IMEKFEKOMETRIC METHODS 



superimposed \ibrations in c' is equal to the 

 difference of amplitude of the two vibrations 

 falling in c' at the same time : 



<p 



— Lii — Li\ — 



[a sin 2. (^ - f + «)_ 



_ (^7) 



or: 



ip = 2-Kp/\ 



{28) 



This value of (p is independent of a. The 

 amplitude L resulting from the composition 

 of the two vibrations arriving in c' with the 

 difference of phase ^ is practically equal to 

 Li + L2 if the angle 7 is very small: 



L = 2A sin 



in 27r ( - 



Xi + X-y 

 2\ 



+ 



•COS IT 



■) 



(^S) 



= 2A cos TT - sin 

 X 



in 2^ ^^ + /3 j 



and the intensity /c of the Hght in c' is the 

 product of a constant by the square of L or: 



where 



TTp 



Ic = 4A2 cos2 — = 4^2 cos2 wq 



q = p/X 



(50) 



In other words, in c' the intensity of light 

 is four times greater than that produced by 

 either one of the sources alone. In summary, 

 on a plan intersecting the common path of 

 two synchronous rays, the light is distributed 

 along a series of maxima and minima be- 

 tween which the intensity varies according 

 to a simple periodic function. 



A region of space answering to this defini- 

 tion constitutes a fringe system. Its sym- 

 metry may be either axial or radial, depending 

 upon the instrument, but the fundamental 

 relations are the same. 



In the broader sense, an interferometer is 

 an instrument capable of (1) splitting a 



monochromatic sinusoidal wave train of 

 given frequency into two (or more) coherent 

 beams, and (2) allowing these beams to be- 

 come superimposed again after a variable 

 path, in such a way that the resulting in- 

 stantaneous sum sine wave amplitude can be 

 detected. The principle of measurements 

 with such an instrument is contained in the 

 statement that the amplitude of the sine 

 wave is a periodic function of the phase dif- 

 ference between the two component wave 

 trains, with a period equal to 2 tt radians. 



The above definition is sufficiently broad 

 to encompass types of instruments in which 

 the active coherent beams interfere once, 

 those in which only a small sample of many 

 wave trains interfere simultaneously (Fabry- 

 Perrot type), and those in which the inter- 

 fering waves are transported on another car- 

 rier wave. 



In the latter case, the only requirement is 

 that the wave under question be recoverable 

 (by some demodulation process). In inter- 

 ferometry the nature of the transport 

 mechanism need not be specified. 



Such a definition is rather close to that 

 adopted by Dayhoff (80).* Extended implica- 

 tions and practical applications in the micro- 

 wave field will be found in the report of this 

 author. 



This definition is compatible with classifi- 

 cations of possible interferometers from sev- 

 eral points of view. In every case, the basic 

 information supplied bj^ an interferometer is 

 a phase difference. A knowledge of the phase 

 difference is complete if its angle — or cor- 

 responding amplitude difference — and its 

 algebraic sign are ascertained. 



In equations (27) to (30), it is assiuned 

 that the rays of light travel from A and B 

 to c and c' in an isotropic medivmi of refrac- 

 tive index 1. Obviously, equation (29) re- 

 mains valid if two different media of 

 refractive indices ni and no , respectively, 

 are interposed on the trajectories Ac and Be. 



* See references on page 500. 



505 



