Image curvature

To increase light throughput in Raman systems, the CCD chip size can be increased vertically to match the spectrograph slit height. However, large-format CCD detectors show pronounced slit image curvature that must be corrected in preprocessing (described below). 

Zhao J. Image curvature correction and cosmic removal for high-throughput dispersive Raman spectroscopy. Applied Spectroscopy 2003, 57, 1368-1375. 

There are three common types of lens aberrations. An aberration is the failure of a lens to produce an exact point-to-point correspondence between an object point and an image point, or in other words, an image distortion. The types of aberrations are spherical, chromatic, and curvature of field as illustrated in Figure 22A-22C. Spherical aberration is the failure of the lens to focus light onto the same focal plane (Fig. 22A). Chromatic aberration is when the different colors focus on different focal planes (Fig. 22B), which makes the image appears blurry. Curvature of field is when the plane of sharpest focus is curved due to this image curvature the whole image cannot be in focus (Fig. 22C). 

Berri C. E. Image curvature caused by fringing flelds in magnetic sector mass spectrometers. Rev. Sci. Instrum. 1956, 27, 849-853. 

In Fig. 4 we show an atomic resolution image of a carbon tube. The structure imaged at the upper right corner of the picture comes from another tube. Both of them were —1000 A long. A perfect honeycomb surface structure is observed. By taking into account the curvature of the tube surface and the STM imaging profile, we find the same lattice parameter as that of. graphite (1.42 A). This directly proves that the tubu-... 

The second problem is how we can obtain a linear relationship between the coefficients describing the wavefront and our measurements. It is how this linear relationship is obtained that differentiates, for example, a Shack-Hartmann and a curvature sensor. In all wavefront sensors to transform a wavefront aberration into a measurable intensity fluctuation it is necessary to propagate the wavefront. As a first approximation this propagation is described by geometric optics, and we discuss the linear relationship between the wavefront slope and the image displacement in Section 24.3. 

The curvature sensor first proposed by Roddier (Roddier, 1988), does not make measurements at the focal plane. Instead measurements are taken at two planes symmetrically distributed around the focal plane as shown in Fig. 10. These measurements are best thought of as blurred images of the aperture and consequently our ability to measure the tilt is affected since as we move from the focal plane the hght is spread over a wider angle. Consequently we would expect the tilt signal to degrade as we move away from the aperture. This can be formalized by the CRLB and Fig. 11 shows the best attainable tilt performance (Marcos, 2002). 

The parallel surface method (PSM) has been invented to measure the average interface curvature (and the Euler characteristic) from the 3D data images [222]. First, a parallel surface to the interface is formed by translating the original interface along its normal by an equal distance everywhere on the surface (see Fig. 33). The change of the surface area at the infinitely small parallel shift of the surface is... 

Concerning the nature and structure of such amyloid peptide or protein channels, oligomers with annular morphologies have in fact been observed by EM for a-synuclein (Lashuel et al., 2002) and equine lysozyme (Malisauskas et al., 2003) even in the absence of any lipids or membranes. Channel-like structures have also been reconstituted in liposomes and observed by SFM for A/ i 4o, A/ j 42, human amylin, a-synuclein, ABri, ADan, and serum amyloid A (Fig. 5A Lin et al., 2001 Quist et al., 2005). Doughnut-shaped structures with a diameter of 10-12 nm and a central hole size of 1-2 nm (Fig. 5B) were imaged on top of lipid membranes (Quist et al., 2005). However, the radius of curvature of the SFM tips meant that it is not possible to say whether the pores were really traversing the lipid bilayer. 

Fig. 4.4 Molecular model of (a) surface containing positive and negative curvature induced by a pentagon (red) and a heptagon (blue), respectively (b) molecular model of 5-7 defects (yellow) and a Thrower-Stone-Wales defect (green) [82] (c) high-resolution transmission electron microscopy (HRTEM) images of bond rotations V2 (555-777) divacancy, and (d) V2(5555-6-7777) divacancy within graphene scale bar is 1 nm [75].

On an image with a scale factor of 500 to 800 this additional component leads to significant shift of the reflection position (6 to 9 pixels). The shift of the reflection centre caused by the Ewald sphere curvature is seen easily while analyzing the positions of reflections lying on the minor... 

Another way to define the direction of the minor axis is to manually locate it by choosing a single reflection lying on the axis. The disadvantages of this method are (i) the difficulties with a reflection location on complex images due to overlapping problems and (ii) the curvature of the Ewald... 

---