Speckle-noise computing by two-parameter analysis of the reflected light’s periodic variations

Abstract

The paper presents the original method of calculating the speckle noise that appear in the light wave reflected from the electro optical medium that periodically modulates the wave. It has been shown that the problem is mathematically described by the Rice statistical model. The calculation of the noise component at processing the periodic electro optical modulation of the reflected light is implemented by means of the so called two parameter method of moments, namely-by processing the data for the second and the fourth moments of the signal to be measured. As a result both the useful signal and the noise dispersion are being jointly estimated. The estimation of the speckle noise value in the reflected periodically modulated light allows increasing the accuracy of the medium's electro optical coefficients' determination if compared with the traditional techniques. The dependence of the estimations' precision on the sample length has been studied.

Peculiarities of the Rice Statistical Distribution: Mathematical Substantiation

“…The existence and the uniqueness of the solution of equation (10) are obviously determined by the presence and the quantity of the points of intersection of the curves depicting the right-hand side and the left-hand side of (10).…”

“…The considered curves' intersection point, in virtue of the above substantiated smoothness, monotonous character and upward-convexity of both curves and with account of their radii of curvature, may be only a single one, i.e. the non-zero solution of equation (10) and exists and is a unique. The proved existence and uniqueness of the solution for parameter ν obviously means the existence and the uniqueness of the solution for the second parameter σ .…”

“…Such a random variable is known to obey to the Rice statistical distribution. The range of the problems that are mathematically described by the Rice distribution includes the tasks of magnetic-resonance visualization [7,8], the radio signals reception and processing, the tasks of the radar signals analysis [9], as well as the analysis of the sonar signals, the measurements of the optical medium's properties by analyzing the reflected wave [10,11], etc.…”

“…upward-convex function that in virtue of the properties of function ɶ left-hand side of equation(10) also presents a monotonous and upward-convex function sides of equation(10) are monotonically increasing convex function outgoing from the origin of coordinates. These functions asymptotically approach to horizontal lines 10) is less that the asymptotic value l ν of its left-hand side ( ) l g ψ .…”

“…These functions asymptotically approach to horizontal lines 10) is less that the asymptotic value l ν of its left-hand side ( ) l g ψ . So, the right-hand and the left-hand sides of equation(10) are depicted by the upward-convex curves outgoing from the origin of coordinates and having different asymptotes. It is obvious that these two monotonically increasing convex curves may intersect only in the case if in the vicinity of zero point 0 g → the derivative of the equation's right-hand side…”