Phase retrieval from a high-numerical-aperture intensity distribution by use of an aperture-array filter

Almost all noninterferometric phase-retrieval methods used in coherent diffractive imaging have been based on the measurement system with low numerical aperture, in which Fresnel or Fraunhofer approximation is valid to express the wave propagation between an object and a detector. In microscopy, which is a typical application of coherent diffractive imaging, the measurement of the diffraction intensity with high numerical aperture is required for object reconstruction at high spatial resolution. We here propose an extension procedure to apply the previous phase-retrieval method using an aperture-array filter [J. Opt. Soc. Am. A25, 742 (2008)] to the system with high numerical aperture, in which the first Rayleigh-Sommerfeld integral for spherical waves is utilized instead of the Fresnel integral for parabolic waves. Computer-simulated examples in the high-numerical-aperture system demonstrate object reconstruction at high lateral resolution and retrieval of information in the depth direction of an object.