Radial image

Figure 10.3 Definition of geometrical parameters for a CMA shown for the case of off-axis focusing of a point source (Q). Rt and Ra are the radii of the inner and outer field cylinders, respectively 4, is the radial image distance to the inner cylinder (in analogy, one can introduce a radial source distance ds, in the present case one has ds = R,) z is the total distance between source and image measured along the symmetry axis of the analyser zf is the corresponding distance for the field region is the entrance angle into the analyser (due to symmetry properties this is equal to the exit angle).

Different approaches can be taken to obtain radial images. Radial field gradients can be applied by the use of dedicated hardware [Hakl, Leel, Lee2]. Alternatively, a 2D image can be reconstructed from one projection by the backprojection technique, and a radial cross-section can be taken through it. The most direct way to access the radial image from a projection consists in computing the inverse Hankel transformation (cf. Section 4.4.2) of the FID measured in Cartesian k space (cf. Fig. 4.4.1) [Majl]. But in practice, the equivalent route via Fourier transformation of the FID and subsequent inverse Abel transformation (cf. Section 4.4.3) is preferred because established phase and baseline correction routines can be used in the calculation of the projection as an intermediate result. 

Fig. 4 70 % radial image height positions to evaluate the comer resolution (MTF) in the diagonal points... 

For the confocal arrangement in transmission, the objective and the collector are used for imaging in reflection the objective is used twice. Therefore, the radial mtensity distribution in tlie image is the square of that of the conventional microscope ... 

Schleef D ef a/1997 Radial-histogram transform of scanning probe microscopy images Phys. Rev. B 55 2535... 

Neir-Johnson geometry. An arrangement for a double-focusing mass spectrometer in which a deflection of nil radians in a radial electrostatic-field analyzer is followed by a magnetic deflection of 7t/3 radians. The electrostatic analyzer uses a symmetrical object-image arrangement, while the magnetic analyzer is used asymmetrically. 

Tubes with diameters larger than 2 nm usually exhibit defects, kinks, and twists. This is illustrated in the TEM image of several relatively large nanotubes shown in Fig. 3b. The diameter of the tubes seems to vary slightly along the tube axis due to radial defor-... 

Fig. 7. TEM image of SWCNT growing radially from a La-carbide particles [10b].

The framework we adopted for measuring the scaling behavior from AFM images is the following. The 2-D power spectral density (PSD) of the Fast Fourier Transform of the topography h(x, y) is estimated [541, then averaged over the azimuthal angle

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Before the slit. Motion of the image delivered by the telescope with respect to the slit causes both a loss of throughput and an error in the barycentre of the spectral lines recorded on the detector, unless the object uniformly fills the slit (which implies low throughput). This can cause errors in measurement of radial velocities. For MOS, there is the particular problem of variations in the image scale or rotations of the mask. These can cause errors which depend on position in the field resulting in spurious radial trends in the data. Fibre systems are almost immune to this problem because the fibres scramble posifional information. 

A sample PIV image and the corresponding two-dimensional velocity map. The axial velocity along with distance from nozzle exit is plotted accordingly. This minimum point is defined as the reference flame speed. At this reference point, the linearity of the radial velocity profile is illustrated. 

A single image recorded for a fixed enantiomer and fixed circular polarization state in principle carries the full information sought consisting, after inversion, of the parameters and the radial distribution function n r). After... 

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