Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the hologram is then processed using a plane wave in the reconstruction. This physical compensation can be avoided, and several numerical methods exist to retrieve phase contrast images in which the microscope curvature is compensated. Usually, a digital array of complex numbers is introduced in the reconstruction process to perform this curvature correction. Different corrections are discussed in terms of their influence on the reconstructed image size and location in space. The results are presented according to two different expressions of the Fresnel transform, the single Fourier transform and convolution approaches, used to propagate the reconstructed wavefront from the hologram plane to the final image plane.