transfer function analysis
Many groups have worked on the forward problem, of simulating images by multislice propagation from upstream to downstream sides of the specimen, followed by simulation of microscope contrast transfer. The latter is also important to image formation in aberration-corrected microscopy.
Our particular application area has focused on real time simulation and inverse problem solving by taking advantage of the speed of the (single-slice) strong-phase-object model of wave-propagation through the specimen, and only first-order models of microscope aberrations. Since many physical processes show up with these fast but simplified models, they serve as a good platform (i) for real-time pedagogical simulators as well as (ii) for first-order inverse problem-solving e.g. using zeros in the transfer function of an experimental specimen image to learn more about the specimen itself (than may be apparent at first glance).
For example at top right, an image we took for an AFRL project shows the hex-BN/C region in a c-ZrO2 box-grain inclusion, found in crystal of 3% carbon-doped ZrB2 being developed by researchers at MST-Rolla for ultra-high temperature application at external leading & trailing edges of hypersonic aerospace-vehicles. Below and at insets of that image you'll find a model for astigmatism based on contrast transfer function zeros which show up in the the image Fourier transform. Downstream, this model might allow one to learn more about the specimen structure shown in the image.
Interpreting image contrast transfer, of course, requires doing '''the inverse problem''' i.e. combining information from the image with plausible optics, scattering and specimen models to make inferences about a larger research problem (e.g. about synthesis, design, or subsystem failure) to which the specimen was related. Interpreting '''image contrast transfer''' is thus one of the '''data analysis skills''' that dovetail with the '''instrumentation skills''' needed to record images, the '''physical manipulation skills''' needed to prepare the specimen, and the '''people skills''' needed to acquire information, the specimen, as well as funding for the instrumentation facility itself.
Models for (i) imaging optics and (ii) illumination scattering from a specimen may be combined with (iii) '''models of a specimen''' to do '''the forward problem''', i.e. to simulate an image if the specimen were known. In the transmission electron microscope case, for example, specimens often contain billions of atoms and may be modeled as collections of atom positions or as finite-sized crystals with specific orientations, surfaces, and internal crystallographic defects.
One also needs to adopt a practical model of '''illumination scattering''' by the specimen. In the transmission electron microscope case, for example, the specimen is generally an unknown or partly-known assemblage of atoms in a solid or nearly-solid array with interatom spacings much larger than the illumination wavelength itself. Electron scattering, particularly from periodic arrays of atoms, is unfortunately quite unlike the kinds of everyday scattering of light to which our innate pattern recognition facilities are adapted. Moreover, models for multi-atom electron scattering can be arbitrarily complex so an ability to choose and justify a particular scattering model is crucial for the credible analyst.
To put the information in images like this to use, one needs to know something about the '''imaging optics''' which delivered the intensities to the film or detector array which recorded the image. This includes things like source geometry and coherence, illumination geometry, and post specimen optics and aberrations.
Images are often used to record information about objects. In other words, they contain correlation information. Our visual systems are in that context highly sophisticated instruments for interpreting the information in images. For instance, not much schooling is needed for a child to see something coming at him which suggests that he should get out of the way.
When it comes to interpreting images outside of our evolved context, e.g. as formed by scattering processes not accessible without modern technology and/or with help from computers, the story is actually quite complex. For example, consider '''the meaning of light and dark regions''' in a transmission electron microscope image of an unknown specimen.
