Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic...

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.