Limit of resolution

X-Ray Microscopy. Because of the short wavelength of x-rays, they have, for nearly 100 years, held out the hope of being utilized in order to significantly lower the diffraction limit of resolution when visible light is used. The difficulties of focusing x-rays and the relative weakness of x-ray sources have, until recently, fmstrated efforts to teach that goal (25). 

A number of devices suggest the possibiUty of improvement in the basic limitations of resolution and sensitivity for single-photon instmmentation. One device (24) employs an array of pinholes in a hemispherical shield that Hes inside a hemispherical soHd-state detector array. Simulations and initial experience using early models have suggested that the device could achieve a resolution in the brain of less than 3 or 4 mm and possibly as low as 1 mm. 

Whereas a bacterial cell like a staphylococcus might be lOOOnm in diameter, the largest of the human pathogenic viruses, the poxviruses, measure only 250 nm along their longest axis, and the smallest, the poliovirus, is only 28 nm in diameter. They are mostly, therefore, beyond the limit of resolution of the light microscope and have to be visualized with the electron microscope. 

Electron Microscopy can be used for resolution of smaller objects the practical limit of resolution being a few angstrom units. Electron Microscopy has been used in the study of the morphology of crystalline polymers. The usual techniques of replication, heavy-metal shadowing, and solvent etching are widely used. The direct observation of thin specimens, like polymer single crystals, is also possible and permits the observation of the electron-diffraction pattern of some specimen area, which is invaluable for... 

Epoxies are good candidates for solid state C studies because of their relative chemical simplicity but even so some spectral lines overlap, as was shown in Fig. 2. We enquire into the limits of resolution to see what improvements can be expected. 

This result is equivalent to Eq. (5.12), except that the left-hand side is no longer an integral over all space, but a summation up to the limit of resolution. 

This chapter has attempted to give some flavor of the historical development of nonlinear methods. Early investigators of these methods expended great effort in overcoming the popular notion that bandwidth extrapolation was not possible or practical. It was, for example, believed that the Rayleigh limit of resolution was a limit of the most fundamental kind—unassailable by mathematical means. To be sure, the popular notion was reinforced by a long history of misfortune with linear techniques and hypersensitivity to noise. Anyone who still needs to be convinced of the virtues of the nonlinear methods would benefit from reading the paper by Wells (1980) the nonlinear point of view is nowhere else more clearly stated. 

Jhe theoretical lower limit of resolution of the light microscope is about 0.2 micron—i.e., 2000 A. This figure can be reduced in favorable circumstances by using phase-contrast or interference microscopy. Ultraviolet microscopy of coal was attempted at the Division of Coal Research, but without success owing to the opacity of coal to ultraviolet radiation. Vigorous attempts are being made to develop x-ray microscopy, and its limit of resolution is already an order better than that of the light microscope. 

Colloidal particles are often too small to permit direct microscopic observation. The resolving power of an optical microscope (i.e. the smallest distance by which two objects may be separated and yet remain distinguishable from each other) is limited mainly by the wavelength A of the light used for illumination. The limit of resolution 8 is given by the expression... 

Particle sizes as measured by optical microscopy are likely to be in serious error for diameters less than c. 2 pm, although the limit of resolution is some ten times better than this (see Table 3.1). 

Two techniques for overcoming the limitations of optical microscopy are of particular value in the study of colloidal systems. They are electron microscopy36-37, in which the limit of resolution is greatly extended, and dark-field microscopy, in which the minimum observable contrast is greatly reduced. 

The optical microscope is one of the most basic instruments for particle sizing and is applicable to a typical size range of 0.8 /xm to 150 /xm. The lower limit is a result of the diffraction effects on the particle image as observed in a microscope. The limit of resolution of an optical microscope can be estimated by (Yamate and Stockham, 1977)... 

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