Application of wavelet transform to hologram analysis: three-dimensional location of particles

The wavelet analysis provides an efficient tool in numerous signal-processi ng problems and has been implemented in optical processing techniques, such as in-line holography. When the diffraction pattern recorded on a hologram is analyzed by means of a wavelet transform, the 3-D location of small par ticles can be determined very accurately. The diffraction process can, in f act, be interpreted as a convolution with a family of wavelet functions, or , merely, as a wavelet transform. The scale parameter of the wavelet family is related to the axial distance z that the wave propagates. The original field is then reconstructed by searching for the optimum value of the scale parameter which produces a maximum of the wavelet transform modulus. The t echnique proposed is implemented and experimental results are presented. (C ) 2000 Elsevier Science Ltd. All rights reserved.