| 释义 |
eikonal, n. and a.|ˈaɪkənəl, aɪˈkəʊ-|
[a. G. Eikonal (H. Bruns 1895, in Math.-Phys. Abhandl. d. K. Sächs. Ges. d. Wissensch. XXI. 323), f. Gr. εἰκών image: see -al1. Cf. icon n.]
A. n. The optical path length of a ray between specified points in the object and image spaces; more widely, a function of position denoting the time taken by a wave-front to reach a specified point.
1923Glazebrook Dict. Appl. Physics IV. 310/1 The function has the dimensions of a length, and in the case of the characteristic function represents the length of the optical path between the points whose co-ordinates are taken as variables, and in the eikonal the length of the optical path between the feet of perpendiculars to the ray from two selected points in the object and image spaces respectively. 1957Encycl. Brit. XVI. 821/1 This symmetrical function of the direction cosines..will be referred to as the Eikonal, a name proposed by Bruns. 1959Born & Wolf Princ. Optics iv. 132 The characteristic functions of Hamilton are themselves often referred to as eikonals. 1981A. D. Pierce Acoustics viii. 374 This partial-differential equation is the eikonal equation, τ(x) being the eikonal. 1987Jrnl. Optical Soc. Amer. A. IV. 1342 Lagrange's theorem is used to show how the eikonal, or angle characteristic function, can be calculated for a single refracting or reflecting surface and for an optical system composed of an arbitrary number of elements.
B. adj.
1. Physics. Designating an equation which expresses the eikonal in terms of the wave velocity.
1952Jrnl. Acoustical Soc. Amer. XXIV. 456/2 Weak acoustic shocks in moving fluids are propagated according to a generalized eikonal equation {vb}∇ϕ{vb}2 = µ2 [1-(V.∇ϕ/c0)]2 , where c0 is the reference sound velocity, V the vector velocity of the moving fluid, and µ the refractive index. 1959Born & Wolf Princ. Optics iii. 111 The eikonal equation will also be recognized as the Hamilton–Jacobi equation of the variational problem δ∫n ds = 0 , the optical counterpart of which goes back to Fermat. 1968Jrnl. Acoustical Soc. Amer. XLIV. 1115 Geometrical acoustics stems from the solution of the eikonal equation, which is a form of the wave equation in the limit of infinite frequency. 1987Appl. Optics XXVI. 2946/1 We have developed several ray trace algorithms by changing the independent variable for describing the ray and eikonal equations to the quasiray path, the ray path, the optical path length, and the quasioptical path length.
2. Particle Physics. Of, pertaining to, or designating a method of approximating the behaviour of particles by the use of eikonals.
1968Physical Rev. CLXXIV. 152 The use of the eikonal approximation permits the coupled equations of scattering theory to be reduced to one-dimensional equations defined along classical trajectories. The theory for rearrangement collisions is developed into a form appropriate for use with the eikonal description of heavy-particle motion. 1971Sci. Amer. July 100/1 The adjective ‘eikonal’ is applied to models in which the [optical] theorem is important. The term eikonal, meaning pertaining to a picture or image, seems particularly appropriate in that the diffracted photons form an image of the target..and the absorbed photons account for its shadow. 1976Physics Bull. June 268/1 The use of the eikonal approximation to describe the scattering of high energy particles from atomic and nuclear systems. 1983Nature 17 Feb. 642/3 Much of the prolific data on medium energy proton–nucleus scattering has been analysed within the framework of the eikonal approximation. |