Diffraction limited resolution

B1.18.5.7 THE FUTURE RESOLUTION BEYOND THE DIFFRACTION LIMIT IN CONFOCAL FLUORESCENCE... 

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). 

Using a visible light probe NSOM is the eadiest of the probe scopes, at least in conception, and is another apparent exception to the diffraction-liinited resolution rule, in that NSOM illuminates an object with a beam of visible light smaller than the diffraction limit. The resolution then is limited only by the size of that beam. To achieve this, light issuing from a very tiny aperture at the end of a glass capillary scans a very near sample. The tip must be located on the order of X/2 from that surface. Resolution in the range of 10—20 nm has been achieved (31). 

Sample preparation is straightforward for a scattering process such as Raman spectroscopy. Sample containers can be of glass or quartz, which are weak Raman scatterers, and aqueous solutions pose no problems. Raman microprobes have a spatial resolution of - 1 //m, much better than the diffraction limit imposed on ir microscopes (213). Eiber-optic probes can be used in process monitoring (214). 

It gives the crossover between diffraction-limited and turbulence-limited resolution. For aperture diameters smaller than ro, close to diffraction limited imaging is possible without phase correction, for aperture diameters larger than ro, the resolution is limited by the turbulence. For a circular aperture of diameter D, the phase variance over the aperture is... 

Interferometry in astronomy is used to surpass the limitations on angular resolution set by the Earth s atmosphere (i. e., speckle interferometry), or by the diffraction of the aperture of a single telescope. We will focus in this lecture on interferometry with multiple telescope arrays with which it is possible to obtain information on spatial scales of the source beyond the diffraction limit of its member telescopes. 

The resolution of an acoustic lens is determined by diffraction limitations, and is 7 = 0.51 /N.A [95], where is the wavelength of sound in liquid, and N.A is the numerical aperture of the acoustic lens. For smaller (high-frequency) lenses, N.A can be about 1, and this would give a resolution of 0.5 Kyj. Thus a well designed lens can obtain a diameter of the focal spot approaching an acoustic wavelength (about 0.4 /Ltm at 2.0 GHz in water). In this case, the acoustic microscope can achieve a resolution comparable to that of the optical microscope. 

Rugar, D., Resolution Beyond the Diffraction Limit in the Acoustic Microscope A Nonlinear Effect, J. Appl. Phys., Vol. 56,1984, pp. 1338-1346. 

Similarly, the first-order expansion of the p° and a of Eq. (5.1) is, respectively, responsible for IR absorption and Raman scattering. According to the parity, one can easily understand that selection mles for hyper-Raman scattering are rather similar to those for IR [17,18]. Moreover, some of the silent modes, which are IR- and Raman-inactive vibrational modes, can be allowed in hyper-Raman scattering because of the nonlinearity. Incidentally, hyper-Raman-active modes and Raman-active modes are mutually exclusive in centrosymmetric molecules. Similar to Raman spectroscopy, hyper-Raman spectroscopy is feasible by visible excitation. Therefore, hyper-Raman spectroscopy can, in principle, be used as an alternative for IR spectroscopy, especially in IR-opaque media such as an aqueous solution [103]. Moreover, its spatial resolution, caused by the diffraction limit, is expected to be much better than IR microscopy. 

It is therefore clear that MaxEnt redistribution of all electrons, using a uniform prior prejudice and carried out in the absence of very high-resolution diffraction measurements, cannot be expected to reproduce a physically acceptable picture of atomic cores. The reconstruction of total electron densities from limited-resolution diffraction measurements amounts to a misuse of the MaxEnt method, especially when the prior prejudice is uniform. 

Global Raman imaging can be a fast and simple technique, providing high lateral spatial resolution (down to the diffraction limit corresponding with the excitation laser wavelength) images of the sample of interest. There are several techniques available. 

Figures 21(a) and 21(b) show the SEM micrographs of the freeze-fractured cross-section of the film used in the construction of the bag. There are two distinct layers and possibly a third very much thinner tie layer. The outside layer is a layer of nominal thickness 13 pm. The inside layer is much thicker and is approximately 70 pm thick. At the interface between the outer and inner layers the apparent very thin tie layer is about 1 pm thick. This is too thin to be identified by FUR microscopy on a cross-section of the sample, since the technique is diffraction-limited, which means that layers of about 10 pm thickness or greater can only be readily identified [1]. The tie layer thickness is also probably too thin for fingerprinting by Raman microspectroscopy on a cross-section the lateral spatial resolution of Raman microspectroscopy is about 1-2 pm.

Rotational spectroscopy and microwave astronomy are the most accurate way to identify a molecule in space but there are two atmospheric windows for infrared astronomy in the region 1-5 im between the H2O and CO2 absorptions in the atmosphere and in the region 8-20 xrn. Identification of small molecules is possible by IR but this places some requirements on the resolution of the telescope and the spacing of rotational and vibrational levels within the molecule. The best IR telescopes, such as the UK Infrared Telescope on Mauna Kea in Hawaii (Figure 3.13), are dedicated to the 1-30 xm region of the spectrum and have a spatial resolution very close to the diffraction limit at these wavelengths. 

Comparisons of the measured coupling constants to the geometry of the H-bond are hampered by the limited availability of very high-resolution diffraction data. Especially, no crystallographic data are available for most of the nucleic acids for which H-bond cou-... 

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