Depth-resolved measurement of phase gradients in a transient phase object field using pulsed digital holography

A technique to gain depth information from an image-plane digital holographic recording of a transient phase object positioned between a diffuser and an imaging system is demonstrated. The technique produces telecentric reconstructions of the complex amplitude throughout the phase volume using numerical lenses and the complex spectrum formulation of the diffraction integral. The in-plane speckle movements as well as the phase difference between the disturbed field and a reference field are calculated in a finite number of planes using a cross-correlation formulation. It is shown that depth information about in-plane phase gradients can be determined in two planes using reconstructed speckle fields from four different depths. In addition, the plane of optimum reconstruction for calculating the phase difference with maximum contrast is detected from the technique. The method is demonstrated on a measurement of a laser ablation process.