Pixel size adjustment in coherent diffractive imaging within the Rayleigh-Sommerfeld regime

The reconstruction of the smallest resolvable object detail in digital holography and coherent diffractive imaging when the detector is mounted close to the object of interest is restricted by the sensor's pixel size. Very high resolution information is intrinsically encoded in the data because the effective numerical aperture (NA) of the detector (its solid angular size as subtended at the object plane) is very high. The correct physical propagation model to use in the reconstruction process for this setup should be based on the Rayleigh-Sommerfeld diffraction integral, which is commonly implemented via a convolution operation. However, the convolution operation has the drawback that the pixel size of the propagation calculation is preserved between the object and the detector, and so the maximum resolution of the reconstruction is limited by the detector pixel size, not its effective NA. Here we show that this problem can be overcome via the introduction of a numerical spherical lens with adjustable magnification. This approach enables the reconstruction of object details smaller than the detector pixel size or of objects that extend beyond the size of the detector. It will have applications in all forms of near-field lensless microscopy.