By Peter R. Fontana (Auth.)
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114), see J a k e m a n (21) a n d F r a n c o n (6, Chapter 9)]. The term which is independent of the delay τ comes from the dc components of the currents. The second term which is p r o p o r t i o n a l t o the square of the first-order correlation function is d u e t o t h e correlated beat frequencies. This term gives a measure of the correlation of the fluctuations of the currents. In o u r analysis g \x) is real a n d the spectrum C/(co) must have both positive a n d negative frequency components.
The distributions | / ) ( ω ) | have maxima at + ω and — ω ·, respectively. W e can obtain the convolution of /(ω) with itself by shifting the distribution along the ω axis and for each position determine the c o m m o n area of the two sets of curves. In Fig. 9 the spectrum of two decaying sinusoidal wave trains is plotted as a function of ω together with the real part of the convolution η(ω). The Fourier transforms /}(ω) are given by Eq. 52). The peak at zero frequency is the main detector response.
These results can be checked directly by calculating first Ρ(ω) from Eq. 111) a n d then integrating the result over ω. The result of Eq. 114) is valid for an incoherent point source. In deriving it we implicitly assumed that the electric field of the source is stationary (11, p. 7). This means that averages of [£ (i)] d o not depend on the origin of time. The detector measures the intensity of light due to m a n y atoms with each a t o m emitting a wave train at a r a n d o m time. The assumption of stationarity was used in the integration over t [Eq.