The Ultimate Resolution Limit

In Chap.10 several techniques have been presented which allow the Doppler width to be overcome. Provided that all other sources of line broadening could be eliminated, the spectral resolution of these techniques can reach at least in principle the limit imposed by the natural linewidth at 

In this chapter we discuss several techniques which can reduce or even completely avoid time-of-flight broadening. Some of these methods have already been realized experimentally while others are only theoretical proposals which could not be proved up to now. These techniques allow ultrahigh resolution, in some cases even within the natural linewidth. This raises the interesting question about the ultimate resolution limit and the experimental or fundamental factors that determine such a limit. 

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Columns filled with polymer solutions are extremely simple to prepare, and the packing can easily be replaced as often as desired. These characteristics make the pseudostationary phases excellent candidates for use in routine CEC separations such as quality control applications where analysis and sample profiles do not change much. However, several limitations constrain their widespread use. For example, the sample capacity is typically very low, pushing typical detection methods close to their sensitivity limits. Additionally, the migration of the pseudostationary phase itself may represent a serious problem, e. g., for separations utilizing mass spectrometric detection. The resolution improves with the concentration of the pseudostationary phase. However, the relatively low solubility of current amphiphilic polymers does not enable finding the ultimate resolution limits of these separation media [88]. 

J.L. Hall, Sub-Doppler spectroscopy, methane hyperfine spectroscopy and the ultimate resolution limit, in Colloq. Int. due CNRS, vol. 217 (Edit, due CNRS, Paris, 1974), p. 105... 

The wealth of information obtained on the general principles of crystalline bacterial cell surface layers, particularly on their structure, assembly, surface, and molecular sieving properties have revealed a broad application potential. Above all, the repetitive physicochemical properties down to the subnanometer-scale make S-layer lattices unique self-assembly structures for functionalization of surfaces and interfaces down to the ultimate resolution limit. S-layers that have been recrystallized on solid substrates can be used as immobilization matrices for a great variety of functional molecules or as templates for the fabrication of ordered and precisely located nanometer-scale particles as required for the production of biosensors, diagnostics, molecular electronics, and nonlinear optics [2,3,6]. 

J.L. Hall Sub-Doppler spectroscopy methane hyperfine spectroscopy and the ultimate resolution limit, in Laser Spectroscopy II, ed. by S. Haroche, J.C. Pebay-Peyroula, T.W. Hansch, S.E. Harris, Lecture Notes Phys., Vol.43 (Springer, Berlin, Heidelberg 1975) p.l05... 

J.L. Hall "Sub-Doppler-Spectroscopy, Methane Hyperfine Spectroscopy and the Ultimate Resolution Limits", in Ref. 1.7, p. 105 ff... 

The composite filter 7(g)) may either be the true inverse filter, truncated for oo large if necessary, or any of the variations described in Section IV. In their original work, Rendina and Larson chose 7(g)) = (co)/t(co), where //(co) is a Gaussian line-broadening function that limits the ultimate resolution obtainable but yields a manageable 7(g)). For their studies Rendina and Larson used Ns = 4. 

When using a pneumatic nebulizer, an unheated spray chamber, and a quadrupole mass spectrometer, ICP-MS detection limits are 1 part per trillion or less for 40 to 60 elements (Table 3.4) in clean solutions. Detection limits in the parts per quadrillion range can be obtained for many elements with higher-efficiency sample introduction systems and/or a magnetic sector mass spectrometer used in low-resolution mode. Blank levels, spectral overlaps, and control of sample contamination during preparation, storage, and analysis often prohibit attainment of the ultimate detection limits. 

Modern frequency meters allow fast measurements with good resolution, i.e., 60 ms (Philips PM6654) or 100 ms (HP5384) for 0.1 Hz resolution. The ultimate resolution of the QCM is limited, however, to miliseconds by the time required in equilibrating the crystal with the deposited mass, which is determined by the operating frequency and the quality factor of the QCM [3]. 

Finally, it is worthwhile imagining the possible ultimate resolution limits. So, if we had the perfect switchable marker emitting a bunch of m 3> 10 photons, what would we obtain for the stochastic single molecule switching mode We would obtain the (average) position of a molecule with a precision of a fraction of a nanometer. While this information would be invaluable for mapping the sample, it would not tell us much about the molecule itself. 

For conventional molecules with relatively small unit cells and low thermal parameters, all the theoretically possible data may be collected and included in the Fourier synthesis. The value X/2 is then the practical as well as the theoretical resolution limit. For macromolecular crystals, X/2 is never the practical limit, simply because the consistency of structural detail from molecule to molecule, and unit cell to unit cell throughout the crystal is not adequate. Thus, beyond a certain Bragg spacing, usually considerably short of the theoretical limit of 0.77 A for CuK radiation, the intensities decline and ultimately become unobservable. In... 

Fourier synthesis, as shown by the optical analogy in Figure 4.54. A resolution of 6 A reveals the course of the polypeptide chain but few other structural details. The reason is that polypeptide chains pack together so that their centers are between 5 A and 10 A apart. Maps at higher resolution are needed to delineate groups of atoms, which lie between 2.8 A and 4.0 A apart, and individual atoms, which are between 1.0 A and 1.5 A apart. The ultimate resolution of an x-ray analysis is determined by the degree of perfection of the crystal. For proteins, this limiting resolution is usually about 2 A. 

The resolution of X-ray microscopy is between the visible light microscope on the one hand and the electron microscope on the other. Instruments available today deliver about five times better resolution than visible light microscopes on a routine basis and the best achievable resolution today is 20-30 nm. The ultimate resolution of X-ray microscopy is limited, in principle, only by the wavelength ... 

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