Lens, spherical

The finite size effects in the contact between a spherical lens of polyurethane and a soft flat sheet of crosslinked polyfdimethyl siloxane) (PDMS) has been addressed by Falsafi et al. [37]. They showed that for deformations corresponding to contact diameters larger than the sheet thickness, the compliance of the system was affected by the glass substrate supporting the soft sheet. In order to minimize the finite size effects in the adhesion measurement of small elastomeric lenses, Falsafi et al. [38] and Deruelle et al. [39] used relatively thick elastic sheets to support their samples. 

Fig. 5.10. The top two panels show the transverse image of two filaments (top left panel) and the corresponding interference pattern (top right panel) observed in the far field obtained using a cylindrical lens. The lower panels show the corresponding images when a spherical lens is used...

Figure 2. Transient Raman spectra of Ni(PP) (60-80 ]iM) in pyrrolidine. Traces a) and b) were obtained with 406 nm excitation at high and low power, respectively, while traces c) and d) were generated with 420 nm excitation (which i.s a compromise frequency which resonantly enhances both species to some extent) at high and low power, respectively. For low power spectra the average laser power (at 10 Hz) was. 75-1.0 mW. The beam was only slightly focused onto the sample with a cylindrical lens. High power spectra were generated with 5-6 mW of average laser power sharply focused at the sample via a spherical lens. Spectra are the unsmoothed sum of 3-5 scans at 7-9 cm" spectral resolution.

High polishing speeds are essential in todays economy, and the latest equipment employs much higher spindle speeds and pressures than those used just a few years ago. Cerium oxide is ideal under these more modern conditions, A spherical lens that required 8 minutes to polish 15 years ago is now polished in less than one minute, A toric (cylinder) lens that previously took 15 minutes to polish, now requires 4-1/2 minutes. 

The LFB microscope gives good azimuthal resolution in 0, but is not suitable for imaging. The imaging microscope gives good spatial resolution, but the spherical lens averages over all 0. Therefore, the contrast for an anisotropic specimen becomes... 

In order to calculate V(x, z) for a spherical lens in the presence of a crack a summation must be made over ky. For each value of ky a double summation is first made over kx and k x. A wave is considered to be incident with components of wavevector k x and ky. It is then transmitted by the crack with components of wavevector kx and ky, and reflected with components —kx and ky transmitted and reflected waves may be summed in the same integration. If the axis of the lens is displaced a distance x from the crack, the resulting phase change is kxx for the incident wave and —kxx for the scattered wave. Then, by extension of eqn (12.2),... 

Changing the variables, this may be used in the expression for V(z) for a spherical lens with axial symmetry, and integrated over 0... 

The experimental setup employed 785 nm excitation with a 90° collection geometry. Each spectrum was obtained with excitation power 300 mW and integration time equivalent to 2.5 min. Because filtered serum is nearly transparent at 785 nm, excitation of Raman scattering is effectively along the entire laser path, creating a line source in the cuvette. Thus, the authors surmise that better collection efficiency could be obtained with optics designed specifically for this type of source, as opposed to the standard spherical lens they employed. 

To acquire this information, the two displaced continuum beams are imaged with a cylindrical and a spherical lens onto different positions along the length of the entrance slit of a low dispersion spectrograph (Instruments SA, model UFS-200). The two resulting parallel dispersed spectra are fully separated from each other at the focal plane, where they are detected by the model 1254 SIT detector head of an EG + G Princeton Applied Research Corporation optical multichannel analyzer system. In conjunction with a model 1216 detector controller and model 1215 console, this detector is programmed with a two dimensional... 

L. B. Lerman, L. G. Grechko, and V. V. Gozhenko, Electromagnetic waves interaction with a lamellar spherical lens, in Proceedings of the 5th International Conference on Antenna Theory and Techniques, (National technical university KPI , Kyiv, Ukraine, 2005), pp. 234-237. 

Figure 2. Schematic representation of the experimental apparatus. Key CL, cylindrical lens DM, dielectric mirror SL, spherical lens and DF, neutral density filter.

Beam condensers, by using a pair of ellipsoid mirrors, produce very small images of the Jacquinot stop or the entrance slit at the sample position. The size of these images may be even further reduced by making use of a Weierstrass sphere. Weierstrass (1856) showed that a spherical lens has two aplanatic points . If a sphere of a glass with a refractive index n is introduced into an optical system which has a focus at a distance of r n from its center, then the beam is focused inside the sphere at a distance of r/n from the center (Fig. 3.5-9). In this case the angle O in Eq. 3.4-5 may approach 90°. Thus, a sample with a very small area can fully fit the optical conductance of the spectrometer (Fig. 3.4-2d). Microscopes usually have an optical conductance which is considerably lower than that of spectrometers. In this case, the sample and the objective are the elements limiting the optical conductance (Schrader, 1990 Sec. 3.5.3.3). 

Refractive index—(characteristic of a medium) Degree to which a wave is refracted, or bent. Spherical lens—lens where the curved surface is part of a spherical surface. This is the simplest type of lens to manufacture. 

Fig. 1.3 Comparison of elastic Hertzian contact (left) and adhesive JKR contact (right), (a) Hertzian contact Dashed line (sphere) shape of contacting spherical lens prior to pressing to the flat surface by force L. Hertzian contact profile shown by solid line, with radius under external load L aH (b) JKR contact Schematic of adhesion force (adhesive zone model, forces schematically indicated by vectors) further deforming a spherical lens from Hertzian contact (solid line) to JKR contact (dotted line) with radius aJKR. Reproduced from [7] with permission copyright Springer Verlag...

Fig. 9.2.1 Sketch of (A) a Raman immersion probe and (B) an immersion probe tip and spherical lens.

B. J. Marquardt, L. W. Burgess, Optical immersion probe incorporating a spherical lens, US Pat. 6,831,745 B2, issued December 2004. 

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