Lens diffraction

Figure 1.4. Degradation of the projected image at the diffraction limit of the lens. Diffraction effects transform an initially square-wave image into a sinusoidal pattern of intensity at the image plane.

Object Object lens Diffraction pattern Image... 

The results of the tests validate the lens-telescope concept the lens diffracts the gamma rays concentrating them into a small focal spot on the detector surface. Because the signal is associated with the collection surface and the background is associated with the detection volume, the large lens collection area combined with the small Ge array volume makes an optimal instrument for maximizing the signal-to-noise ratio. 

Figure Bl.18.2. Diffraction figure of a grating If only the zeroth-order beam were collected by the lens, only a bright area would be visible without any stnicture indicating the presence of the grating. If the zeroth- and ifirst-order beams are collected, as indicated in the figure, the grating can be observed, albeit with incomplete object fidelity.

Focusing Laser Light. One of the most important properties of laser radiation is the abiHty to coUect all of the radiation using a simple lens and to focus it to a spot. It is not possible to focus the laser beam down to a mathematical point there is always a minimum spot size, set by the physical phenomenon of diffraction. A convenient equation is... 

The ratio F/d is the F number of the lens. For F numbers much less than unity, spherical aberration precludes reaching the ultimate diffraction-limited spot size. Therefore a practical limit for the minimum spot size obtainable is approximately the wavelength of the light. Commonly this is expressed as the statement that laser light may be focused to a spot with dimensions equal to its wavelength. 

The final set of magnetic lenses beneath the specimen are jointly referred to as post-specimen lenses. Their primary task is to magnify the signal transferred by the objective lens. Modern instruments typically contain four post-specimen lenses diffraction, intermediate, projector 1, and projector 2 (in, order of appearance below the specimen). They provide a TEM with its tremendous magnification flexibility. 

Collectively, the post-specimen lenses serve one of two purposes they magnify either the diffraction pattern from the sample produced at the back focal plane of the objective lens or they magnify the image produced at the image plane of the objective lens. These optical planes are illustrated in the elearon ray diagram in... 

A TEM provides the means to obtain a diffraction pattern from a small specimen area. This diffraction pattern is obtained in diffraction mode, where the post-specimen lenses are set to examine the information in the transmitted signal at the back focal plane of the objective lens. 

All the energy-filter systems referred to above are incorporated into the electron-microscopic column, usually between the diffraction lens and the following intermedium lens. They are, therefore, known as in-column filters, which are also commer-... 

Low-energy Electron Diffraction (LEED) 73 crystal lens... 

The particle size analyzer, based on laser light diffraction, consists of a laser source, beam expander, collector lens, and detector (Fig. ] 3.45). The detector contains light diodes arranged to form a radial diode-array detector. The particle sample to be measured can be blown across the laser beam (dry sample), or it can be circulated via a measurement cell in a liquid suspension. In the latter case, the beam is direaed through the transparent cell. 

In order to observe fringes, the screen should be placed in the regime of Fraunhofer diffraction where F/B B/X. In practice, such an interferometer can be realized by placing the stop immediately in front of a collecting optics, e. g., a lens or a telescope, and by observing the fringes in its focal plane (F = fes). 

As an example, consider a planar wavefront from an incoherent source passing through an aberration-free circular lens. When the image is diffraction-limited, an Airy disc pattern is observed (Goodman, 1996). For an aperture of radius 1 / 2n) the pdf for photon arrival is given by... 

The resolution of an acoustic lens is determined by diffraction limitations, and is 7 = 0.51 /N.A [95], where is the wavelength of sound in liquid, and N.A is the numerical aperture of the acoustic lens. For smaller (high-frequency) lenses, N.A can be about 1, and this would give a resolution of 0.5 Kyj. Thus a well designed lens can obtain a diameter of the focal spot approaching an acoustic wavelength (about 0.4 /Ltm at 2.0 GHz in water). In this case, the acoustic microscope can achieve a resolution comparable to that of the optical microscope. 

Since optical measurements of monolayers at the water-oil interface are rather difficult to carry out, a configuration was suggested where a monolayer at the water-air interface was in contact with an oil lens which was partly wetting the monolayer [23]. The thermodynamic relation between this monolayer and that residing at the water-oil interface was discussed. This configuration was utilized in the X-ray diffraction experiments [24] where the structural changes of dipalmitoyl phosphatidylcholine (DPPC) and DPPE were followed. 

Fig. 2. (a) Ray diagram in the electron microscope under imaging (microscopy) conditions. E electron source C condenser lens S sample O objective lens bfp back focal plane of O I intermediate lens P projector lens, (b) Structural imaging, diffraction and compositional functionalities of TEM. 

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