Synthetic aperture engineering for superresolved microscopy in digital lensless fourier holography

We present a method capable to improve the resolution limit of an imaging system in digital lensless Fourier holographic configuration. The method is based on angular- and time-multiplexing of the object's spatial frequency information. On one hand, angular multiplexing is implemented by using tilted beam illumination to get access to high order spectral frequency bands of the of the object's spectrum. And, on the other hand, time multiplexing is needed to cover different directions at the spatial frequency domain. This combination of angular- and time- multiplexing in addition with holographic recording allows the complex amplitude recovery of a set of elementary apertures covering different portions of the object's spectrum. Finally, the expanded synthetic aperture (SA) is generated by coherent addition of the set of recovered elementary apertures. Such SA expands up the cut-off frequency limit of the imaging system and allows getting a superresolved image of the input object. Moreover, if a priori knowledge about the input object is available, customized SA shaping is possible by considering the addition of those elementary apertures corresponding with only the directions of interest and, thus, reducing the whole consuming time of the approach. We present experimental results in concordance with theoretical predictions for two different resolution test objects, for different SA shapes, and considering different resolution gain factors.