Limiting resolution

In this approach one uses narrow-band continuous wave (cw) lasers for continuous spectroscopic detection of reactant and product species with high time and frequency resolution. Figure B2.5.11 shows an experimental scheme using detection lasers with a 1 MFIz bandwidth. Thus, one can measure the energy spectrum of reaction products with very high energy resolution. In practice, today one can achieve an uncertainty-limited resolution given by... 

The camera actually images the annihilation events, not the radioactive decay events directiy. Thus imaging of high energy positron emitters can have a limiting resolution owing to the range of the positron. 

The resolution of a monochromator is the smallest frequency interval the instrument can separate. The limiting resolution is the bandwidth measured at half height when scanning across an infinitely narrow intense source 22). As already mentioned, the broader excitation line width of Ar+ lasers (0.15 to 0.25 cm-1) compared to that of the He-Ne lasers (0.05 cm-1) means a lower resolution limit when the Ar+ laser is used as a Raman source. 

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... 

The two limitations of optical interferometry, the one-quarter wavelength of light limit and the low resolution, have been addressed by using a combination of a fixedthickness spacer layer and spectral analysis of the reflected beam. The first of these overcomes the minimum film thickness that can normally be measured and the second addresses the limited resolution of conventional chromatic interferometry. 

Atomic force microscope (AFM) is a powerful nanotechnology tool for molecular imaging and manipulations. One major factor limiting resolution in AFM to observe individual biomolecules such as DNA is the low sharpness of the AFM tip that scans the sample. Nanoscale 1,3,5,7-tetrasubstituted adamantane is found to serve as the molecular tip for AFM and may also find application in chemically well-defined objects for calibration of commercial AFM tips [113]. 

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. 

The gas reaction chamber and the objective aperture assembly occupied the gap between the upper and lower objective pole pieces, leading to a gas reservoir around the sample. Such ECELL systems were a major step forward in scientific capability, being used by Gai et al. (3,73-78), Doole et al. (79), Crozier et al. (80), and Goringe et al. (81) to characterize catalysis. Other developments for catalytic studies include an ex situ reaction chamber attached externally to the column of a TEM, for example, by Parkinson and White (82) and Colloso-Davila et al. (83). Reactions were carried out in the ex situ chamber (and not in situ), and the sample was cooled to room temperature and inserted into the column of the TEM (without exposure to the atmosphere) under vacuum. Baker et al. (84) used ETEM at gas pressures of a few mbar with limited resolution, and, in these experiments, representative higher gas pressures were not employed. 

The loading capacity of SEC columns is quite modest compared to interactive modes of chromatography. A rule of thumb dictates that the sample volume capacity is about 2% of the column volume. A typical analytical SEC column with dimensions of 8 x 300 mm has a VM of 10 to 11 ml, providing a sample volume limit of about 200 pi. The mass loading limit for such a column is about 1 to 2 mg. Above these volume and mass limits, resolution will be compromised. Sample capacity will scale in proportion to column volumes for different column lengths and diameters. 

While in the ideal case S(g) according to Eq. (57) clearly reflects the singular behavior at T due to substrate inhomogeneity and/or limited resolution the actual behavior of scattering data is quite smooth see Fig. 13b for an example. A detailed analysis of finite resolution effects on the structure factor of two-dimensional lattice gas models has been presented by Bartelt et af. If the... 

The limited resolution and mass accuracy of the early MALDI-TOF instruments made the combination of MALDI with magnetic sector instruments (Chap. 4.3) desirable, [148,149] but this set-up suffered from low shot-to-shot reproducibility and poor sensitivity getting a full scan spectrum required thousands of laser shots while scanning the magnet. Even though eutectic matrix mixtures were introduced to circumvent such problems, [90,91] the MALDI-magnetic sector combination never became established. 

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