Probe retrieval in ptychographic coherent diffractive imaging

Ptychography is a coherent diffractive imaging method that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen. Until recently, reconstruction algorithms for ptychographic datasets needed the a priori knowledge of the incident illumination. A new reconstruction procedure that retrieves both the specimen's image and the illumination profile was recently demonstrated with hard X-ray data. We present here the algorithm in greater details and illustrate its practical applicability with a visible light dataset. Improvements in the quality of the reconstruction are shown and compared to previous reconstruction techniques. Implications for future applications with other types of radiation are discussed.     

Influence of the overlap parameter on the convergence of the ptychographical iterative engine

The ptychographical iterative engine (PIE) algorithm is examined with both simulated and experimental scanning coherent-diffraction microscopy data. The optimum overlap in terms of image quality, dose on the sample and time of measurements is determined using simulated diffraction data. The validity of the results is supported by experimental helium-neon laser light diffraction data.     

A compact Schwarzschild soft X-ray microscope with a laser-produced plasma source

A compact Schwarzschild soft X-ray microscope using a laser-produced plasma soft X-ray source has been developed. The laser-produced plasma source, which is small but of high brilliance, has made it possible to use the soft X-ray microscope in a small laboratory. The microscope is composed of a Schwarzschild objective and a grazing incidence mirror condenser. Image contrast for biological specimens in soft X-ray regions is investigated briefly. It is possible to observe the fine structures of a thin specimen at a wavelength of 15 nm; at this wavelength high-contrast images of biological specimens have been obtained with a single laser shot of pulse width of 8 ns at a resolution of 0·3 μm. The resolution of the system is limited by the detector.     

High-resolution wave field reconstruction using a through-focus series of images taken under limited electron dose

The three-dimensional Fourier filtering method and Schiske's Wiener filtering method are compared with the aim of high-resolution wave field reconstruction of an unstained deoxyribonucleic acid (DNA) molecular fiber using a through-focus series of images taken under a limited electron dose. There were some definite differences between the two reconstructed images, although the two kinds of processing are essentially equivalent except for the dimension and the filter used for processing. Through theoretical analyses together with computer simulations, the differences were proved to be primarily due to specimen drift during the experiment. Although the observed structure of the DNA molecular fiber was heavily damaged by electron beam irradiation, reconstructed images by the three-dimensional Fourier filtering method provided higher resolution information on the molecular structure even when relatively large specimen drift was included in the through-focus series. In contrast, in Schiske's Wiener filtering method, the detailed information of the structure was lost because of the drift, although the reconstructed image showed a higher signal-to-noise ratio. The three dimensional Fourier filtering method seems to be more applicable for observing radiation-sensitive materials under an extremely low electron dose, because specimen drift cannot be completely avoided.     

Optimization of a Wolter type I mirror for a soft X-ray microscope

The demand for an X-ray microscope has received much attention because of the desire to study living cells under high resolution. A Wolter type I mirror used for soft X-ray microscope optics has a number of advantages. Although much progress has been made, it is still not easy to fabricate this mirror and satisfy the surface roughness and figure error requirements. From the mirror fabrication point of view, it is necessary to see the mirror design and the tolerance budget, especially with respect to the surface roughness and the figure errors. This paper deals with the design and optimization of a Wolter type I microscope mirror. The optimization was carried out by choosing an optimum central grazing incidence angle for which a merit function had the maximum value. The image quality of the mirror was also examined. A smaller diameter gave better image quality because of the Abbe sine condition. Finally, the figure errors for the axial and the radial directions were simulated by sinusoidal deformation waves, and the figure tolerance was obtained.     

In-line holographic electron microscopy in the presence of external magnetic fields

It is now a well-known fact that the phase of electron waves is altered by external magnetic fields via the Aharonov-Bohm effect. This implies that any electron interference effects will be to some degree affected by the presence of such fields. In this study we examine the distortion effects of external (constant and variable) magnetic fields on electron interference and holography. For digital holography, the reconstruction of the object is done via numerical calculations and this leaves the door open for correcting phase distortions in the hologram reconstruction. We design and quantitatively assess such correction schemes, which decidedly depend on our knowledge of the magnetic field values in the holographic recording process. For constant fields of known value we are able to correct for magnetic distortions to a great extent. We find that variable fields are more destructive to the holographic process than constant fields. We define two criteria, related respectively to global and local contrast of the hologram to establish the maximum allowed external field which does not significantly hinder the accuracy of in-line holographic microscopy with electrons.     

A formula for the image intensity of phase objects in Zernike mode

I present an analytical expression for the image intensity of a phase object visualized in Zernike phase contrast mode. The formula is valid for periodic and non-periodic weak and strong objects, and accounts for the effects of finite illumination. The expression provided is intended as a generalization of the standard reference formula given in the Born and Wolf [Principles of Optics, sixth ed., Pergamon Press, New York, 1980, p. 427] textbook as well as of the formalism employed to evaluate imaging doses in Zernike mode [M. Malac, M. Beleggia, R. Egerton, Y. Zhu, Ultramicroscopy 108 (2008) 126]. I illustrate the usefulness of the improved expression by means of three examples: a sinusoidal phase grating, a Gaussian object, and a phase step. The optimal Zernike phase angle yielding maximum image contrast is found to be object-dependent and not necessarily equal to pi/2. Phase plate optimization criteria are derived and presented for two of the examples considered.     

Investigation of photoconductivity of silicon solar cells by a near-field scanning microwave microscope

The photovoltaic effect in silicon solar cells were investigated by using a near-field scanning microwave microscope (NSMM) technique by measuring the microwave reflection coefficient at an operating frequency near 4 GHz. As the photoconductivity in the solar cells was varied due to the incident light intensities and the wavelength, we could observe the photoconductivity changes at heterojunction interfaces inside the solar cells by measuring the change of reflection coefficient S₁₁ of the NSMM. By measuring the change of reflection coefficient, we also directly imaged the photoconductivity changes at heterojunction interfaces inside the solar cells.     

Theoretical aspects of image formation in the aberration-corrected electron microscope

The theoretical aspects of image formation in the transmission electron microscope (TEM) are outlined and revisited in detail by taking into account the elastic and inelastic scattering. In particular, the connection between the exit wave and the scattering amplitude is formulated for non-isoplanatic conditions. Different imaging modes are investigated by utilizing the scattering amplitude and employing the generalized optical theorem. A novel obstruction-free anamorphotic phase shifter is proposed which enables one to shift the phase of the scattered wave by an arbitrary amount over a large range of spatial frequencies. In the optimum case, the phase of the scattered wave and the introduced phase shift add up to −π/2 giving negative contrast. We obtain these optimum imaging conditions by employing an aberration-corrected electron microscope operating at voltages below the knock-on threshold for atom displacement and by shifting optimally the phase of the scattered electron wave. The optimum phase shift is achieved by adjusting appropriately the constant phase shift of the phase plate and the phase shift resulting from the defocus and the spherical aberration of the corrected objective lens. The realization of this imaging mode is the aim of the SALVE project (Sub-Å Low-Voltage Electron microscope).     

Absorption microanalysis with a scanning soft X-ray microscope: mapping the distribution of calcium in bone

This article describes the scanning transmission X-ray microscope operated at the National Synchroton Light Source. The application of the instrument to elemental analysis is detailed. In particular, qualitative results on the calcium distribution in human skull tissue are presented.     

Imaging of soft and hard materials using a Boersch phase plate in a transmission electron microscope

Using two levels of electron beam lithography, vapor phase deposition techniques, and FIB etching, we have fabricated an electrostatic Boersch phase plate for contrast enhancement of weak phase objects in a transmission electron microscope. The phase plate has suitable dimensions for the imaging of small biological samples without compromising the high-resolution capabilities of the microscope. A micro-structured electrode allows for phase tuning of the unscattered electron beam, which enables the recording of contrast enhanced in-focus images and in-line holograms. We have demonstrated experimentally that our phase plate improves the contrast of carbon nanotubes while maintaining high-resolution imaging performance, which is demonstrated for the case of an AlGaAs heterostructure. The development opens a new way to study interfaces between soft and hard materials.     

The three-dimensional point spread functions of a microscope objective in image and object space

The three-dimensional point spread function (3-D PSF) of an optical system in image space is distinguished from the 3-D PSF in object space and the relation between the two 3-D PSFs is derived. By using this relation one 3-D PSF can be easily obtained from the other. The 3-D PSFs are given in a single integral expression, which can be computed numerically. The results of this study can be used in 3-D image processing for microscopy and have been applied to the analysis of the diffusion of fluorescent molecules in a 3-D porous medium.     

Manufacture and tests of objective zone plates for use in a scanning transmission X-ray microscope

A method of making high resolution zone plates for use as the focusing elements in soft X-ray microscopy is briefly described. Tests carried out on these zone plates indicate a first-order diffraction efficiency of ～0.3% rather than the calculated value of ～0.9%. This indicates that the zones are not positioned as accurately as expected, a conclusion also drawn from tests at optical wavelengths on electron micrographs of the zone plates. Modifications to the manufacturing method to enable zone plates with improved imaging properties to be made are described.     

Effect of a physical phase plate on contrast transfer in an aberration-corrected transmission electron microscope

In this theoretical study we analyze contrast transfer of weak-phase objects in a transmission electron microscope, which is equipped with an aberration corrector (C(s)-corrector) in the imaging lens system and a physical phase plate in the back focal plane of the objective lens. For a phase shift of pi/2 between scattered and unscattered electrons induced by a physical phase plate, the sine-type phase contrast transfer function is converted into a cosine-type function. Optimal imaging conditions could theoretically be achieved if the phase shifts caused by the objective lens defocus and lens aberrations would be equal to zero. In reality this situation is difficult to realize because of residual aberrations and varying, non-zero local defocus values, which in general result from an uneven sample surface topography. We explore the conditions--i.e. range of C(s)-values and defocus--for most favourable contrast transfer as a function of the information limit, which is only limited by the effect of partial coherence of the electron wave in C(s)-corrected transmission electron microscopes. Under high-resolution operation conditions we find that a physical phase plate improves strongly low- and medium-resolution object contrast, while improving tolerance to defocus and C(s)-variations, compared to a microscope without a phase plate.     

软X射线多层膜设计中表面粗糙度对反射率的影响

给出了一种改进的软X射线波段的多层膜设计方法.在设计过程中,考虑了反射镜基底和各膜层之间的均方(RMS)粗糙度对反射率的影响 ;在Stearns提出的散射理论的基础上给出了粗糙界面的数学模型.文中以波长为λ=1.03nm的软X射线为例进行设计,设计结果表明 :要使波长为λ=1.03nm的多层膜的反射率大于10%,反射镜基底的均方粗糙度不应超过0.6nm.实验中选择几块表面粗糙度为 0.5nm(RMS)的熔石英平面镜作为基底来制作适用于该波长的、层对数超过70的多层膜.然后在的入射角下测量反射率,测得的值为10%,这与采用本设计方法得到的计算结果一致.该反射镜作为X射线谱仪的分光元件被应用于惯性约束聚变(ICF)的过程诊断中.     

Skirting: a limitation for the performance of X-ray microanalysis in the variable pressure or environmental scanning electron microscope

The variable pressure or environmental scanning electron microscope (VP-SEM; ESEM) has become the microscope of choice for many scientists and technologists. Hence, the development of robust methods for X-ray microanalysis, limited by skirting, has become critical. In this paper, two pressure variation correction methods (Doehne and Gauvin) are compared. Both of these methods appear to be effective; the results were found to be well within 10% of the values obtained at 0 Pa. The Doehne method is dependent on an empirical factor (D), therefore the accuracy of the results will depend on the accuracy of this value. Also the Doehne method is compromised by the nonlinearity of the response with pressure. The Gauvin method is more user-friendly and more precise when considering the total range of pressure.     

A new method of compositional image formation by a four-element backscattered electron detector in an SEM

A special mixing procedure for signals from a four element backscattered electron (BSE) detector is proposed for compositional image formation when a sample with a rough surface is examined by a scanning electron microscope (SEM). The new method allows appreciable suppression of the influence of the sample surface topography in a compositional mode for take-off angles less than about 30°, relative to the microscope axis. The theoretical approach based on the analysis of BSE angular distribution is compared with the experiment. The mixing procedure uses a dimensionless parameter, which depends mainly on take-off angle. Photographs of the Ge-Zn structure with its rough surface were taken in conventional and proposed compositional modes for take-off angle 11° and electron energy 20 keV and show a considerable suppression of the topographic effect when the new method is used.     

Quantification of the NA dependent change of shape in the image formation of a z-polarized fluorescent molecule using vectorial diffraction simulations

The point spread function of a fixed fluorophore with its dipole axis colinear to the optical axis appears donut-shaped when seen through a microscope, and its light distribution in the pupil plane is radially polarized. Yet other techniques, such as photolithography, report that this same light distribution in the pupil plane appears as a solid spot. How can this same distribution lead to a spot in one case but a donut in the other? Here, we show how the tube lens of the system plays a critical role in determining this shape. Using a vectorial treatment of image formation, we simulate the relative contributions of both longitudinal and radial components to the image of a dipole emitter and thus show how the donut (typically reported for z-polarized single molecule fluorescence microscopy) transforms into a solid spot (as commonly reported for photolithography) as the numerical aperture of the tube lens increases. We find that the transition point occurs around 0.7 NA, which is significantly higher than used for most microscopy systems and lower than for common photolithography systems, thus resolving the seeming paradox of dipole shape.     

Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration

This article presents the calibration of a compact prover using the weighing method. An evaluation of measurement uncertainty of the prover calibration has been developed using the GUM and Monte Carlo methodologies. A water draw kit was utilized to direct the liquid flow from the compact prover to a water container in order to weigh the transferred water mass on a balance. This amount of mass was used as reference for the calculation of the prover base volume. A modeling of the flow rate into the water draw kit as a function of time was conceived. This modeling was applied for calculating the error in the liquid volume of the water container due to the switching of two solenoid valves of the water draw kit. A mathematical model of the prover base volume has been developed. This model is non-linear and the two largest sources of uncertainty are related to the balance calibration certificate that together account for 31.84% of the uncertainty budget. This work showed that the GUM approach was validated by Monte Carlo method in the calculation of the measurement uncertainty of the calibration of a compact prover. The absolute differences of the respective endpoints of the coverage intervals of these two methods are less than 0.00023% of estimate of the prover base volume whose value is 151.427 dm³. This result was obtained for a coverage probability of 95% and ${10}^6$ Monte Carlo iterations. The density of the calibration water and its uncertainty have been calculated through an innovative approach.     

Study of energy transfer from excited TPD to Alq in organic electroluminescent devices by time-resolved fluorescence spectroscopy using a scanning near-field optical atomic force microscope

We demonstrate the direct measurement of molecular diffusion at organic/organic interfaces of organic electroluminescence devices by use of a scanning near-field optical atomic force microscope. Our preliminary study shows that the degradation of an electroluminescence device is partly caused by crystallization of the organic layers. Because the initial stage of degradation cannot be observed by microscopic methods, nanoscale optical properties of the interface in multilayer systems are currently receiving a great deal of attention. Defects of organic electroluminescence devices were investigated using a scanning near-field optical atomic force microscope. This instrument is capable of measuring both a topographic and a fluorescence image at the same time. The defect area and other areas are clearly observed and time-resolved near-field fluorescence spectra demonstrate emission of the different species. These results suggest that defects occur at the organic solid interface, and that energy transfer occurs from excited TPD, as donor, to Alq, as acceptor.