Resolution limitations

Spatial Resolution or Unsharpness The total resolution of the system is to be established via a platinum duplex wire penetrameter according to EN 462-5. The resolution limit that has been determined by this IQI can be directly converted to the system unsharpness. 

Recently commercially available X-ray systems for laminography have a spatial resolution limited to hundred microns, which is not enough for modem multilayer electronic devices and assembles. Modem PCBs, flip-chips, BGA-connections etc. can contain contacts and soldering points of 10 to 20 microns. The classical approach for industrial laminography in electronic applications is shown in Fig.2. 

Hell S W and Kroug M 1995 Ground-state-depletion fluorescence microscopy a concept for breaking the diffraction resolution limit Appl. Phys. B 60 495-7... 

Finally, instmmental broadening results from resolution limitations of the equipment. Resolution is often expressed as resolving power, v/Av, where Av is the probe linewidth or instmmental bandpass at frequency V. Unless Av is significantly smaller than the spectral width of the transition, the observed line is broadened, and its shape is the convolution of the instrumental line shape (apparatus function) and the tme transition profile. 

The electron probe X-ray microanalyzer provides extraordinary power for measuring the elemental composition of solid matter with pm lateral spatial resolution. The spatial resolution, limited by the spread of the beam within the specimen, permits pg samples to be measured selectively, with elemental coverage from boron to the actinides. By incorporating the imaging capability of the SEM, the electron probe X-ray microanalyzer combines morphological and compositional information. 

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. 

Fig. 7a, b. PMIM-image of (a) a poly-p-bromostyrene surface [118], (b) a PS/polybutadiene diblock copolymer, PS-b-PB, at approximately 100 fold magnification. The lateral resolution is of the order of 1 pm while the height resolution is of the order of 0.6 nm. The root-mean-square roughness averaged over the area shown is 0.8 nm in (a) close to the resolution limit of the technique. It is much larger (10 nm) in (b) due to the formation of steps after annealing. The scale in z-direction in (a) and (b) is different by a factor of 7... 

TABLE 2—Practical resolution limits and penetration depth in a SAM [100]. 

Operation Frequency Resolution Limit Penetration Depth... 

Ideally one would like to visualize the molecular-scale details at the edge of a droplet to obtain direct information about the molecular nature of wetting. This is not always possible, particularly when these details have dimensions below 300 A, the resolution limit of SPFM. However, the height and curvature of a droplet can usually be measured accurately. These parameters can then be used to obtain an effective contact angle, as defined in Eq. (10). We present here a few examples of this type of study. 

The resolution of the zeolite MR image is 100 x 100 x 100 gm3 and has therefore reached the resolution limit that defines NMR microscopy. For the instrumentation used for this experiment, it will take at least a few milliseconds due to the ramping time of the field gradients. If the mean displacement of the xenon atoms during this experimental time scale reaches the dimension of the voxels or pixels, the resolution limit is reached. For instance, for the aerogel experiments in Figure... 

Figure 1. Amplitudes of the Fourier coefficients of log(model density, from a multipolar tit to 23 K diffraction data protect [45]. Continuous line m(x) = uniform distribution. Dotted line m(x) = core and valence monopoles. The vertical bar marks the experimental resolution limit 0.463 A. 

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