Geometric optics, principles

The law of geometrical optics anticipated by Hero of Alexandria was formulated by Fermat (1601-1655) as a principle of least time, consistent with Snell s law of refraction (1621). The time for phase transmission from point P to point Q along a path x(r) is given by... 

High frequency approximations in the solution of an acoustic wave equation The reader, familiar with the background of seismic exploration methods, should recall that many successful seismic interpretation algorithms are based on the simple principles of geometrical seismics, which resembles the ideas of geometrical optics. The question is how this simple but powerful approach is connected with the... 

As we have noted in the introduction, experimental evidence for a kinematic description of excitable wave fronts is rich. Based on hyperbolic wave equations and the Huygens principle, Wiener and Rosenblueth [81] recommend the eikonal approach of geometric optics waves propagate at a constant normal speed... 

The interpretation of PDA principles based on geometrical optics is valid only for particles considerably larger than the wavelength and also when only one scattering mode is present on the detector aperture. Extensions can be introduced to account for the Gaussian beam intensity distribution (Sankar and Bachalo 1991). 

Because of basic optical principles, the light injected into the fiber must belong to a geometrical acceptance cone in order to be guided within the core. This condition is given by the numerical aperture, defined as NA = sint ni = ( i — with 0, the maximum angle of the cone, and n and 2 the refractive indices of the core and cladding, respectively. Numerical apertures are usually between 0.1 and 0.3 for telecommunication applications, with the refractive index of pure silica equal to 1.4586 at sodium D-line. 

Born, M. and E. Wolf, 1999 Principles of Optics. Cambridge University Press. Grynko, Y. and S. Yu, 2003 Scattering matrix calculated in geometric optics approximation for semitransparent particles faceted with various shapes. J. Quant. Spectros. Radiat. Transfer, 78, 319-340. 

The scientific potential of nuclear gamma-ray astronomy is outlined in section 2. In sections 3 instruments for spectroscopy in the low and medium gamma-ray channel are presented modulating aperture systems, Compton telescopes and diffraction lens telescopes. The three techniques actually reflect our current perception of light itself - they are based on the principles of geometrical optics, quantum optics and wave optics, respectively. 

Operational satellite instruments based on the principles of geometrical optics include SIGMA, OSSE and BATSE (Paul et al. 1991, Johnson et al. 1993, and Fishman et al. 1989). While the detection plane of all three of them is based on scintillators AEfE 10), different aperture systems are used. Whereas OSSE and BATSE perform temporal modulation with collimators and the earth (an anticollimator ) respectively, SIGMA is a multiplexing device using spatial modulation with a coded mask. 

Hawkes PW and Kasper E (1989) Principles of Electron Optics-, vol. 1, Basic Geometrical Optics-, vol. 2, Applied Geometrical Optics. London Academic Press. 

The semi-angular divergence of rays from a point on the object is shown as a, limited by an aperture in the back focal plane. The divergence on a point on the image, a = alM. This demonstrates a general principle in geometric optics. 

The reduction of dimensions also reduces volumes which are accessible to the detector. Thus, detection principles related to geometric dimensions of the detector cell ai e not ideally suited for coupling to microsystems, whereas surface sensitive principles, such as electrochemical methods or optical methods utilizing the evanescent field of a waveguide, or methods which can be focussed on a small amount of liquid, such as electrochemiluminescence (ECE), ai e better suited. This is why electrochemiluminescence detectors ai e combined to microsystems. Moreover ECE has found wide applications in biochemistry because of its high sensitivity, relatively simplicity and feasibility under mild conditions. 

Besides the fluorescence coefficient, the optical absorption and scattering coefficients of the sample are the most important parameters in quantative fluorescence spectroscopy of turbid media. In principle two or, if the anisotropy parameter has to be determined, three independent measurements are sufficient to separate the coefficients that appear in all equations as sums or proportions. However, for better accuracy, one of the geometrical parameters (sample thickness, angle of incidence, distance from the irradiated spot) as well as the wavelength of irradiation should be varied over a wide range, and then the data should be fitted with the help of the corresponding model equation. 

Although both geometrical and optical isomerism are in principle possible in seven-coordinate complexes, no examples are known. Note, for example, that the py3tren complexes must be optically active (see Fig. 12 35b), subject of course to kinetic stability with respect to racemizciion. 

In keeping with the principles and definitions in Chapter 9, isomers are compounds with the same number of atoms of each kind per molecule, but they are different substances because of differences in molecular structure. There are three classes of isomers structural, geometric, and optical. 

The last two decades have been marked by an ever increasing interest in the theory of solids as is indicated by the development of the electronic band approximation which has been so successful in the understanding and interpretation of the optical, electrical, and magnetic properties of solids. This and similar advances made by the physicists have provided new tools for the interpretation and elucidation of the catalytic efficacy of a solid. These tools had been sorely needed and long awaited, for it was Roginskif and Schultz (337) and Russell (357) who had emphasized the importance of the electronic factor even before the introduction of the geometric factor by Balandin (13) and the ensemble principle by Kobozev. 

Born M, Wolf E and Bhatia AB, "Principles of Optics", 7th Ed, Cambridge University Press, Cambridge, 1999. Longhurst RS, "Geometrical and Physical Optics", 3rd Ed, Longmans, London, 1973. 

In photonic materials, the band gap is determined by geometric arrangement of a dielectric material. The underlying principle of how photonic materials work is best explained using Maxwell s equations (Joannopoulos et al., 1995). Once again, the central importance of Maxwell s equations is confronted when optical properties of materials are discussed. In photonic materials, a periodic stmcture is produced in one, two, or three dimensions. The periodic property is a dielectric constant. A trivial macroscopic onedimensional example would be a collection of individual microscope shdes separated by layers of Saran Wrap . This would produce a one-dimensional modulation in the... 

---