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Nanometer-Scale and Low-Density Imaging with Extreme Ultraviolet and Soft X-ray Radiation
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Ptychography is a technique [147] that was developed to solve a lost-phase problem in diffraction imaging. The idea was to determine the relative phases between adjacent diffraction patterns, as can be seen in Figure 7.29. A focused EUV/SXR beam illuminates the object placed, i.e. on top of a thin silicon nitride membrane. The focus spot size might be of the order of a few hundreds of nanometers. The object diffracts the EUV/SXR radiation, and downstream the beam, a single diffraction pattern is collected. Then the object is raster scanned point by point to record a number of diffraction patterns. The scanning step is usually smaller than the diameter of the focus. For the reconstruction, numerical algorithms are used. Those are, typically, “ePIE” algorithm [148], difference map approach [149] or conjugate gradient [150].
Picometer Detection by Adaptive Holographic Interferometry
Published in Klaus D. Sattler, Fundamentals of PICOSCIENCE, 2013
In principle, ptychography is only limited by electron wavelength and the degree of coherence of the electron source. With typical TEM electron wavelengths of 2.5pm, it has the potential for resolutions far into the picometer range. It is well adapted to map electrostatic and magnetic potentials around very thin specimens, such as thin bamboo nanowires. But, at present, ptychography is only applicable to very thin phase objects. Ptychography places severe demands on raster patterns, and instrumental and environmental noise within the scan generator, and the entire instrument will probably place the lower bound on the achievable resolution. Gabor's idea that the highest resolution imaging would not involve magnetic lenses at all is still very much alive.
Ptychographic Imaging of Biological Samples with Soft X-Ray Radiation
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
Ptychography is a variant of coherent imaging techniques that uses multiple far-field diffraction patterns from overlapping illuminations on an object. The far-field offers a reciprocal relationship of sizes where objects and their microscopic features produce diffraction signal at large angles, which is essentially the magnification that is a demand in microscopy. Using pixelated image detectors, the coherent diffraction intensity pattern can be used to retrieve an estimate of the phase that is required to reconstruct the complex valued specimen by simple Fourier transform.
Median momentum reweighted amplitude flow for phase retrieval with arbitrary corruption
Published in Journal of Modern Optics, 2021
Zhang Quanbing, Liu Dequn, Hu Feihang, Li Aoya, Cheng Hong
It is well known that a great deal of the information available in an optical system resides in the phase; however, ordinary optical detectors cannot measure the phase due to the very high frequency of light [1]. Phase retrieval methods are able to recover the phase from available amplitude or intensity measurements and have proved very important in practice. This problem is prevalent in coherent diffraction imaging [2], X-ray crystallography [3], Fourier ptychography [4], and other areas [5–7].
Sparsity-assisted phase retrieval in the Fresnel zone
Published in Journal of Modern Optics, 2019
Phase imaging is an active research area relevant to several applications in Optics such as astronomical imaging (1), wave-front sensing for adaptive optics (2, 3), optical metrology (3), microscopy of transparent biological cells (4, 5), coherent X-ray imaging (6–8), electron microscopy (9), optical encryption, etc. (10). Interferometry/holography is a well-known technique to measure the phase of a light wave where the phase of an unknown wave-front is measured by interfering it with another (known) mutually coherent field. Non-interferometric methods based on single or multiple intensity (integrated power on the detector pixels) measurements offers an alternative solution to the problem of phase measurement that requires much simpler optical systems compared to environment sensitive interferometers (11). Popular iterative algorithms such as Gerchberg–Saxton (GS) and Fienup’s hybrid input output (HIO) utilize some prior information about the object to be imaged to determine the phase of an unknown wave-front from measured intensity data (12–14). Non-interferometric phase diversity techniques involve computational algorithms to recover the phase using two or more intensity measurements recorded with a known transformation between them. Phase estimation using two or more longitudinal intensity measurement in the Fresnel zone has shown promising results (15). Further, it has been demonstrated in (16) that the effectiveness of iterative procedure improves with a large number of intensity measurements (∼15–20). Phase retrieval using multiple structured illumination patterns (∼ 20) in an iterative framework is also demonstrated (17, 18). However, the large number of measurements required for the phase estimation make this process difficult and inconvenient. Transport of intensity (TIE) based deterministic phase imaging techniques have also been quite popular due to its defocus based experimental configuration (19, 20). We have proposed a spiral phase diversity technique requiring two complementary intensity measurement (21). Another popular phase diversity technique is Fourier ptychography which uses multiple angled illumination for achieving super-resolved phase images (22, 23).