Angle resolution

Shot noise in the rotation experiments is very small. The rms fluctuation in angle due to shot noise in the detected photons is 

The lasers used in these experiments produce typical powers greater than 2mW. The detectors often are of nearly unity quantum efficiency. Thus, in one second, A shot 10 rad. Even with the decreased efficiency of photomultiplier tubes, and less light intensity in experiments which use many absorption lengths of vapor, one finds A shot 10 rad in an observation time (A ) = 1 sec. In practice, the noise in the measured angles often turns out to be larger than the shot noise limit, owing to a combination of mechanical and optical instabilities, and detector noise in some cases. In the most recent experiments, 10 rad can be resolved in less than 1 min of averaging time. 

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Fajardo, C.M. and V. Sick, Flow field assessment in a fired spray-guided spark-ignition direct-injection engine based on UV particle image velocimetry with sub crank angle resolution. Proceedings of the Combustion Institute, 31(2) 3023-3031, 2007. 

In summary, the H + HD reaction shows little sign of resonance scattering in the ICS. Furthermore, the product distributions without angle resolution show no unusual behavior as functions of energy that might indicate resonance behavior. On the other hand, the forward peaking in the angular product distribution does appear to reveal resonance structure. Since time-delay analysis is at present not possible in a molecular beam experiment, it is the combination of a sharp forward peak with the unusual... 

Surface chemical changes created by these surface chemical reactions will be monitored by Electron Spectroscopy for Chemical Analysis (ESCA)(2), a very powerful spectroscopic technique for investigating surface compositions extending from 1-20 monolayers in depth from the surface. When the spectrometer is equipped with angle resolution capability, it also offers a means of non-destructive depth profiling of the upper 50A of substrate layers. 

For ANITA, we expect the time resolution between antenna clusters to improve to a At - 0.1 ns due to the increase in the number of measurements by the full array. Using 3.3 m vertical separation between the upper and lower antenna arrays, d, the expected intrinsic zenith angle resolution a is... 

Slits. Slits are used to shape the beam and to reduce parasitic scatter aroimd the primary beam. The latter is of overriding importance in small-angle scattering beamlines since it is the amoimt of parasitic scatter that is the most important factor in determining the possible low angle resolution and therefore the maximum size of the structures that can be observed (see Fig. 3). 

Fig. 3. Schematic description of an x-ray scattering beamline. The optical system is represented by a lens. The parasitic scatter cone is represented by the gray area. The scattering information which falls in this region is useless since the parasitic scatter is orders of magnitude more intense than the scattering pattern itself The importance of the positioning of the slits in determining the extent of the parasitic scatter cone, which is the limiting factor in achieving low angle resolution, can be observed. Most beamlines are in fact equipped with three or more slit systems between the last optical element and the sample position.

Fig. 33. Small-angle diffraction pattern of a sheared micellar-forming diblock copolymer. The sample was sheared and slowly cooled down on-line so that the formation of the hexagonal structure could be observed. The low angle resolution is about 120 nm. Unpublished results, courtesy of G.P.R Fairclough, R.N. Young, L.Messe, A.J. Ryan, W. Bras.

In X-ray scattering experiments the low angle resolution depends on which SAXS beam line one utilises. However, even with the best collimated beam lines the useable real space size range is limited to about 200 nm in the transmission geometry. At present the achievable time resolution is hardly dictated by the photon flux but more by the sample environments which are required to perturb the samples controlled and homogeneously over the dimensions of the X-ray beam size. X-ray experiments down to a millisecond are possible but the sample environments generally impose limits of around 0.1 sec/frame. Specifically in combination with XAS experiments the time-resolution is dominated by the amount of time it takes for the spectroscopy data to be collected. The fastest energy scans can be done in 5-10 seconds. 

The sample detector distance and the photon energy ultimately determine the low angle resolution which is achievable. In many cases it is most beneficial to be able to observe as large a q-range as possible instead of optimising the low angle resolution. If both the Guinier as well as the Porod... 

In the standard reflection measurement (Fig. 19-15(a) the sample is fixed on arotation stage in order to check the best angle resolution. The main problem of this configuration is that is difficult to use low angles of excitation. To overtake this problem the back excitation configiuation can be used (Fig. 19-15(b)). 

A conventional SAXS apparatus whose optical systems consist upally of some kind of slit system has an upper limit of resolution about 1000 A. This limit is caused by the requirement to remove the influence of strong direct beam. To get a much better small-angle resolution for investigation of micron-size structures, it is necessary to make the beam width very narrow or extend the camera length to several hundred meters. The former technique reduces the intensity dramatically and is mechanically very difficult, and the latter is impossible on a laboratory scale... 

On the other hand, there have frequently been requests to make the small-angle resolution of SAXS instruments much higher for study of the structure of various systems. Our direct incentive for the higher resolution was related to, among other things, the questions ... 

The slits themselves play an important role in determining the spectral resolution and throughpnt of the monochromator. In most cases, the positions of the entrance and exit slits are fixed but the width is adjustable. Typical sht widths can vary from a few microns to several millimeters but it is usual for the exit and entrance slits to be the same width. Several characteristics are important in a monochromator, snch as the linear dispersion,/-number of solid angle, resolution, stray light rejection, and thronghput factors. These factors are described in more detail below. 

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