Esem 2.5

[Robyn Ruder]

ESEMis a variety of SEM called environmental scanning electron microscope. It can produce images of sufficient quality and resolution with the samples being wet or contained in low vacuum or gas. This greatly facilitates imaging biological samples that are unstable in the high vacuum of conventional electron microscopes. The major disadvantage of transmission electron microscope is the need for extremely thin sections of the specimens, typically about 100 nanometers. Biological specimens are typically required to be chemically fixed, dehydrated and embedded in a polymer resin to stabilize them sufficiently to allow ultrathin sectioning. Sections of biological specimens, organic polymers and similar materials may require special treatment with heavy atom labels in order to achieve the required image contrast.

ESEM is especially useful for non-metallic, uncoated and biological materials. The presence of gas, mainly Argon, around a sample permits to work with pressure greater than 500 Pa compared to conventional SEM requirements samples under vacuum about 10-3 to 10-4 Pa. This vacuum level creates the possibility to operate on non-conductive samples without any preparation or hydrated specimens without charging.

In a Transmission Electron Microscope (TEM), the electron beam is accelerated by an anode typically at +100 keV (40 to 400 keV) with respect to the cathode, focused by electrostatic and electromagnetic lenses, and transmitted through the specimen that is in part transparent to electrons and in part scatters them out of the beam. When it emerges from the specimen, the electron beam carries information about the structure of the specimen that is magnified by the objective lens system of the microscope.

A transmission electron microscope can achieve better than 50 pm resolution and magnifications of up to about 10,000,000x whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000x. Generally, the image resolution of an SEM is at least an order of magnitude poorer than that of a TEM. However, because the SEM image relies on surface processes rather than transmission, it is able to image bulk samples up to many centimeters in size and (depending on instrument design and settings) has a great depth of field, and so can produce images that are good representations of the three dimensional shape of the sample.

The Scanning Transmission Electron Microscope (STEM) rasters a focused incident probe across a specimen that (as with the TEM) has been thinned to facilitate detection of electrons scattered through the specimen. The high resolution of the TEM is thus possible in STEM. The focusing action (and aberrations) occurs before the electrons hit the specimen in the STEM, but afterward in the TEM.

Focused ion beam, also known as FIB, is a technique used particularly in the semiconductor industry, materials science and increasingly in the biological field for site-specific analysis, deposition, and ablation of materials. A FIB setup is a scientific instrument that resembles a scanning electron microscope (SEM). However, while the SEM uses a focused beam of electrons to image the sample in the chamber, a FIB setup uses a focused beam of ions instead. Unlike an electron microscope, FIB is inherently destructive to the specimen.

When the high-energy gallium ions strike the sample, they will sputter atoms from the surface. Gallium atoms will also be implanted into the top few nanometers of the surface, and the surface will be made amorphous. A FIB-SEM consists in a system with both electron and ion beam columns, allowing the same feature to be investigated using either of the beams. A FIB-SEM system uses a beam of Ga+ ion to mill into the surface to locate a feature or defect of interest. The integrated SEM then uses a focused beam of electrons to image the sample in the chamber.

A collection of functions developed to support the tutorial on using Exploratory Structural Equiation Modeling (ESEM) (Asparouhov & Muthn, 2009) ) with Longitudinal Study of Australian Children (LSAC) dataset (Mohal et al., 2023) . The package uses 'tidyverse','psych', 'lavaan','semPlot' and provides additional functions to conduct ESEM. The package provides general functions to complete ESEM, including esem_c(), creation of target matrix (if it is used) make_target(), generation of the Confirmatory Factor Analysis (CFA) model syntax esem_cfa_syntax(). A sample data is provided - the package includes a sample data of the Strengths and Difficulties Questionnaire of the Longitudinal Study of Australian Children (SDQ LSAC) in sdq_lsac(). 'ESEM' package vignette presents the tutorial demonstrating the use of ESEM on SDQ LSAC data.

Structural Equation Modeling (SEM) is a powerful tool for confirming multivariate structures and is well done by the lavaan, sem, or OpenMx packages. Because they are confirmatory, SEM models test specific models. Exploratory Structural Equation Modeling (ESEM), on the other hand, takes a more exploratory approach. By using factor extension, it is possible to extend the factors of one set of variables (X) into the variable space of another set (Y). Using this technique, it is then possible to estimate the correlations between the two sets of latent variables, much the way normal SEM would do. Based upon exploratory factor analysis (EFA) this approach provides a quick and easy approach to do exploratory structural equation modeling.

Factor analysis as implemented in fa attempts to summarize the covariance (correlational) structure of a set of variables with a small set of latent variables or ``factors". This solution may be `extended' into a larger space with more variables without changing the original solution (see fa.extension. Similarly, the factors of a second set of variables (the Y set) may be extended into the original (X ) set. Doing so allows two independent measurement models, a measurement model for X and a measurement model for Y. These two sets of latent variables may then be correlated for an Exploratory Structural Equation Model. (This is exploratory because it is based upon exploratory factor analysis (EFA) rather than a confirmatory factor model (CFA) using more traditional Structural Equation Modeling packages such as sem, lavaan, or Mx.)

Although the output seems very similar to that of a normal EFA using fa, it is actually two independent factor analyses (of the X and the Y sets) that are then mutually extended into each other. That is, the loadings and structure matrices from sets X and Y are merely combined, and the correlations between the two sets of factors are found.

Interbattery factor analysis was developed by Tucker (1958) as a way of comparing the factors in common to two batteries of tests. (Currently under development and not yet complete). Using some straight forward linear algebra It is easy to find the factors of the intercorrelations between the two sets of variables. This does not require estimating communalities and is highly related to the procedures of canonical correlation.

The difference between the esem and the interbattery approach is that the first factors the X set and then relates those factors to factors of the Y set. Interbattery factor analysis, on the other hand, tries to find one set of factors that links both sets but is still distinct from factoring both sets together.

principal for principal components analysis (PCA). PCA will give very similar solutions to factor analysis when there are many variables. The differences become more salient as the number variables decrease. The PCA and FA models are actually very different and should not be confused. One is a model of the observed variables, the other is a model of latent variables.

predict.psych to find predicted scores based upon new data, fa.extension to extend the factor solution to new variables, omega for hierarchical factor analysis with one general factor. codefa.multi for hierarchical factor analysis with an arbitrary number of higher order factors.

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