A trabecular bone consists of trabeculae whose mechanical properties differ significantly from the surrounding marrow, therefore an ultrasonic wave propagating within the bone structure is strongly scattered. The aim of this paper was to evaluate the contribution of the first, second and higher order scattering (multiple scattering) into the total scattering of ultrasound in a trabecular bone. The scattering due to the interconnections between thick trabeculae, usually neglected in trabecular bone models, has been also studied. The basic element in our model of the trabecular bone was an elastic cylinder with a various finite-length and diameter as well as orientation. The applied model was taking into account variation of both, elements size and their spatial configuration. The field scattered on the bone model was evaluated by solving numerically the integral form of the generalized Sturm-Liouville equation describing a scalar wave in inhomogeneous and lossy media. For the scattered fields calculated numerically the effective cross-sections were determined. The influence of absorption on the scattering coefficients was demonstrated. The results allowed to conclude that within the frequency range from 0.5 to 1.5 MHz contribution of the second order scattering to the effective backscattering cross-section is at least 500 times lower than that due to the first order scattering. It was noticed that for a frequency higher than 1.5 MHz fast growth of the backscattering (reflection) coefficients, calculated for the second order scattering, occurs.

This paper presents two methods for evaluation of the effective wavenumber of nearly-Gaussian beams in laser interferometers that can be used for determination of a so called diffraction correction in absolute gravimeters. The first method, that can be simply used in situ, is an empirical procedure based on the evaluation of the variability of g measurements against the amount of light limited by an iris diaphragm and transmitted to a photodetector. However, precision of this method depends on the beam quality similarly as in the case of the conventional method based on measurement of a beam width. The second method, that is more complex, is based on beam profiling in various distances and on calculation of the effective wavenumber using the second spatial derivative of a non-ideal beam field envelope. The measurement results achieved by both methods are presented on an example of two absolute gravimeters and the determined diffraction corrections are compared with the results obtained by measurements of beam width. Agreement of methods within about 1 mGal have been obtained with average diffraction corrections slightly exceeding +2 mGal for three FG5(X) gravimeter configurations.