Refractive lenses

The compound cerium oxide (either Ce Oj or CeO ) is used to coat the inside of ovens because it was discovered that food cannot stick to oven walls that are coated with cerium oxide. Cerium compounds are used as electrodes in high-intensity lamps and film projectors used by the motion picture industry. Cerium is also used in the manufacturing and polishing of high-refraction lenses for cameras and telescopes and in the manufacture of incandescent lantern mantles. It additionally acts as a chemical reagent, a misch metal, and a chemical catalyst. Cerium halides are an important component of the textile and photographic industries, as an additive to other metals, and in automobile catalytic converters. Cerium is also used as an alloy to make special steel for jet engines, solid-state instruments, and rocket propellants. 

Step-and-repeat (S/R) cameras use refractive lenses with numerical apertures of 0.2 to 0.4. The best lenses expose a field of about 2 cm x 2 cm at a numerical aperture of 0.3. Higher numerical aperture is available for smaller field-size. The field-size and numerical aperture for many of the lenses used in microcircuit cameras are shown in Figure 3. Most lenses are designed to operate at a single wavelength that corresponds to a strong line in the mercury spectrum (365 nm, 405 nm, or 436 nm), but lenses have also been corrected for two wavelengths (405 nm and 436 nm) in order to reduce the effects of... 

Refractive lenses must always be used in the step-and-repeat mode because the field size they cover is very much smaller than a silicon wafer. Sample position is either tracked by a laser interferometer, after an initial reticle to wafer alignment, or the reticle and sample are aligned with respect to each other at every chip site (12-17). Alignment at every chip avoids errors... 

In the x-ray range, the refractive index n in matter is very close to unity and thus the refractive index decrement <5=l-n is extremely small, typically of the order of 10-6. For example, a refractive lens normally has spherical curvatures of radius R, typically 100 mm in the optical range, and its focal length F=R/28 for the x-rays would be 50 km, too long to be useful. The renaissance of refractive optics for x-rays came from an idea of compound refractive lenses (CRL), which consist of a linear array of many concave lenses [81, 82]. The CRL has been made of different kinds of polymers, including PTFE and PMMA, as well as other low-Z materials [83], and is able to focus the x-rays at a reasonable distance, typically of the order of a few meters. However, its thickness leads to absorption so strong that it has not resulted... 

To produce micrometer sized focused beams, one employs highly demagnifying optics to image the source onto the sample. Such optics can include Kirkpatrick-Baez mirrors, Fresnel zone plates, tapered capillaries, and compound refractive lenses, all of which have been used to produce submicron focal spots at third generation storage rings. 

Righini G.C., Molesini G., Design of optical-waveguide homogeneous refracting lenses, Appl. Opt. 27 (20), 4193-4199 (1988). 

If large and heavy filters are used to maximize retention of airborne contaminants, they must be worn on the body using suitable assemblies connected to the mask by an air line. In such a case the support of a power-assisted filtering device is recommended (see Section 6.8.4.1.3). Persons using refractive lenses quite often complain about problems with low wearing comfort when using full-face masks, and they also have fogging problems with the visors. This problem does not occur with half masks. 

Refractive lenses act as a normal conventional lens and we can apply the Gauss lens formula, which relates the source distance L-, the image distance L2, and the focal distance F via L2 = FLi(Li - F). The diffraction-limited resolution of the lens A is defined by an effective aperture A = 0.75A/2NA, where the numerical aperture is NA = Aeff/2L2. is the effective aperture of the lens, reduced by photon absorption and scattering, compared with the geometrical aperture 2Rq. Nowadays, the parabolic refractive lenses, made of aluminum and beryllium, are available and widely used for hard X-ray microscopy applications providing resolution in the order of 300-500 nm. 

Limiting the flux throughput through pinholes is insufficient for most practical analytical purposes hence, techniques for generating intense X-ray microbeams are based on the use of various types of X-ray optics. Refractive lenses that are extensively used in visible or ultraviolet light optics are more difficult to use for X-rays because the refractive index, n, is very close to and slightly smaller than 1.000 by a factor d. The refractive index can be expressed as... 

Microfocusing devices that are based on refraction operate in the same way as visible light optics but there are some differences (Schroer et al. 2005). Firstly, the X-ray refractive index of a material is smaller than in vacuum or air and, therefore, an X-ray focusing lens has a double concave shape. Secondly, because the refractive index of all materials is very close to unity for hard X-rays, the deflection is usually very small and many lenses have to be placed in series to achieve reasonably short focal lengths. In order to keep absorption to a minimum, these compound refractive lenses (CRTs) should be made from low-Z materials such as beryUium, carbon, aluminum, and silicon. CRTs with parabolic shapes made from polycrystalline aluminum by a pressing technique have proven to be well suited for microanalysis and full field microscopy applications for 20-120 keV X-rays (Lengerer et al. 1998). 

Techniques for the formation of intense X-ray microbeams are readily available using various types of X-ray optics. Bent mirrors, crystals and multilayers, tapered glass monocapillaries, complex polycapillary lens systems, Bragg-Fresnel lenses, one- or two-dimensional waveguides, and refractive lenses have been developed and tested for use in micron (pm) size to... 

The entire microprobe setup is positioned on a movable granite table. Compound refractive lenses are used for focusing to a routinely achievable spot size of 1-2 pm vertically and 12-15 pm horizontally. The intensity of the incoming, the focused, and the transmitted beam is monitored by ionization chambers and photodiodes. A miniature ionization chamber with an aperture of 50 pm diameter as an entrance window was developed at the ESRF for measuring the intensity of the focused beam close to the sample (Somogyi et al. 2003). The characteristic X-ray line intensities are detected with a Si(Li) detector of 30 mm active area, 3.5 mm active thickness, and 8 pm thick Be window placed at 90° to the incoming linearly polarized X-ray beam. Fast scanning XRF measurements (>0.1 s live time/spectrum) are possible. 

Principles and Characteristics Microfluorescence handles very small analysed areas and yields spatially resolved information of the sample composition. There are several technical solutions for obtaining a primary X-ray beam with a small diameter and sufficient intensity, from capillary optics and refractive lenses to highly sophisticated X-ray optical elements with focusing characteristics [744], Modern compact and mobile /xEDXRF spectrometers with Si drift detection for quality control, material testing, and in situ art and archaeometry applications nowadays offer down to 50 /xm minimum focal spot size, <160 eV energy resolution and detection limits of the order of 20 ppm [745-747]. Using capillary optics it is possible to focus the X-ray beam of uXRF to 10 to 100 urn areas. 

Frielinghaus, H. Pipich, V. Radulescu, A. Heiderich, M. Hanslick, R. Dahlhoff, K Iwase, H. Koizumi, S. Schwahn, D. (2009). Aspherical Refractive Lenses for Small-Angle Neutron Scattering. Journal of Applied Crystallography, Vol.42, No.4, p>p.681-690, ISSN 0021-8898... 

There has also been a tremendous development of designing and manufacturing X-ray focusing lenses such as compound refractive lenses. Highly efficient in terms of flux are mirrors aligned in Kirkpatrick-Baez geometry. Ref. [30] includes a detailed review on the recent developments of X-ray optics for microscopy. 

From the point of view of coupling efficiency (minimization of reflection losses), the best solution is monolithic or hybrid integration however, in practical situations one can encounter all of the mentioned approaches. Two main types of focusing lenses may be used—either refractive lenses fabricated in material with high real part of refractive index and low absorption coefficient at IR wavelengths, or diffractive lenses. Any of them may be either discrete or arrayed. Reflective optical concentrators may be used, also reflective holographic optical elements or any of their combinations. 

One of the molding methods often used to fabricate refractive lenses is to deposit a cube of lens material on the substrate using, e.g., some of the planar technology procedures, and then to treat it thermally until it melts. Surface tension turns it then into a hemisphere, calotte, or a flattened hemisphere [112]. An even better method is to use a similar procedure to deposit a base for the microlens with a desired diameter, and then to deposit lens material on it [113]. After melting, the lens material flows exactly to the edge, where surface tension prevents it to go farther (melt stop.) In this way, the lens surface is formed with an extreme accuracy. 

Another relevant extension of the pinhole SANS technique is the focusing of a small source aperture by refractive lenses in front of the sample onto high-resolution deteaor. Aspherical lenses of Mgp2 are the latest development permitting... 

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