Reduction methods of the reconstruction error for large-scale implementation of near-field acoustical holography

New extrapolation methods in real and wave number spaces are proposed to extend near-field acoustical holography (NAH) toward a more quantitative technique applicable to the vibration measurement of actual large-scale structures. The finiteness of the measurement aperture is a serious impediment to such large-scale implementation of NAH because the measurement aperture sufficiently larger than the vibrating structure of interest is usually needed. We should thus investigate how to reduce the reconstruction error when the measurement aperture is restricted to a fraction of the vibrating structure. The following practical suggestions are derived from simulations and underwater experiments: (1) A wave number-space extrapolation method can reduce the reconstruction error to about 25% for the measurement aperture corresponding to 1/16th of the vibrating structure when 10,000 iterations of the extrapolation process are applied. (2) A real-space extrapolation method can reduce the reconstruction error to negligible degree (10(-10)%) for the measurement aperture corresponding to four times as large as the vibration structure when ten iterations of the extrapolation process are applied. (3) The former method may be widely and safely applied, but many iterations are necessary; the latter method can reduce the reconstruction error very quickly, but a wider measurement aperture than that in the former is needed. Therefore, when the measurement aperture cannot be larger than the vibrating structure, the former method is recommended, while when the measurement aperture is larger than the structure, the latter method is recommended. Summing up, the accuracy of our proposed methods, which is attributed to the property of data extrapolation method that the data inside the measurement aperture is conserved after adequately extrapolating the data outside the aperture, will be relevant to a more quantitative measurement and analysis of real large-scale structures.