Electric field lenses

The ECAP incorporates an electrostatic lens in the time-of-flight spectrometer in order to improve the mass resolution by compensating for small spreads in the energies of the ions evaporated from the specimen under the pulsed electric field. A lens design by Poschenrieder or a reflectron type of electrostatic lens is used for this purpose, and is standard equipment for metallurgical or materials applications of APFIM. These typically improve the mass resolution at full width half maximum (FWHM) from m/Am 250 to better than 2000. 

We first review the essentials of the phase distribution of the electric fields at the focus of a high numerical aperture lens in Section II. After discussing the phase properties of the emitted signal, in Section HI we zoom in on how the information carried by the emitted held can be detected with phase-sensitive detection methods. Interferometric CARS imaging is presented as a useful technique for background suppression and signal enhancement. In Section IV, the principles of spatial interferometry in coherent microscopy are laid out and applications are discussed. The influence of phase distortions in turbid samples on phase-sensitive nonlinear microscopy is considered in Section V. Finally, in Section VI, we conclude this chapter with a brief discussion on the utility of phase-sensitive approaches to coherent microscopy. 

A simple and practical way to achieve the field enhancement is to use backside illumination of a dielectric plate, for instance a cover glass, in a standard DLW geometry with an oil-immersion focusing lens. According to the Fresnel formulas for the right angle incidence (0, = 0°), the coefficients of the in-plane ( ) polarized amphtudes of transmitted and reflected electric fields are, respectively ... 

Figure 2. Schematic diagram of the imaging apparatus with ion lens. The detector is a dual microchannel plate/phosphor screen assembly (40 mm active diameter) coupled with a CCD camera. Electric field lines are shown to illustrate the ion lens. Equipotential surfaces in the repeller/extractor region are also included.

The passage of electrons or other particles with charge q and mass m through an electrostatic lens system is governed by their motion under the action of the electric field. In the case considered here, cylindrical symmetry around the optical axis (z-axis) and paraxial rays will be assumed. Of the cylindrical coordinates only the transverse radial coordinate p and the distance coordinate z are of relevance, and the electrostatic potential of the lens is given by q>(p, z). As shown in Section 10.3.1, in the paraxial approximation the potential q>(p, z) is fully determined by the potential symmetry axis. Hence, the equations of motion and the fundamental differential equation of an electrostatic lens depend only on this potential. The fundamental lens equation is given by (see equ. (10.38))... 

In order to derive the optical properties of an electrostatic lens, one has to establish and solve the equations of motion for a transmitted particle of mass m and charge q. Since the particle moves in the lens under the action of an electric field which can be derived from a potential cylindrical symmetry around the optical axis (z-axis) and treating paraxial rays only, the potential cylindrical coordinates p and z. It can be expanded as a power series in p with z-dependent coefficients. Due to the rotational symmetry, only even powers of p appear in the expansion, and one has the ansatz... 

In 1949 Herzog and Viehbock reported a novel ion source for mass spec-trography (Fig. 4.2) [9]. This source provided separate accelerating fields for the primary and secondary ions and thus became the first modem instrument designed specifically for SIMS. The design included acceleration of the positive secondary ions from an equipotential surface through an electric field acting as an electron-optic lens. 

Since the Y-photon ionization rate is R = aN F, where ionization cross-section and Fthe photon fluence, both the electron and ion signals can be increased by tight focussing of the laser. Because the ion yield should increase as the Y-th power of the intensity, focussed lasers tuned to an intermediate resonance will ionize virtually every atom in the focal volume. For a typical dye laser with 0.5-mrad divergence, the spot size for a 5-cm focal length lens is 25 /mi which, for an assumed energy of ca 10 mJ per 10 ns pulse (i.e. 1 MW of power), yields a flux p of ca 1011 W cm-2. This power density corresponds, for 500-nm photons, to a fluence of ca 5 x 1022 photon cm-1. Since the peak electric field, E V cm 1, is related to p by... 

In passive mode-locking, an additional element in the cavity can be a saturable absorber (e.g., an organic dye), which absorbs and thus attenuates low-intensity modes but transmits strong pulses. Kerr lens mode-locking exploits the optical Kerr63 or DC quadratic electro-optic effect here the refractive index is changed by An = (c/v) K E2, where E is the electric field and K is the Kerr constant. 

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