Device for determining a refractive index in a large number of points of a physical environment

Apparatus for determining a refractive index in a large number of points p, of a physical medium, each point being defined by a fixed reference point occupying the centre of gravity of an elementary grid unit or block, in which p elementary grid units form a grid-like array of the physical medium, wherein the apparatus comprises:

• a light laser, preferably an infra-red laser, displaceable in elementary steps along a displacement guide or fixed with respect to a mirror displaceable in elementary steps along the displacement guide, in order to carry out a series of p coplanar pulsed laser rays each starting from a starting point Ap defined with respect to the displacement guide and arriving at an arrival point Bp defined by a detection means, after having passed through the physical medium along an optical path defined as being the shortest optical trajectory between the two points Ap and Bp;
• a counter time-synchronised with each pulsed laser ray so as to record an instant Tp when each pulsed laser ray reaches the arrival point Bp counting from the initial instant when the pulsed laser ray has left the starting point Ap;
• and
• a computer programmed to carry out the following steps:
• (1) to investigate the optical path from among the optical trajectories all leaving from the starting point Ap and all arriving at the arrival point Bp, each optical trajectory being defined by a sequence of elementary optical paths (L), each equal to the arithmetic product of two terms, in which the first term is a modulus of a vector connecting two centres of gravity of two adjacent elementary grid units, and in which the second term is an estimated refractive index at each centre of gravity;
• (2) starting from p linear equations connecting, for each of the p investigated optical paths, the elementary optical paths (L) and the indices of refraction (N) to the detected passage time Tp, to construct a square matrix of the elementary optical paths [L], a vector of the refractive indices of the elementary grid units [N] and a vector of the passage times of the light ray [T] and to solve the matrix equation;
• [N]*[L]=[T]
• with respect to the vector of the refractive indices of the elementary grid units [N];
• and
• (3) to repeat the steps (1) and (2) so as to investigate new optical paths with the refractive indices of the elementary grid units calculated during an immediately preceding iteration, to solve the matrix equation with the new elementary optical paths corresponding to the new investigated optical paths, and obtain a new vector of the refractive indices of the elementary grid units until the matrix of the elementary optical paths [L] converges and the vector of the refractive indices of the elementary grid units [N] also converges.