Improvement of resolution for phase retrieval by use of a scanning slit

Abstract

An improved method for resolution of object reconstruction using phase retrieval by use of a scanning slit aperture is proposed. The reconstruction is based on measurements of the Fraunhofer diffraction intensities of wave fields transmitted through a scanning slit in the Fresnel-zone plane of an object. In the improved method, the measurement coordinates of the intensities depend not only on the slit's position used in a previous method but also on the slit's position scaled by the ratio between two distances among the object, Fresnel-zone, and detector planes. The spatial-frequency band for the object reconstruction, which is limited in a previous method by the extent of the Fourier transform of the slit function, can be extended to the bandwidth dependent on the scanning area with the slit. In addition, even in the measurement of the Fresnel diffraction intensities of wave fields transmitted through the slit, the improved resolution can be retained by compensation for a transverse shift of the intensities.

Lensless coherent imaging by a deterministic phase retrieval method with an aperture-array filter

“…1. As mentioned in the previous paper [32], the intensity distributions at the points of coordinates (ξ n ,η m ) , (ξ n ± τ ,η m ) , and (ξ n ,η m ± τ ) in the detector plane have sufficient information for one to retrieve the phase of the correlation integral in Eq.…”

“…Then one can retrieve the two-dimensional (2-D) phase of the correlation integral in the Fresnel-zone plane from Eqs. (4), (6), and (7) by using the phase-retrieval method [31,32] based on the properties of entire functions.…”

“…4, (6), and 7, the inverse Fourier transform of the square aperture ′ R (x, y) has an extent large enough to be approximated into a Gaussian function within the extent of the object function. In the previous paper [31,32], it was found from studies of numerical experiments that the inverse Fourier transform of that aperture function can also be approximated into a Gaussian function with a quadratic phase, provided that the Fresnel number N F concerning the quadratic phase within the aperture width w in Eq. 5is less than about 1.0, which is defined by…”

“…into a Gaussian function with a quadratic phase numerically. Note that the parameter a of the Gaussian amplitude is introduced here for the improvement upon the accuracy of the fitting in the previous paper [32]. It can be seen from Eq.…”

Coherent diffractive imaging beyond the Fresnel approximation using a deterministic phase-retrieval method with an aperture-array filter

“…where p exp−πτaw∕ 6 p λl 2 , s bτ∕πλl, and c πτaw 2 ∕6λl, in which w, τ, λ, and l are the known parameters of the measurement system, and a, b are constants that are numerically determined by fitting the inverse Fourier transform of R 0 x; y into a Gaussian function with a quadratic phase as described in Section 3 of the previous paper [21].…”