Ivan Lazic

Image formation modeling in cryo-electron microscopy.

Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimens scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvents dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson-Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.

Phase contrast STEM for thin samples: Integrated differential phase contrast.

It has been known since the 1970s that the movement of the center of mass (COM) of a convergent beam electron diffraction (CBED) pattern is linearly related to the (projected) electrical field in the sample. We re-derive a contrast transfer function (CTF) for a scanning transmission electron microscopy (STEM) imaging technique based on this movement from the point of view of image formation and continue by performing a two-dimensional integration on the two images based on the two components of the COM movement. The resulting integrated COM (iCOM) STEM technique yields a scalar image that is linear in the phase shift caused by the sample and therefore also in the local (projected) electrostatic potential field of a thin sample. We confirm that the differential phase contrast (DPC) STEM technique using a segmented detector with 4 quadrants (4Q) yields a good approximation for the COM movement. Performing a two-dimensional integration, just as for the COM, we obtain an integrated DPC (iDPC) image which is approximately linear in the phase of the sample. Beside deriving the CTFs of iCOM and iDPC, we clearly point out the objects of the two corresponding imaging techniques, and highlight the differences to objects corresponding to COM-, DPC-, and (HA) ADF-STEM. The theory is validated with simulations and we present first experimental results of the iDPC-STEM technique showing its capability for imaging both light and heavy elements with atomic resolution and a good signal to noise ratio (SNR).

Analysis of HR-STEM theory for thin specimen.

A compact mathematical model of the STEM imaging process including bright field (BF) and dark field (DF) is derived. This description is valid for thin samples, does not rely on the weak phase approximation and does not require time-consuming simulation of the scanning process. It is well-known that STEM imaging is a nonlinear technique and therefore cannot be described in terms of a sample-independent linear contrast transfer function (CTF). In this work we derive a nonlinear description showing that a STEM image can in fact be described with two terms. Both terms are cross-correlations between a function that is independent of the sample and a function that depends only on the sample. The latter two can be seen as two different objects. These objects directly correspond to two specific cases: the weak phase approximation (WPA) and annular dark field (ADF) imaging, which are known from the literature. We clarify the need for recognizing and understanding what the object is of any particular STEM technique. The model was validated using simulated STEM images and an excellent agreement as well as a reduction in computation time of 3 orders of magnitude was found.

Integrated Differential Phase Contrast (iDPC)–Direct Phase Imaging in STEM for Thin Samples

Imaging the phase of the transmission function has always been the ultimate goal of any (S)TEM imaging technique as it is, for thin samples, directly proportional to the projected potential in the sample. Customarily this information is obtained using Holography [1] or by performing focus series reconstruction in TEM (FSR-TEM) [2], recently also in combination with Phase Plates (PP) [3] and/or image Cs correction. Ptychographic reconstruction has also been considered as an alternative [4].

Quantitative Phase Imaging of Ba 2 NaNb 5 O 15

High-Resolution Transmission Electron Microscope (HRTEM) is one of the most powerful imaging tools to study the structure of materials at atomic resolution. However, HRTEM images, generally speaking, are not directly interpretable and also suffer from aberrations introduced by the objective lens. Last decade the resolution of HRTEM images is greatly improved by utilization of spherical aberration correctors [1]. Direct interpretation of HRTEM images can be achieved by restoring the amplitude and phase of the specimen exit-wave function using electron holographic met such as Through Focus Series Reconstruction (TFSR) and off-axis electron holography [2, 3]. Such reconstruction methods provide an aberration free complex exit-wave function and reconstructed exit waves also benefits from improved signal to noise ratio compared to a single electron micrograph, making direct imaging of atom columns with high precision and accuracy [4]. The phase and amplitude of the reconstructed exit wave can also be used to quantitatively analyze the atomic column composition and positions, respectively [4].

Integrated differential phase contrast (iDPC) STEM

In this talk we present Integrated Differential Phase Contrast (iDPC) STEM [1-3], an electron microscopy (EM) technique that directly images the electrostatic potential field produced by charged particles forming the sample. The electrostatic potential field of the sample has clear maxima at the atomic core positions. Therefore it represents an ideal sample map and is the ultimate goal for any EM imaging technique. For thin samples, the phase of the transmission function of the sample is directly proportional to the projected electrostatic potential field. The iDPC-STEM is therefore also a direct phase imaging technique. For non-magnetic samples we know from basic electrostatics that the electric field of the sample (which is a conservative vector field) is the gradient (differential) of the electrostatic potential field of the sample (a scalar field). An electron passing the sample is influenced by this electric field. If the sample is thin, the electric field at the impact point deflects the electron proportionally to its inplane component. This deflection can be measured by detecting the position of the electron at the detector in the far field. Measurement of the electron (beam) deflection is the subject of Differential Phase Contrast (DPC) techniques [4, 5]. In reality, the motion of the electron is described quantum mechanically with its electron wave function. By focusing the electron wave (the probe) we increase the probability that the electron passes at a certain position and is influenced by the electric field at that position. In the far field, at the detector plane, we obtain a corresponding convergent beam electron diffraction (CBED) pattern, a result of many electrons passing the sample. It was indicated [5] and strictly proven [2] that the mathematical expectation of the electron position in the detector plane, in other words, the center of mass (COM) of the CBED pattern preserves a linear relation to the local electric field at the position of the probe. By scanning the probe, the full COM vector field can be obtained as a linear measure of the electric vector field of the sample. An ideal DPC technique should therefore acquire the COM vector field. A straightforward way of performing this is to use a camera. By recording each CBED pattern COM components can be computed directly [2, 6]. Because this requires fast readouts and stable drift-free samples, in practice COM components are measured using detectors with only a few segments [2, 3]. These methods are fast and enable live imaging, as in (A)BFand (HA)ADF-STEM. By integrating the measured COM vector field we obtain the iCOM scalar field, a linear measurement of the electrostatic potential field of the sample [1-3]. iDPC-STEM is a practical method of obtaining iCOM. In this talk iDPC-STEM using a 4 quadrant segmented detector will be explained. Various experimental results and applications will be presented and compared to standard (S)TEM imaging results. It will be demonstrated that iDPC-STEM is capable of imaging light and heavy elements together, has full low frequency transfer and is a low dose technique.

Integrated Differential Phase Contrast (iDPC) STEM: A New Atomic Resolution STEM Technique To Image All Elements Across the Periodic Table

A new, recently introduced Integrated Differential Phase Contrast (iDPC) STEM imaging technique [1] is enabling live imaging of the phase of the transmission function of thin samples. One of the first striking advantages of this new technique is that it is able to image light (C, O, N ...) and heavier elements (Sr, Ti, Ga ...) together in one image whereas a standard (HA)ADF-STEM image shows only the heavier atoms. Figure 1 shows an example of SrTiO3 imaged using the conventional ADF-STEM technique vs. our new iDPC-STEM technique. The oxygen columns and carbon contamination (low frequency information) are clearly visible in the latter and missing in the former.