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Introduction to Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
Reflection is the process in which light bounces back or is deflected at the boundary between two media. Refraction is the process of change of direction in which light bends in crossing from one medium to another of different density. The ratio of the speed of light in a vacuum to the speed of light in a medium is called the refractive index of the medium. Dispersion is the splitting of light of mixed wavelengths into its component colors. Diffraction is the spreading of light when it passes through an aperture or around the edge of a barrier. Polarization is the process of restricting the vibrations of the electric vector of light waves to one direction; in unpolarized light, the electric field vibrates in all directions perpendicular to the direction of propagation.
Optical Materials
Published in Abdul Al-Azzawi, Light and Optics, 2018
The refractive indices of all materials change with wavelength. This can lead to optical distortions, such as chromatic aberration, occurring when the light source in the system is not monochromatic. An optical designer can reduce these distortions by using a combination of different glass types. The lens combination balances these refractive deviations in such a way that light of different wavelengths will focus at the correct position in the image plane. The glass map available to optical designers, shown in Figure 16.5, is a plot of the index of refraction versus the Abbe number for different glasses. The Abbe number is a measure of the chromatic dispersion of the glass: larger values correspond to lower dispersion.
Design of Optical Components
Published in Christoph Gerhard, Optics Manufacturing, 2018
After the correction of chromatic aberration for two wavelengths, a residual chromatic error, the so-called secondary spectrum, remains. This secondary spectrum is given by the chromatic aberration of the corrected wavelengths with respect to the center wavelength, which is used for the specification of the nominal focal length. The underlying reason for the formation of secondary spectra is the difference in bending of the dispersion curves of the used crown and flint glasses as expressed by the partial dispersion (see Section 3.2.3.2.4). The secondary spectrum becomes minimal, if the bending of the particular dispersion curves of both glasses is identical, which is not possible when using standard glasses. For the correction of this residual chromatic aberration, complex systems such as apochromatic lenses, consisting of at least three lenses, or the use of optical media with abnormal dispersion characteristics are required.
Geometric calibration method based on Euler transformation for a large field of view polarimetric imager
Published in Journal of Modern Optics, 2020
Chan Huang, Yuyang Chang, Lin Han, Su Wu, Shuang Li, Donggen Luo, Liang Sun, Jin Hong
The optical structure, composed of the front group, focusing group and back group, is made up of 12 lenses with the ‘negative-positive’ inverse telephoto structure which can achieve wide field of view and long working distance. The front group is an afocal system whose main function is to reduce the angle between the beam and the optical axis and to decrease astigmatism and distortion of the system. To avoid radiation from space environment, the first lens is made of fused silica. The second lens is designed as parabolic, in combination with a meniscus lens back to stop in the third position aiming to correct astigmatism and distortion. The focusing group consists of three cemented lenses. The back group is applied to balance residual astigmatism, distortion and spherical aberration from the front group, in which the thick lens in the first doublet is mainly used to correct the curvature of the field. Low dispersion material is exploited to decrease chromatic aberration. An aperture stop is placed between the telescope and the focusing group, in such a way that the lens is telecentric in image space. For optical systems of small field of view, the aperture of the entrance pupil is unique regardless of field of view. However, it is not applicable to optical systems of large field of view. To improve uniformity of illumination on the image surface, the off-axis beam vignetting is adopted, i.e. the aperture of the entrance pupil changes with field of view. Thus it can be seen from Figure 1 that in the front group, the sizes of beam apertures corresponding to different field of view are inconsistent and distributed in different positions of the lens.
Love wave propagation characteristics in a fluid-saturated cracked double porous layered structure
Published in Mechanics of Advanced Materials and Structures, 2022
Bhanu Pratap Rajak, Santimoy Kundu, Shishir Gupta, Dharmendar Kumar
In this study, Love wave propagation in a heterogeneous fluid-saturated fractured double porous structure has been examined. The heterogeneity in the considered structure are linear, quadratic, and exponential in nature. The purpose of considering different types of heterogeneity is to analyze the impact of various parameters associated with the model on the phase and damped velocity of Love wave in different heterogeneous fluid saturated dual-porosity media. Methodology separation of variables has been used for converting the ordinary differential equation to a partial differential equation. Also, methodology WKB asymptotic approach has been used to calculate the displacement components throughout the structure. With the implementation of ideal boundary conditions, the dispersion equation has been achieved in its compact form, which contains real and imaginary parts of the relation. The real part of this relation is termed as phase velocity, and the imaginary part of this relation is termed as damped velocity. Basically, in physical sciences and engineering fields, the dispersion relation explains the effect of dispersion in an intermediate on the properties of waves traveling within that medium. A dispersion relative relates the wavelength or wavenumber of a wave to its frequency. From this relation, the phase velocity and group velocity of the wave can be calculated. It can be caused by either the boundary conditions or by interface of the waves within the transmitting medium. In addition, geometry-dependent and material-dependent dispersion relations, the overarching Kramers-Kronig relations describe the frequency dependence of wave propagation. So based on that, the phase and damped velocity of the Love wave has been calculated. Furthermore, a special case has been calculated in the absence of heterogeneity, cracked porous, which further reduced to classical Love wave condition [43], which validated the authenticity of the problem. Graphs have been plotted for phase and damped velocity against wave number to analyze the effect of heterogeneity, attenuation and fracture pores associate with layer and half-space for all the considered cases. This study results in decrement of phase and damped velocity with the higher regime of wave number for all the considered cases. Phase and damped velocity increases with increasing values of heterogeneity and attenuation parameters. It can also be noted that fracture pore associated with layer and half-space mitigates and enhances the phase and damped velocity, respectively. This study may be beneficial in the field of petroleum engineering, subsurface hydrology, geophysics, and seismology.
Dynamics of lump-periodic and breather waves solutions with variable coefficients in liquid with gas bubbles
Published in Waves in Random and Complex Media, 2023
Tukur Abdulkadir Sulaiman, Abdullahi Yusuf
It is well understood that interaction solutions between nonlinear phenomena can be represented by lump solutions and soliton solutions [11]. Many scholars have researched in the past few decades on soliton and lump solutions as well as the other types of integrable equations [12–16]. There are also lump solutions for certain nonintegrable equations [17–19]. In addition, the presence of interaction solutions between lumps and other forms of exact solutions to the nonlinear integrable equations is shown in different studies [20–25]. It is important to note, however, that numerous approaches have been used vehemently to construct interaction phenomena for NPDEs, especially for equations of constant coefficients. In certain cases, values are assigned to these constant coefficients to guarantee the existence of solutions. Nevertheless, it can be noticed that, treating such interaction phenomena with variable coefficients are dealt with by very scholars. So, in order to build many other physical characteristics and features, it is of great importance to study several other equations with variable coefficients since very few can be found. Motivated by this, we aim to use novel suited algorithms to draw the necessary constraints on these variable-coefficients that produce lump periodic and breather complexiton wave solutions to the generalized variable-coefficient -dimensional nonlinear-wave equation given by [26,27] where χ is the wave-amplitude function of x, y, z and t. The parameter is the coefficient of the nonlinear terms, and are the coefficients of the dispersion terms. The parameters are the coefficients of the dispersionless terms. Nonlinearity arises when the change of the output is not proportional to the change of the input. Dispersion means that waves of different wavelength propagate at different phase velocities. The phase velocity of a wave is the rate at which the wave propagates in some medium. This is the velocity at which the phase of any one frequency component of the wave travels. Studies have shown that when the dispersion effect and nonlinear effect of the medium reach a stable equilibrium, the pulse can maintain its shape and velocity in the form of solitons during the transmission process [28,29]. Equation (1) demonstrates the waves pressure in admixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer [26].