Intensity fluctuations in forward scattering and temporal coherence.
The problem of forward scattering by a nonergodic system of identical particles is considered. The analysis of statistical characteristics of intensity fluctuations arising as a result of finite observation time shows that the mean dispersion of intensity fluctuations can be expressed as a function of the wavelength, diffusion coefficient, scattering angle, and observation time. The relation between the temporal correlation function of the scattered radiation and its second-order intensity moments is established. Quantitative estimates of the effect with the infrared laser beam propagating through fog give results comparable to the dispersion due to refractive index fluctuations in a pure atmosphere (Tatarskii).
Some Properties of Coherent Light
The present paper is concerned with the study of some general properties of coherent light. A clear definition of coherence is given, which appears to be preferable to definitions previously proposed by other authors. Several new theorems relating to correlation functions and the spectral density functions of coherent light are derived. The results are used to establish the Huygens-Fresnel principle for a coherent optical field. This principle has previously been freely applied to such a field, although the validity of the principle has only been justified for the much more idealized (and physically unrealizable) case of a field which is strictly monochromatic. The present formulation of the Huygens-Fresenel principle involves only observable quantities and not the instantaneous amplitudes and the instantaneous phases of the light vibrations.
A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width
The results of part I of this investigation are generalized to stationary fields with a spectral range of arbitrary width. For this purpose it is found necessary to introduce in place of the mutual intensity function of Zernike a more general correlation function Γ(⁡x1,x2,τ)=, which expresses the correlation between disturbances at any two given points P1(x1), P2(x2) in the field, the disturbance at P1 being considered at a time τ later than at P2. It is shown that Гˆ is an observable quantity. Expressions for Гˆ in terms of functions which specify the source and the transmission properties of the medium are derived. Further, it is shown that in vacuo the correlation function obeys rigorously the two wave equations Γ(⁡x1,x2,τ)=, where ∇23 is the Laplacian operator with respect to the co-ordinates (xs, ys, zs) of Ps(xs). Using this result, a formula is obtained which expresses rigorously the correlation between disturbances at P1 and P2 in terms of the values of the correlation and of its derivatives at all pairs of points on an arbitrary closed surface which surrounds P1 and P2. A special case of this formula (P2 = P1, τ = 0) represents a rigorous formulation of the generalized Huygens principle, involving observable quantities only.