Previously, we have proposed a lensless coherent imaging using a nonholographic and noniterative phase-retrieval method that allows the reconstruction of a complex-valued object from a single diffraction intensity measured with an aperture-array filter. The proof-of-concept experiment of this method has been demonstrated under the Fresnel diffraction approximation. In applications to microscopy, however, the measurement of the diffraction intensity with high numerical aperture beyond the Fresnel approximation is required to obtain the object information at high spatial resolution. Thus we have also presented an extension procedure to apply the method to the cases beyond the Fresnel approximation by means of computer simulations. Here the effectiveness of the procedure is demonstrated by the experiments, in which the reconstruction with about 10 times the resolution of our previous experiment has been achieved and the object information in depth direction has been retrieved.
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