Decentred optical axes and aberrations along principal visual field meridians

Suggestions that peripheral imagery may affect the development of refractive error have led to interest in the variation in refraction and aberration across the visual field. It is shown that, if the optical system of the eye is rotationally symmetric about an optical axis which does not coincide with the visual axis, measurements of refraction and aberration made along the horizontal and vertical meridians of the visual field will show asymmetry about the visual axis. The departures from symmetry are modelled for second-order aberrations, refractive components and third-order coma. These theoretical results are compared with practical measurements from the literature. The experimental data support the concept that departures from symmetry about the visual axis in the measurements of crossed-cylinder astigmatism J45 and J180 are largely explicable in terms of a decentred optical axis. Measurements of the mean sphere M suggest, however, that the retinal curvature must differ in the horizontal and vertical meridians.

Multi-factor password-authenticated key exchange

We consider a new form of authenticated key exchange which we call multi-factor password-authenticated key exchange, where session establishment depends on successful authentication of multiple short secrets that are complementary in nature, such as a long-term password and a one-time response, allowing the client and server to be mutually assured of each other's identity without directly disclosing private information to the other party. Multi-factor authentication can provide an enhanced level of assurance in higher-security scenarios such as online banking, virtual private network access, and physical access because a multi-factor protocol is designed to remain secure even if all but one of the factors has been compromised. We introduce a security model for multi-factor password-authenticated key exchange protocols, propose an efficient and secure protocol called MFPAK, and provide a security argument to show that our protocol is secure in this model. Our security model is an extension of the Bellare-Pointcheval-Rogaway security model for password-authenticated key exchange and accommodates an arbitrary number of symmetric and asymmetric authentication factors.

Elastic lateral buckling of simply supported LiteSteel beams subject to transverse loading

The buckling strength of a new cold-formed hollow flange channel section known as LiteSteel beam (LSB) is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion for its intermediate spans. Recent research has developed a modified elastic lateral buckling moment equation to allow for lateral distortional buckling effects. However, it is limited to a uniform moment distribution condition that rarely exists in practice. Transverse loading introduces a non-uniform bending moment distribution, which is also often applied above or below the shear centre (load height). These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors to allow for these effects. But they were derived mostly based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The moment distribution and load height effects of transverse loading for LSBs, and the suitability of the current design modification factors to accommodate these effects for LSBs is not known. This paper presents the details of a research study based on finite element analyses on the elastic lateral buckling strength of simply supported LSBs subject to transverse loading. It discusses the suitability of the current steel design code modification factors, and provides suitable recommendations for simply supported LSBs subject to transverse loading.

Lateral buckling strength of simply supported LiteSteel beams subject to moment gradient effects

The flexural capacity of of a new cold-formed hollow flange channel section known as LiteSteel beam (LSB) is limited by lateral distortional buckling for intermediate spans, which is characterised by simultaneous lateral deflection, twist and web distortion. Recent research has developed suitable design rules for the member capacity of LSBs. However, they are limited to a uniform moment distribution that rarely exists in practice. Many steel design codes have adopted equivalent uniform moment distribution factors to accommodate the effect of non-uniform moment distributions in design. But they were derived mostly based on the data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The effect of moment distribution for LSBs, and the suitability of the current steel design code rules to include this effect for LSBs are not yet known. This paper presents the details of a research study based on finite element analyses of the lateral buckling strength of simply supported LSBs subject to moment gradient effects. It also presents the details of a number of LSB lateral buckling experiments undertaken to validate the results of finite element analyses. Finally, it discusses the suitability of the current design methods, and provides design recommendations for simply supported LSBs subject to moment gradient effects.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

The Dragon stream cipher: Design, analysis and implementation issues

Dragon is a word-based stream cipher. It was submitted to the eSTREAM project in 2005 and has advanced to Phase 3 of the software profile. This paper discusses the Dragon cipher from three perspectives: design, security analysis and implementation. The design of the cipher incorporates a single word-based non-linear feedback shift register and a non-linear filter function with memory. This state is initialized with 128- or 256-bit key-IV pairs. Each clock of the stream cipher produces 64 bits of keystream, using simple operations on 32-bit words. This provides the cipher with a high degree of efficiency in a wide variety of environments, making it highly competitive relative to other symmetric ciphers. The components of Dragon were designed to resist all known attacks. Although the design has been open to public scrutiny for several years, the only published attacks to date are distinguishing attacks which require keystream lengths greatly exceeding the stated 264 bit maximum permitted keystream length for a single key-IV pair.

The structure of selected magnesium carbonate minerals : a near infrared and mid-infrared spectroscopic study

The approach to remove green house gases by pumping liquid CO2 several kilometres below the ground implies that many carbonate containing minerals will be formed. Among these minerals the formation of dypingite and artinite are possible; thus necessitating a study of such minerals. Two carbonate bearing minerals dypingite and artinite with a hydrotalcite related formulae have been characterised by a combination of infrared and near-infrared spectroscopy. The infrared spectra of both minerals are characterised by OH and water stretching vibrations. Both the first and second fundamental overtones of these bands are observed in the NIR spectra in the 7030 to 7235 cm-1 and 10490 to 10570 cm-1. Intense (CO3)2- symmetric and antisymmetric stretching vibrations confirm the distortion of the carbonate anion. The position of the water bending vibration indicates water is strongly hydrogen bonded to the carbonate anion in the mineral structure. Split NIR bands at around 8675 and 11100 cm-1 indicates that some replacement of magnesium ions by ferrous ions in the mineral structure has occurred.

Raman spectroscopic study of the phosphate mineral Churchite-(Y) YPO4.2H2O

Raman spectroscopy has been used to study the rare earth mineral churchite-(Y) of formula (Y,REE)(PO4) •2H2O. The mineral contains yttrium and depending on the locality, a range of rare earth metals. The Raman spectra of two churchite-(Y) mineral samples from Jáchymov and Medvědín in the Czech Republic were compared with the Raman spectra of churchite-(Y) downloaded from the RRUFF data base. The Raman spectra of churchite-(Y) are characterized by an intense sharp band at 975 cm-1 assigned to the ν1 (PO4)3- symmetric stretching mode. A lower intensity band observed at around 1065 cm-1 is attributed to the ν3 (PO43-) antisymmetric stretching mode. The (PO43-) bending modes are observed at 497 cm-1 (ν2) and 563 cm-1(ν4). Some small differences in the band positions between the four churchite-(Y) samples from four different localities were found. These differences are possible to explain as different compositions of the churchite-(Y) minerals.

Modeling videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.

Describing ocular aberrations with wavefront vergence maps

A common optometric problem is to specify the eye’s ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero-cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

Raman spectroscopic study of the antimonate mineral brizziite NaSbO3

Raman spectra of antimonate mineral brizziite NaSbO3 were studied and related to the structure of the mineral. Two sharp bands at 617 and 660 cm-1 are attributed to the SbO3- symmetric stretching mode. The reason for two symmetric stretching vibrations depends upon the bonding of the SbO3- units. The band at 617 cm-1 is assigned to bonding through the Sb and the 660 cm-1 to bonding through the oxygen. The low intensity band at 508 cm-1 is ascribed to the SbO antisymmetric stretching vibration. Low intensity bands were found at 503, 526 and 578 cm-1. Sharp Raman bands observed at 204, 230, 307 and 315 cm-1are assigned to OSbO bending modes. Raman spectroscopy enables a better understanding of the molecular structure of the mineral brizziite.

Raman spectroscopic study of the mineral finnemanite Pb5(As3+O3)3Cl

The arsenite minerals finnemanite Pb5(As3+O3)3Cl been studied by Raman spectroscopy. The most intense Raman band at 871 cm-1 is assigned to the ν1 (AsO3)3- symmetric stretching vibration. Three Raman bands at 898, 908 and 947 cm-1 are assigned to the ν3 (AsO3)3- antisymmetric stretching vibration. The observation of multiple antisymmetric stretching vibrations suggest that the (AsO3)3- units are not equivalent in the molecular structure of finnemanite. Two Raman bands at 383 and 399 cm-1 are assigned to the ν2 (AsO3)3- bending modes. DFT calculations enabled the position of AsO32- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. Raman bands are observed at 115, 145, 162, 176, 192, 216 and 234 cm-1 as well. The two most intense bands are observed at 176 and 192 cm-1. These bands are assigned to PbCl stretching vibrations and result from transverse/ longitudinal splitting. The bands at 145 and 162 cm-1 may be assigned to Cl-Pb-Cl bending modes.

Raman spectroscopic study of the arsenite minerals leiteite ZnAs2O4 , reinerite Zn3(AsO3)2 and cafarsite Ca5(Ti,Fe,Mn)7(AsO3)12.4H2O

The selected arsenite minerals leiteite, reinerite and cafarsite have been studied by Raman spectroscopy. DFT calculations enabled the position of AsO22- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. The Raman spectrum of leiteite shows bands at 804 and 763 cm-1 assigned to the As2O42- symmetric and antisymmetric stretching modes. The most intense Raman band of leiteite is the band at 457 cm-1 and is assigned to the ν2 As2O42- bending mode. A comparison of the Raman spectrum of leiteite is made with the arsenite minerals reinerite and cafarsite.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

A Raman spectroscopic study of the antimonite mineral peretaite Ca(SbO)4(OH)2(SO4)2•2H2O

Raman spectra of mineral peretaite Ca(SbO)4(OH)2(SO4)2•2H2O were studied, and related to the structure of the mineral. Raman bands observed at 978 and 980 cm-1 and a series of overlapping bands observed at 1060, 1092, 1115, 1142 and 1152 cm-1 are assigned to the SO42- ν1 symmetric and ν3 antisymmetric stretching modes. Raman bands at 589 and 595 cm-1 are attributed to the SbO symmetric stretching vibrations. The low intensity Raman bands at 650 and 710 cm-1 may be attributed to SbO antisymmetric stretching modes. Raman bands at 610 cm-1 and at 417, 434 and 482 cm-1 are assigned to the SO42- 4 and 2 bending modes, respectively. Raman bands at 337 and 373 cm-1 are assigned to O-Sb-O bending modes. Multiple Raman bands for both SO42- and SbO stretching vibrations support the concept of the non-equivalence of these units in the coquandite structure.