Resolution-enhanced reflection ptychography with axial distance calibration

Reflection ptychography is a lens-free computational imaging technology that operates by a coherent beam illuminated to a specimen inclined to the optical axis, a set of distorted diffracted patterns is captured on the far-filed plane. This tilted distortion results from the tilt angle of illumination in a reflection mode as a non-coplanar scattering geometry, which mismatches the Fourier transformed distribution and blocks the operation of FFT (fast Fourier Transform) in standard ptychographic reconstruction algorithms. This distortion can be corrected by performing a coordinate transform from the tilted geometry combined with knowledge of the axial distance of diffraction and the radiation wavelength. However, practically the axial distance usually cannot be measured with accuracy instead of a rough estimate, which may disrupt the correction from distortion, and degrade the reconstructed quality significantly. Here, we propose and analyze for the first time a straightforward axial distance calibration approach to improve the reconstructed resolution in reflection ptychography. Firstly, a uniform Fraunhofer-shaped diffraction is transformed from the tilted distorted scatterings by a coordinate transform at a coarse estimate of axial distance. Then, the axial distance error can be precisely corrected from the periodic unwrapped phase of the retrieved probe by ptychography. Finally, a resolution-enhanced reconstruction is generated from the reflection ptychography with axial distance calibration. A group of proof-of-concept experiments was performed for verification. Results demonstrate that the axial distance can be precisely calibrated within a fraction of a millimeter. Moreover, the reconstructed resolution is remarkably improved (2 times improvement in our experimental tests) by utilizing the proposed approach in reflection ptychography.