Digital in-line holography with a sub-picosecond laser beam

The diffraction of an ultrashort pulsed laser beam by an opaque particle is studied. The case of a pulse with a Gaussian spectrum is investigated analytically by using the steepest descent method. This analytical solution allows us to calculate the intensity distribution of the diffraction field. This result enables to determine the optimal fractional orders Fourier transform to reconstruct digital in-line particle hologram.