Basic Imaging Theory

Because light is a wave, its transmission through apertures is, perforce, described by the wave equation. The presence of an aperture modifies the propagation of such waves relative to transmission through free space or air. 

Walker, Reduction of photoresist standing wave effects by post exposure bake, IEEE Trans. Electron Dev. ED-22(7), 464 466 (1975). 

Mathematically, these modifications serve as the boundary conditions for the wave 

Optics for photolithography, in Microlithography Science and Technology, J.R. Sheats and B.W. Smith, Eds., p. 172, Marcel Dekker, New York (1998). 

Let us define the objective lens pupil (aperture) function P for an ideal lens as the portion of light that enters the lens it is 1 inside the aperture and 0 outside  

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One such approach to counter the effects of spherical aberration is to record a through-focus series, which allows reconstruction of the electron exit-wave function and thereby removal of the spherical aberration. The basic idea of this reconstruction approach, as implemented in the Truelmage software package, will be described after a simplified introduction to HRTEM imaging theory (for more details see Williams and Carter 1996, Reimer 1984, Spence 1988). Furthermore, two application examples are shown to discuss the benefits of focal-series reconstruction and illustrate the information that can be obtained. 

Sutton M. A., Orteu J.-J. and Schreier H. (2009) Image correlation for Shape, Motion and Deformation Measurements Basic Concepts, Theory and Applications, Springer, New York. 

Theory and Equipment. The basic principle behind nuclear medical imaging is that a radiopharmaceutical can be introduced into the body which emits radiation detectable outside of the body. Radiopharmaceuticals are biologically active and have a short half-life (Si/q)- The detectable radiation... 

B. Blumich 2000, NMR Imaging of Materials, Clarendon Press, Oxford, 568 pp. Focus on theory and basics, collection of specific applications in the sense of examples some flow topics covered. 

Price, W.S. 1998a. Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion. II. Experimental aspects. Basic theory. Concepts in Magn. Reson. 10, 197-237. Price, W.S. 1998b. NMR imaging. In Annual Reports on NMR Spectroscopy (G.A. Webb, ed.), Vol. 34, pp. 140-216. Academic Press, New York. 

This section introduces the reader to the basic principles of MRI and the concept of the k-space raster. The basic MRI pulse sequence, the spin-echo imaging sequence, is described at this point. For more detailed discussion of the background theory of MRI the interested reader should refer to texts by Callaghan5 and Kimmich.6... 

Values of the radiative rate constant fcr can be estimated from the transition probability. A suggested relationship14 57 is given in equation (25), where nt is the index of refraction of the medium, emission frequency, and gi/ga is the ratio of the degeneracies in the lower and upper states. It is assumed that the absorption and emission spectra are mirror-image-like and that excited state distortion is small. The basic theory is based on a field wave mechanical model whereby emission is stimulated by the dipole field of the molecule itself. Theory, however, has not so far been of much predictive or diagnostic value. 

Thus, according to these theories, all univalent (1 1) electrolytes should behave the same way. However, this is not what was observed experimentally. Solutions of different 1 1 electrolytes (e.g., NaCl, NaBr, Nal, KI) show species-specific behavior. In order to interpret this specific behavior, Grahame (5) proposed a new model of the interphase the triple-layer model. The basic idea in the interpretation of the ion-specific behavior is that anions, when attracted into the interphase, may become dehydrated and thus get closer to the electrode. Each anion undergoes this to a different extent. This difference in the degree of dehydration and the difference in the size of ions results in the specific behavior of the anions. Ions that are partially or fully dehydrated are in contact with the electrode. This contact adsorption of ions allows short-range forces (e.g., electric image forces) to act between the metal elec-... 

A quantitative understanding of molecular electronic structure is vital to advances in chemical imaging. This understanding can be achieved through molecular dynamics (MD) simulations. In order to improve MD simulations, a number of specific areas need to be addressed in basic molecular dynamics theory. There is a need to develop a next generation of readily accessible, easy-to-use MD simulation packages. 

Chemical imaging would be invigorated by innovations in basic theory of molecular dynamics. At the same time, the specific needs of chemical imaging should play a role in guiding the development of MD theory. 

Thus far, we have reviewed basic theories and experimental techniques of Raman spectroscopy. In this chapter we shall discuss the principles, experimental design and typical applications of Raman spectroscopy that require special treatments. These include high pressure Raman spectroscopy, Raman microscopy, surface-enhanced Raman spectroscopy, Raman spectroelectro-chemistry, time-resolved Raman spectroscopy, matrix-isolation Raman spectroscopy, two-dimensional correlation Raman spectroscopy, Raman imaging spectrometry and non-linear Raman spectroscopy. The applications of Raman spectroscopy discussed in this chapter are brief in nature and are shown to illustrate the various techniques. Later chapters are devoted to a more extensive discussion of Raman applications to indicate the breadth and usefulness of the Raman technique. 

Refs. [i] Conway BE (1999) Electrochemical processes involving H adsorbed at metal electrode surfaces. In Wieckowski A (ed) Interfacial electrochemistry, theory, experiment, and applications. Marcel Dekker, New York, pp 131-150 [ii] Climent V, Gomez R, Orts JM, Rodes A, AldazA, Feliu JM (1999) Electrochemistry, spectroscopy, and scanning tunneling microscopy images of small single-crystal electrodes. In Wieckowski A (ed) Interfacial electrochemistry, theory, experiment, and applications. MarcelDekker, New York, pp 463-475 [Hi] Calvo E] (1986) Fundamentals. The basics of electrode reactions. In Bamford CH, Compton RG (eds) Comprehensive chemical kinetics, vol. 26. Elsevier, Amsterdam, pp 1-78... 

Chapter 1 is concerned with the fundamental principles of image formation by a lens. These principles were first formulated by Ernst Abbe in 1873 and are basic to the chapters that follow. According to the Abbe theory, the image of an illuminated object is the result of a twofold diffraction process. First, the Fraunhofer diffraction pattern of the object is formed in the back focal plane of the lens. Second, the light waves travel... 

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