Aberration, optical lenses

Figure 1. Ray optical description of lens aberrations, (a) Perfect lens imaging a point P in the object plane onto a sharp point in the image plane, (b) Lens affected by spherical aberration, (c) Lens underfocused by a distance Z. (d) Lens overfocused by a distance Z. Spherical aberration and defocusing cause a blurring of the point P in the image plane.

Lenses are certainly the most frequently used optical elements. Unfortunately, a simple spherical lens yields a very poor focus quality, even if only the beams parallel to the optical axis are considered. The most important aberrations on the optical axis are spherical and chromatic aberration. The lens has a different foeal length for rays of different distance from the optical axis, and different foeal lengths for different wavelengths (Fig. 7.4). 

More specifically, the chapter describes lenses and lens optics, lens aberrations, the human eye, cameras and projectors, microscopes, and telescopes. 

The first effect is responsible for the aberration of the image formed by the optical system, for example, films, sheets, or optical lens. Typically, loss of clarity is associated with the confusion in the image plane of two distinct points in the object plane. 

For reference, a comparison of the ratio of the spherical aberration and the radius, A 9)/R, between the acoustic lens and the optical lens is shown in Fig. 4. The spherical aberration of the acoustic lens is much smaller than that of the optical lens. This is an important advantage. 

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]. 

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... 

In geometrical optics the numerical aperture of a lens is given by first-order theory and spherical aberrations are given by third-order theory (Jenkins and White 1976 Hecht 2002). In first-order theory the approximation is made... 

In many cases, the profile a spectroscopist sees is just the instrumental profile, but not the profile emitted by the source. In the simplest case (geometric optics, matched slits), this is a triangular slit function, but diffraction effects by beam limiting apertures, lens (or mirror) aberrations, poor alignment of the spectroscopic apparatus, etc., do often significantly modify the triangular function, especially if high resolution is employed. 

Thermal lens microscopy (TLM) is a type of photothermal spectroscopy. TLM depends on the coaxial focusing of the excitation and probe laser beams (see Figure 7.20). Which is achieved using the chromatic aberration of a microscopic objective lens [731]. The excitation beam can be provided by a YAG laser (532 nm) [846,1021] or an Ar ion laser (514.5 nm [846] or 488 nm [732]).The probe beam can be provided by a He-Ne laser (632.8 nm) [846,1021], After optical excitation of the analyte molecules, radiationless relaxation of the analytes occurs,... 

---