Position Correction in Ptychography and Its Applications

Lenses are indispensable tool to perform imaging and see the small details of an object which was otherwise not possible. The smallest feature of an object that one can see using a lens depends on the numerical aperture (NA) of the lens and the used wavelength of light. For a fixed NA, the shorter the wavelength is, the smaller the features of an object can be seen. Therefore, for high-resolution imaging, short wavelengths such as x-rays and e-beams are used. For these wavelengths, the refractive index of the most of the materials is close to 1. Therefore, rays passing through these lenses do not deviate and get absorbed within the materials eventually. To circumvent this problem, different types of diffractive lenses were introduced. Imaging can be performed using these lenses, however, it cannot achieve diffraction limited resolution. The reason for this is the present aberrations in the imaging systems. To this end, computational imaging methods start to play a major role. Lensless imaging is a type of computational imaging which replaces a lens by algorithms. Hence, lensless imaging is not limited by the present aberrations of the lens or imaging system. Besides, with this technique not only amplitude but also phase information can be retrieved. Phase information is important especially for low contrast objects. Since these algorithms solve the phase of the object iteratively, they are also called as phase retrieval techniques. In the past, several phase retrieval techniques were proposed. Some techniques are successful and some techniques have achieved limited success. For the last few decades, ptychography has been evolving dramatically. Ptychography has been found to be more robust than other existing phase retrieval method, and it has shown potential to be implemented for x-rays and e-beams wavelengths. Ptychographic data is so rich in information that not only it retrieves the object function but also it can retrieve the probe function, 3D information of the object, coherent modes of the light, etc. Ptychography is a phase retrieval technique which uses several far-field diffraction patterns of an object. These patterns are created by scanning the object sequentially using an illuminated probe. The probe position should be in a way that neighboring probes overlap with each other. Due to this overlap area, the ptychographic data contains redundancy and this helps the algorithm to converge fast. When ptychography was implemented using e-beam, the reconstructions suffered from the required accuracy of initial parameters. For instance, 50 pm of accuracy is required in probe positions which is difficult to achieve. This high demand in accuracy undermined its applicability to short wavelengths. Therefore, several attempts were made to correct probe positions in ptychography...