  We examine the nature of the 3D image as obtained by replay (or
back-propagation) of the object wave from the hologram recording plane to the
original object volume. While recording of a hologram involves transferring
information from a 3D volume to a 2D detector plane, the replay of the hologram
involves creating information in a set of 3D voxels from a much smaller number
of 2D detector pixels, which at first look appears to be surprising. We point
out that the hologram replay process is a Hermitian transpose (and not inverse)
of the hologram formation process and therefore only provides an approximation
to the original 3D object function. With the knowledge of this Hermitian
transpose property, we show how one may realize true 3D image reconstruction
via a regularized optimization algorithm. The numerical illustrations of this
optimization approach as presented here show excellent slice-by-slice
tomographic 3D reconstruction of the original object under the weak scattering
approximation. In particular, the reconstructed 3D image field has near-zero
numerical values at voxels where the original object did not exist. We note
that 3D image reconstruction of this kind cannot be achieved by the traditional
physical replay process. In this sense the proposed methodology for digital
holographic image reconstruction goes beyond numerically mimicking the
traditional film based holographic replay. The reconstruction approach may find
potential applications in a number of digital holographic imaging systems.
