Image approximation

Hor the periodic boundary conditions described below, the ctitoff distance is fixed by the nearest image approximation to be less than h alf th e sm allest box len gth. W ith a cutoff an y larger, more than nearest images would be included. 

Friedman H L 1975. Image Approximation to the Reaction Field. Molecular Physics 29 1533-1543. 

Figure 2. AFM images, approximately 2.5 im on a side, of phlogopite (001) surfaces after pretreatment acid etch and rinse (top), and after pretreatment acid etch, rinse, and 24 hours in DI water equilibrated with air (bottom). Both images are taken from the same area of the same sample, although the bottom image is rotated about 30 counterclockwise from the top image. The scale bars in both images are 0.5 pm long. See text for additional details.

An alternative application of these ideas has been suggested by Fried-man. In this there are no periodic images. Rather the whole of the sample of N particles is enclosed in a fixed cavity within a dielectric continuum. The reaction field is estimated by an image approximation. In this way one avoids problems inherent in both Ewald and truncation methods, problems that are discussed below. This gain is at the expense of reintroducing surface effects, however. Friedman designed this approach for a particular type of problem in which the surface difficulties may be unimportant, but for conventional thermodynamic applications they are likely to give trouble. We will not discuss this proposal further in this chapter. 

Contrast Ratio Cq The contrast ratio is established on the basis of the ratio of the amplitude of the unattenuated radiation to the amplitude after attenuation through a test piece. This test piece is a lead disk which is mounted in the middle of the image converter it masks approximately 10% of the surface of the image converter. 

In the usual approximation of the object as a weak phase/weak amplitude object, this scattered wave can be used to calculate the intensity of the image transfomi as... 

The factor A has been measured for a variety of samples, indicating that the approximation can be applied up to quasi-atomic resolution. In the case of biological specimens typical values of are of the order of 5-7%, as detemiined from images with a resolution of better than 10 A [37,38]- For an easy interpretation of image contrast and a retrieval of the object infomiation from the contrast, such a combination of phase and amplitude hifomiation is necessary. 

Figure Bl.22.7. Left resonant seeond-hannonie generation (SHG) speetnimfrom rhodamine 6G. The inset displays the resonant eleetronie transition indueed by tire two-photon absorption proeess at a wavelength of approximately 350 mn. Right spatially resolved image of a laser-ablated hole in a rhodamine 6G dye monolayer on fiised quartz, mapped by reeording the SHG signal as a fiinetion of position in the film [55], SHG ean be used not only for the eharaeterization of eleetronie transitions within a given substanee, but also as a mieroseopy tool.

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