive Detector (PSD) and is about 170 times more sensitive than the Z-scan technique while preserving its simple theoretical scheme and ease of implementation. In this paper, we demonstrate both numerically and experimentally that inserting a phase plate before the PSD and setting an opaque disk as close as possible to its active area results in a substantial sensitivity enhancement of the Baryscan technique. [ABSTRACT FROM AUTHOR]

Abstract: Images acquired with a phase plate often exhibit fringing and/or contrast reversal artifacts. The two basic parameters controlling the performance of the phase plate are phase shift and cut-on periodicity. We investigate theoretically and numerically the effect of these parameters on the image quality. The analysis covers not just the typical negative phase shift phase plates but also positive phase shift ones. The theoretical study derives formulas for calculating the optimal phase plate phase shift and for the maximum achievable contrast with a given specimen. Two figures of merit – fidelity and contrast – were defined and used to quantify the numerical results. Larger cut-on periodicities provide better performance with higher contrast and less artifacts in the images. Both, the theoretical results and the simulations indicate that positive phase shift phase plates generate higher contrast with better linearity and are free from contrast reversal artifacts. However, with such phase plates the amplitude and the phase contrast components are opposed to each other and the simulations show stronger fringing outside of objects. Based on these results it is difficult to predict if and to what extent the positive phase shift phase plates will be advantageous in practice. Two methods for reduction of fringing artifacts were compared—tapered phase plate and low-frequency amplification software filter. Overall the software solution produced better results and is much easier to implement than modifying the hardware of the phase plate to realize the taper. [Copyright &y& Elsevier]

Abstract: Transmission electron microscopy phase-contrast images taken by amorphous carbon film-based phase plates are affected by the scattering of electrons within the carbon film causing a modification of the image-wave function. Moreover, image artefacts are produced by non-centrosymmetric phase plate designs such as the Hilbert-phase plate. Various methods are presented to correct phase-contrast images with respect to the scattering of electrons and image artefacts induced by phase plates. The proposed techniques are not restricted to weak-phase objects and linear image formation. Phase-contrast images corrected by the presented methods correspond to those taken by an ideal centrosymmetric, matter-free phase plate and are suitable for object-wave reconstruction. [Copyright &y& Elsevier]

Abstract: To reconsider the problems arising from the use of the phase plate as a test plate inserted into a polarized light microscope system for the analysis of triclinic calcium pyrophosphate dihydrate (t-CPPD) crystals, or Ca2P2O7·2H2O in the synovial fluid of arthritis patients, we made the polarized light microscopy observations using a phase plate with a retardation of 530nm for the synthesized t-CPPD crystals well-characterized by X-ray powder pattern indexing and single crystal X-ray diffraction measurements. The microscopy observations were made of crystals of different sizes, thicknesses and shapes. The retardation was assessed using the interference color chart at four extinction and diagonal positions both with and without the test plate. The addition and subtraction states produced by superimposing the retardations of two anisotropic materials, that is, the t-CPPD crystal and the 530nm phase plate, were deduced from the interference color change by inserting the test plate at four diagonal positions. When the color change of a crystal at a diagonal position resulting from 90-degree rotation exhibits no clear birefringence, the interference color chart was shown to be useless. We suggested the use of a compensator whose retardation can be changed to obtain an accurate value for the retardation of the crystal. [Copyright &y& Elsevier]

A promising novel type of electrostatic phase plate for transmission electron microscopy (TEM) is presented. The phase plate consists of a single microcoaxial cable-like rod with its electrode exposed to the undiffracted electrons. The emerging field is used to shift the phase of the undiffracted electrons with respect to diffracted electrons. The design overcomes the drawback of the spatial frequency-blocking ring electrode of the Boersch phase plate. First, experimental phase-contrast images are presented for PbSe and Pt nanoparticles with clearly varying phase contrast, which depends on the applied voltage and resulting phase shift of the unscattered electrons. With the new phase-plate design, we show for the first time the reconstruction of an object wave function based on a series of only three experimental phase-contrast TEM images obtained with an electrostatic phase plate. [ABSTRACT FROM AUTHOR]

Inner and outer diameters of the phase plate limit the number of electrons passing and can affect the high-resolution information in the phase contrast image. A more practical column model including the First Condenser Lens CL1, Second Condenser Lens CL2, Mini-condenser Lens CM and Objective Lens(OL) was first built to obtain the beam performance at the upper surface of the phase plate. N-body Monte Carlo simulation was used to avoid error caused by big defocus from the Guassian image plane where a lens field exists. In building the motion equation in a practical field, second order finite element method and Hermite function interpolation were applied to get the axial field and its arbitrary order derivative. N motion equations were then solved by fifth-order Runge-Kutta algorithm and the performance of un-scattered and scattered electrons was given for a 200kV TEM. Results show that the beam spots are 2.7µm and 39µm for un-scattered and scattered electrons respectively. N-body Monte Carlo simulation can obtain both positions and velocities of un-scattered and scattered electrons at the arbitrary plane with aberrations being considered, which effectively avoids error from the defocus distance in classic aberration integrated methods. [ABSTRACT FROM AUTHOR]

Abstract: Cryo-tomography in the electron microscope is unique in its ability to provide high-resolution, three-dimensional structural information about cells, organelles and macromolecules in a nearly native, frozen-hydrated state. However, the phase-contrast imaging method used in conventional cryo-electron tomography fails to faithfully represent the full range of structural features in such specimens. Only certain features are recorded with adequate contrast, and overall contrast is low. The recently developed Zernike phase contrast method has the potential to solve this problem, and here we apply it for the first time to cryo-electron tomography. The new method has uniform transfer characteristics for a wide range of spatial frequencies, leading to improved overall signal-to-noise ratio and raising the prospects of higher resolution and quantitative representation of specimen densities in the reconstructed tomograms. [Copyright &y& Elsevier]

Abstract: We present a phase plate loading system developed for a commercial transmission electron microscope (TEM). Our system can be installed without modifying the optical design of the TEM. This system is equipped with a loading monitoring set that allows users to easily and safely locate the phase plate between the pole pieces, and also comes with an airlock that permits quick loading of a phase plate without the need to re-vent the TEM column. The system uses a home-made three-axis nano-positioner to precisely position the phase plate hole at the desired location. Our system has a precision of ∼10nm, an improvement of one order of magnitude compared with the precision of a phase plate holder modified from an objective aperture. We demonstrate the successful installation and the use of the loading system to place a phase plate at the desired position. Our phase plate loading system can be used to accommodate various types of phase plates and thus provides a good way to greatly speed up the development of TEM phase plates. [ABSTRACT FROM AUTHOR]

Abstract: A method is described for the reconstruction of the amplitude and phase of the object exit wave function by phase-plate transmission electron microscopy. The proposed method can be considered as in-line holography and requires three images, taken with different phase shifts between undiffracted and diffracted electrons induced by a suitable phase-shifting device. The proposed method is applicable for arbitrary object exit wave functions and non-linear image formation. Verification of the method is performed for examples of a simulated crystalline object wave function and a wave function acquired with off-axis holography. The impact of noise on the reconstruction of the wave function is investigated. [Copyright &y& Elsevier]

Abstract: A number of practical issues must be addressed when using thin carbon films as quarter-wave plates for Zernike phase-contrast electron microscopy. We describe, for example, how we meet the more stringent requirements that must be satisfied for beam alignment in this imaging mode. In addition we address the concern that one might have regarding the loss of some of the scattered electrons as they pass through such a phase plate. We show that two easily measured parameters, (1) the low-resolution image contrast produced in cryo-EM images of tobacco mosaic virus particles and (2) the fall-off of the envelope function at high resolution, can be used to quantitatively compare the data quality for Zernike phase-contrast images and for defocused bright-field images. We describe how we prepare carbon-film phase plates that are initially free of charging or other effects that degrade image quality. We emphasize, however, that even though the buildup of hydrocarbon contamination can be avoided by heating the phase plates during use, their performance nevertheless deteriorates over the time scale of days to weeks, thus requiring their frequent replacement in order to maintain optimal performance. [Copyright &y& Elsevier]

Abstract: Focal depth and focal splitting of hyperbolic-cosine-Gaussian beams induced by a phase plate were investigated. The pure phase plate consists of three concentric zones: a center circle zone, an inner annular zone and an outer annular zone. The phase variance of the inner annular zone is adjustable. Simulation results show that the focal depth can be adjusted by changing the radii of zones. With the increase of the inner radius of the outer annular zone, the focal spot broadens along the optical axis and splits into two peaks. Then the two peaks combine back into one peak. There are two critical values for the inner radius of the outer annular zone, at which focal spot changes sharply. The tunable range of the focal depth varies considerably. The phase variance of the inner annular zone affects focal depth also; when the phase variance is π, the effect attains maximum. The parameters of cosh parts of the beam affect both focal splitting and focal depth evidently; focal splitting disappears with increasing parameters of cosh parts, and focal depth increases with increasing the parameters of cosh parts in both the low and the high numerical-aperture optical systems. [Copyright &y& Elsevier]

Abstract: In this article, vector diffraction theory is employed to investigate the focusing properties of the Gaussian beam through a phase plate. The phase plate may alter the wavefront phase of an incoming beam by topological charge. Both the circular phase distribution and the annular phase distribution plates are investigated. Numerical simulations show that the focal intensity distribution depends on topological charge. With changing topological charge, focal intensity distribution may evolve into ring shape, and some novel focal spots may occur. Focal intensity distribution evolving process with integer topological charge differs considerably from that with fraction topological charge. When the concentric annular phase plate is placed in the laser path, the focal intensity distribution depends on both the inner radius and topological charge. For small inner radius of the phase plate, doughnut-shape focal pattern occurs. With increasing inner radius, the diameter of the doughnut focal pattern decreases, and doughnut shape disappears slowly in some cases. [Copyright &y& Elsevier]