Improving the spatial resolution of digital holograms using one-dimensional subpixel scanning

The article considers the issue of increasing the spatial resolution during the registration of digital holograms. In practice, discretization is carried out by measuring signal samples using sensors with a certain finite aperture. The resolution is determined by the size of the aperture area over which the averaging takes place. The resolution enhancement method is based on the sampling equation for signals obtained by the subpixel shift method using generalized functions. A subpixel shift is carried out using a spatial shift by a value less than the element of resolution. Apertures of various shapes are used, for example, elliptical, diamond-shaped, hexagonal, but rectangular apertures are most commonly used. The discretization equation involves the use of a two-dimensional aperture function. Below is a way to increase the resolution when using a one-dimensional function. This can be done based on the structure of the holographic signal. In this case, you can use a subpixel shift in only one direction. Digital holography is distinguished by the fact that photodetector matrices which have a spatial resolution much lower than photographic media used in traditional holography methods are used to register the signal,. Therefore, digital holography uses optical schemes with small angles between interfering beams. However, certain restrictions are imposed on the shape of the objects under study. If the objects have a shape that is significantly different from a flat one, it is necessary to use traditional schemes. The article presents mathematical modeling of the resolution enhancement method based on the recovery of signals from a real hologram obtained in the usual way. The increase in resolution is achieved using a one-dimensional subpixel shift. The use of a one-dimensional subpixel shift makes it possible to significantly simplify the optical scheme of the holographic setup.