Abstract
Ptychography is a lensless imaging technology that is validated from hard X-rays to terahertz spectral range. It is most attractive for extreme ultraviolet (EUV) and X-rays as optical elements are expensive and often not available. Typically, the set up involves coherently illuminated object that directs the scattered radiation normally to detector which is parallel to the object plane. Computer processing of diffraction patterns obtained when scanning the object gives the image, more precisely, the distribution of intensity and phase on its surface. However, this scheme is inefficient for EUV and X-rays due to poor reflectivity and low penetration in all materials. Reflection mode ptychography solves the problem if illumination angles do not exceed the critical angle of object material. Changing the geometry of experiment changes physical and mathematical model of image formation. Including: diffraction integral describing beam propagation from object to detector, inverse problem, optimization of object illumination angle, position and orientation of detector, choosing size and grid of coordinate and frequency computer domains. This paper considers the wavefield scattered to detector by obliquely illuminated object and determines a domain for processing of obtained scans. Solution of inverse problem with phase retrieval and resulting numerical images will be presented in the next paper.
Highlights
The retrieval of the field phase on the object under study, is a basis of modern lensless imaging
The development of the ideas of this work led to the emergence of lensless imaging and ptychography as they are currently used in the visible, extreme ultraviolet (EUV) and X-ray ranges [2,3,4,5,6,7,8,9]
As well we present the formulas for calculating diffraction by a tilted object for the case of large apertures and large distances in high resolution ptychography
Summary
The retrieval of the field phase on the object under study, is a basis of modern lensless imaging. The task is formulated as follows: to restore the phase of the coherent wave field from the measurements of its modulus on two parallel planes determined by the object and the detector. For this purpose, the iterative algorithm is used with calculation of the propagation of coherent radiation from the object plane to the plane of the detector. The result is the distribution of the complex field on both planes This problem was solved for the first time, in [1] using one of the best computers at that time with ~1 megabyte memory and ~1 megaflop performance, which made it possible to analyze a large number of 32 × 32 images. One of the main advantages of lensless optical systems is the fundamental possibility to get rid of a problem associated with aberrations of imaging optical elements in approaching the diffraction resolution limit in microscopy, atmospheric and astronomical optics (Obviously, in order to fully realize the indicated advantage of lensless systems, it is necessary to go beyond the paraxial methods of modeling the propagation of light beams from an object to a detector)
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