Effect of beam divergence

For the beam that follows path 2, the pathlength AC is given by 

It may be surprising to note that the path difference for the extreme ray is shorter than for the on-axis, or central, ray, which has a path difference of 21. Hence, the path difference, x, between the central and extreme rays is 

As / increases, the extreme ray will be out of phase with the central ray for the first time when 

The maximum solid angle that can be tolerated is therefore 

The effect of having a large solid angle is similar to the effect of apodization. For this reason, it has been called self-apodization [13]. 

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The effect of a drive mechanism that does not allow the plane of the moving mirror of the interferometer to maintain its angle relative to the plane of the beamsplitter is somewhat analogous to the effect of beam divergence discussed in Section 2.6. In the case of the poor mirror drive, however, an optical path difference is generated between the two extreme rays of the beam passing through the interferometer rather than a path difference between the extreme rays and the central ray. 

Figure 6. Effect of beam size and critical angle on sample size. Typical beam height at SSRL (SPEAR II) is 1 mm or so. In general this requires discarding 90% or more of the bam to achieve useful results. The situation is made worse due to high beam divergence which forces setup further below the critical angle. In the case of 3rd generation sources, practically all of the beam can be used on sample widths down to a few mm.

We do not consider here the dependence of the group velocity on the beam divergence and the related spatiotemporal effeets in the nonlinear medium leading to additional changes in the pulse shape. In the region of the core, these effects are small, and the radiation field power for the levels of the input pulse power considered here is low. 

Figure 4.18 The effect of spherical incident waves on the excitation of Bloch waves, (a) Reciprocal space the divergent incident beam has wavevectors ranging from P j O to P 2 O. (b) Real space energy is distributed throughout the Borrmann fan ABC. The beams generated outside the crystal are indicated...

For laboratory-based systems the instrument function given by the effect of the beam conditioner must now be introduced. In Chapter 2 we discussed beam conditioners in detail and showed that they may be characterised in terms of an intensity which is a function of both divergence and wavelength. 

More seriously, the effect of the above beam divergence also impacts wavenumber accuracy, and the deviation in measured wavenumber for the extreme ray versus the central ray is approximated by ... 

One problem of the measurement of weak absorption in the far IR is that short absorption paths must be used. At wavelengths comparable to the beam apertures diffraction effects lead to beam divergence [252]. (The combination of high gas pressures and short absorption paths may not be useful if many-body induction effects must be avoided, and an accurate measurement of a under conditions of weak absorption, I/Iq 1, is difficult [368].)... 

Figure 14.12 Net focusing effect on a diverging charged particle beam from the combination of a converging and diverging pair of magnetic quadrupole lenses. The key feature of the doublet is that the particles move along paths that are closer to the optical axis in the defocusing element of the pair. (From Harvey, 1964.)...

FIGURE 6.3 Absorption of light of a highly divergent beam by a substance placed in a cylindrical cell. Although the effect of reflection on the window has not been considered here, it can be introduced by a simple application of the laws of geometrical optics. 

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