How many signal photons determine a velocity

The paper considers the variation in the particle velocity due to different realizations of the detected photon signal for the same particle, trajectory, and the same laser power. The accuracy of velocity measurements in LDV depends on the number of signal photons received. The extraction of information by inversion from the Fourier and Laplace transforms and a new analysis method for inversion which uses explicit eigenvalues of 'Mellin kernel' problems were developed. The method allows inversion of Laplace transforms, including the analysis of turbulence from photon correlation functions, and construction of a generalized Shannon information measure for each one. The eigenvalues of different kernels are compared and the potential information transfer capabilities of different experiments are assessed. Results are described which show that 100 photons detected a large signal, with a generalized Shannon theory explaining this result. A new data analysis method based on information theory is described.