Aberration, optical

As was discussed above, the image contrast is significantly affected by the aberrations of the electron-optical... 

The first corrected electron-optical SEM was developed by Zach [10]. Eor low-voltage SEM (LVSEM, down to 500 eV electron energy instead of the conventional energies of up to 30 keV) the spot size is extremely large without aberration correction. Combining and correction and a electrostatic objective lens, Zach showed that a substantial improvement in spot size and resolution is possible. The achievable resolution in a LVSEM is now of the order of 1-2 mn. More recently, Krivanek and colleagues succeeded in building a corrected STEM [53,M]. 

The system of electric and magnetic fields or lenses is called the ion optics of the mass spectrometer. Electric lenses correct aberrations in the shape of the ion beam. 

A low dispersion is desirable in optical glasses used for lenses in cameras, telescopes, etc, because dispersion causes chromatic aberration, a condition which reduces the sharpness of an image. However, it is possible to correct for chromatic aberration by using a combination of glasses having different Abbu numbers (9). 

An example of a serial-recording EEL spectrometer is shown in Eig. 2.33 it features a magnetic prism system which was constructed for a TEM/STEM of the type JEOL JEM lOOS [2.199, 2.200]. Its second-order aberrations are corrected by curved pole-piece boundaries, an additional field clamp, and two extra hexapoles acting as stig-mators. The electron beam can be adjusted relative to the optical axis by use of several deflection coils. A magnetic round lens is positioned just in front of the prism to... 

Run-of-the-mill instruments can achieve a resolution of 5-10 nm, while the best reach 1 nm. The remarkable depth of focus derives from the fact that a very small numerical aperture is used, and yet this feature does not spoil the resolution, which is not limited by dilfraction as it is in an optical microscope but rather by various forms of aberration. Scanning electron microscopes can undertake compositional analysis (but with much less accuracy than the instruments treated in the next section) and there is also a way of arranging image formation that allows atomic-number contrast, so that elements of different atomic number show up in various degrees of brightness on the image of a polished surface. 

In astronomy, we are interested in the optical effects of the turbulence. A wave with complex amplitude U(x) = exp[ irefractive index, resulting in a random phase structure by the time it reaches the telescope pupil. If the turbulence is weak enough, the effect of the aberrations can be approximated by summing their phase along a path (the weak phase screen approximation), then the covariance of the complex amplitude at the telescope can be shown to be... 

Tor the purpose of this brief account we will provide only a notional definition of optical aberrations. In an optical system, the angular coordinates of incident rays are transformed according to sequential applications of Descarte s law from one optical surface to the next. Aberrations are essentially the non-linear terms of the transformation, the angular coordinates of emerging rays not being strictly proportional to those of the incident ones -thereby generating distorted and/or blurred images. 

Figure 5. Spherical aberration rays corresponding to different aperture angles focus at different locations along the optical axis.

We present the basics of optical design as it applies to two mirrored telescope systems. We discuss Zemike decomposition of wave-front error and the description of Strehl in terms of small Zemike errors. We also discuss the balancing of aberrations for a two mirror system and present the Ritchey-Chrdtien design as an example of a zero coma system. 

Conic mirrors produce a perfect spherical wave-front when the light striking the mirror comes from the conic conjugates. In general, most optical systems produce an aberrated wave-front, whose departure from a perfect spherical wave-front, A x, y) can be described quantitatively. 

Two-mirror telescopes are the most common optical design for ground based telescopes. These systems require a parabolic or hyperbolic primary mirror. As mentioned before, more complex optical systems can accommodate a spherical primary with its attendant simplifications, but several additional mirrors are needed to correct the spherical aberration, and the light loss and alignment complexity makes this configuration less commonly used. Here we will assume that a non spherical primary is needed and we will discuss the resulting surface shapes that segments will have. 

The OWL optical design is shown in Fig. 1. It is based on a spherical and flat folding secondary mirrors, with a four-element corrector providing for the compensation of spherical and field aberrations as well as advanced active optics and dual-conjugate adaptive optics. A complete discussion would exceed the scope of this report we shall however mention a few key arguments supporting this solution ... 

Besides the increase of reflections implied by Owl optical design, a price to pay for the spherical primary mirror solution is the difficulty to compensate for its spherical aberration, and in particular the horrendous aspherization of the quaternary mirror (which is conjugated to the primary). A possible test setup has been identified and the state of current technology allows for cautious hope industrial studies are however still required to confirm feasibility and evaluate implied cost and schedule. 

If this expression for the aspheric departure from spherical is expanded and recast in terms of commonly accepted optical aberrations, we find the departure is made up of a linear combination of aberrations and alignment terms shown in Tab. 1. The k is the conic constant if the asphere is not a parabola and the... 

Table 1. Departures of a parabola from a sphere in terms of common optical aberrations.

Abstract This lecture addresses the optical testing of concave aspheric mirrors. Examples of measurements of low order aberrations are shown. There are noises and bisases due to environmental effects, such as air turbulence, mirror temperature. Methods of interferometric testing are discussed. 

This first step makes necessary a correction of the atmosphere aberrations by means of an adaptive optics or at the minimum a tip tilt device. If the turbulence induces high aberrations the coupling efficiency is decreased by a factor VN where N is the number of spatial modes of the input beam. Note that tilt correction is also mandatory in a space mission as long as instabilities of the mission platform may induce pointing errors. Figure 10 (left) illustrates the spatial filtering operation. This function allows a very good calibration of... 

Scattered light noise. It is common in optics to separate the effects of large scale aberrations and the ones of small scale defects. Although this distinction is mathematically meaningless, it is in fact sensitive in practice for two reasons ... 

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