Focusing properties

The distance z has been derived for any trajectory with a preselected entrance angle 0, i.e., a principal trajectory as defined in connection with Fig. 4.4 is not yet specified. In order to fix such a principal trajectory, which goes from the source to the image, one has to find the focusing properties of the analyser. In other words, one has to investigate how the distance function z( ) behaves for small changes in. For this purpose one starts with a Taylor expansion of z in A9 around a still arbitrarily selected 0 value  

As an application of the preceding discussion, the optical properties of the sector CMA mentioned several times in Part B will be given now, based on the formulas given above. The analyser is the rotatable double-sector CMA shown schematically 

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Figure Bl.6.1 Equipotential surfaces have the shape of lenses in tlie field between two cylinders biased at different voltages. The focusing properties of the electron optical lens are specified by focal points located at focal lengthsandy2, measured relative to the principal planes, The two principal rays emanating...

Fig. 4.18. Direction focusing properties of a 180° magnetic sector on a diverging beam of ions of the same m/z and the same kinetic energy and effect on ions of different m/z- In this illustration, B has to come out of the plane towards the reader for positive ions.

An ellipsoidal mirror has the same focusing properties but collects over two axes rather than one... 

Figure 3.2 Radial (a) and axial (b) focusing properties of a magnetic sector field with oblique beam entrance and exit. A/ and A2" are imaging points of ion beams with different path radii (rm and rm + Arm) on imaging curve. (77. Kienitz (ed.), Massenspektrometrie (1968), Verlag Chemie, Weinheim. Reproduced by permission of Wiley-VCH.)...

Mattauch-Herzog type mass spectrometer has double-focusing properties for ions of all masses... 

Figure 16.5—Magnetic analyser mass spectrometer, a) Nier Johnson system, b) directional focusing properties of the magnetic field, c) principle of a double focusing mass spectrometer d) Mattauch-Herzog system.

The proportionality factor / is called the spectrometer factor. Its value is fixed by the geometry and focusing properties of the analyser. Hence, for a given spectrometer, one can use the kinetic energy or alternatively the spectrometer voltage. 

Principal trajectory and focusing properties Usually, electrostatic deflection analysers contain two regions through which the electrons pass, a field region and a field-free region. Very often the field-free region... 

In order to fix the principal trajectory, appropriate focusing properties of the analyser have to be selected. These properties follow from the treatment of the analyser as an electron optical device which images the source Q at the analyser entrance to the image B at the analyser exit, and a detailed treatment for a point source is given in Section 10.2. Here only the main results necessary for a basic understanding will be reproduced. 

Hence, the energy dispersion contains information about the ability of the analyser to sort electrons of different kinetic energies in space and, therefore, it is an important chacteristic property of the energy resolution of an analyser. It depends essentially on the size of the analyser, but also on the focusing properties chosen. For example, for a CM A analyser with axis-to-axis focusing one gets D = 5.60 Rt where Rt is the radius of the inner cylinder of the analyser. 

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