Optics Express, Vol. 21, Issue 6, pp. 7726-7733 (2013).
Tatiana Latychevskaia and Hans-Werner Fink.
Physics Institute, University of Zurich, Winterthurerstrasse 190, CH-8057, Switzerland.
It is generally believed that the resolution in digital holography is limited by the size of the captured holographic record. Here, we present a method to circumvent this limit by self-extrapolating experimental holograms beyond the area that is actually captured. This is done by first padding the surroundings of the hologram and then conducting an iterative reconstruction procedure. The wavefront beyond the experimentally detected area is thus retrieved and the hologram reconstruction shows enhanced resolution. To demonstrate the power of this concept, we apply it to simulated as well as experimental holograms.
© 2013 OSA
The ingenious idea of Dennis Gabor of superimposing the object wave with a known reference wave led to holography providing a record of amplitude and phase of the wave scattered by an object. Extracting the distribution of the complex-valued object wave is thus straightforward. In accordance with Huygens principle, the wavefront is a composition of elementary waves scattered by the object. These continuous waves propagate in space and are mapped wherever an appropriate detector is positioned beyond the sample. However, even outside the detector area where the wave is not mapped, the wave front does exist in a pre-defined manner just given by the scattering object.
We have shown that the holographic record mapped by a limited size detector, in fact contains already sufficient information to recover the full distribution of the elementary waves even where there is no detector present. Already a small fraction of an optical hologram allows reconstructing the entire object. By applying an iterative phase retrieval algorithm where the constraint of a limited detector area is removed, the entire wave front distribution even beyond the detector can be retrieved. In this way, the numerical aperture of the setup and with this the resolution of the reconstructed object is a posteriori increased.