Limits of Elemental Contrast by Low Energy Electron Point Source Holography

Motivated by the need for less destructive imaging of nanostructures, we pursue point-source in-line holography (also known as point projection microscopy, or PPM) with very low energy electrons (-100 eV). This technique exploits the recent creation of ultrasharp and robust nanotips, which can field emit electrons from a single atom at their apex, thus creating a path to an extremely coherent source of electrons for holography. Our method has the potential to achieve atom resolved images of nanostructures including biological molecules. We demonstrate a further advantage of PPM emerging from the fact that the very low energy electrons employed experience a large elastic scattering cross section relative to many-keV electrons. Moreover, the variation of scattering factors as a function of atom type allows for enhanced elemental contrast. Low energy electrons arguably offer the further advantage of causing minimum damage to most materials. Model results for small molecules and adatoms on graphene substrates, where very small damage is expected, indicate that a phase contrast is obtainable between elements with significantly different Z-numbers. For example, for typical setup parameters, atoms such as C and P are discernible, while C and N are not.Comment: 15 pages, 5 figure

높은 공간 대역폭을 위한 복소 진폭 이미징 및 디스플레이 시스템

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·정보공학부, 2021. 2. 이병호.빛을 파동으로 이해하면 간섭과 회절을 포함한 다양한 광학 현상을 해석 할 수 있다. 미래 기술이라 불리는 홀로그램, 3차원 이미징 및 3차원 디스플레이 시스템들은 파동의 복소진폭을 이해하고 변조함으로써 구현될 수 있다. 현존하는 광공학 장치를 넘어서는 파동 광학에 기반한 광공학 장치들을 상용화 및 발전시키기 위해 많은 연구가 진행되어왔지만, 지금껏 구현된 장치들은 공간 대역폭 (space-bandwidth product)의 제한으로 인해 그 성능이 대중의 기대에 부합하기 어려움을 겪고있다. 본 논문은 복소 진폭 이미징 및 디스플레이 시스템에서 공간 대역폭을 향상 시키는 방법을 제안한다. 복소 진폭 변조 시스템의 성능은 광학 시스템의 정보량을 나타내는 공간 대역폭에 의해 제한된다. 이 공간 대역폭을 향상시키기 위하여 저자는 다양한 다중화 기술을 적용하며, 동시에 다중화된 정보를 분리하는 알고리즘과 장치를 고안한다. 첫번째로 디지털 홀로그래피 기술에 공간 주파수를 다중화해 대역폭을 효율적으로 활용하는 방법을 고안하여 획득된 홀로그램의 촬영 영역을 증가시킨다. 두번째로, 단일 촬영 푸리에 타이코그래피 (single-shot Fourier ptychography) 기술에서는 광 조사 다중화를 사용하여 이미지 센서에 기록되는 정보의 양을 확장시킨다. 다중화 된 정보를 분해하고 복소 진폭을 획득하기 위하여 새로운 광학 시스템과 전산 알고리즘을 고안하여 해상도가 향상된 복소 진폭을 획득한다. 세번째로, 저자는 홀로그램 디스플레이에 조명 다중화 및 시분할 기술을 적용한다. 다중화 된 정보는 인간의 인지적 시간 대역폭과 제안된 시스템의 공간 필터링의 결합으로 분해된다. 구현된 홀로그래픽 디스플레이는 공간 대역폭이 확장되어 더 넓은 시야각에 삼차원 홀로그램을 제공한다. 본 논문은 작은 공간대역폭이라는 공통된 문제를 공유하는 이미징 및 디스플레이 분야의 발전에 기여할 것으로 기대된다. 저자는 본 연구에서 제안된 방법이 다양한 복소 진폭 변조 시스템의 성능 향상에 영감을 주며, 나아가 삼차원 계측, 홀로그래피, 가상 및 증강현실을 포함한 다양한 미래 산업에 발전에 기여할 수 있기를 기대한다.Understanding light as a wave makes it possible to interpret a variety of phenomena, including interference and diffraction. By modulating the complex amplitude of the wave, hologram, three-dimensional imaging, and three-dimensional display system, called future technologies, can be implemented that surpass the currently commercialized optical engineering devices. Although a lot of research has been conducted to develop and commercialize the wave optical system, state-of-the-art devices are still far from the performance expected by the public due to the limited space-bandwidth product (SBP). This dissertation presents the studies on high SBP for complex amplitude imaging and display systems. The performance of a complex amplitude modulating system is limited by the SBP, which represents the amount of information in the optical system. To improve the SBP of the complex amplitude in a limited amount of information, the author applies various multiplexing techniques suitable for the implemented system. In practice, the spatial frequency multiplexed digital holography is devised by efficiently allocating frequency bandwidth with dual-wavelength light sources. The author also applies illumination multiplexing to the single-shot Fourier ptychography to expand the amount of information recorded in the image sensor. Computational reconstruction algorithm combined with novel optical design allows the acquired multiplexed information to be decomposed in the imaging system, leading to improvement of size of the image or resolution. Furthermore, the author applied illumination multiplexing and temporal multiplexing techniques to holographic displays. The multiplexed information is decomposed by a combination of human perceptual temporal bandwidth and spatial filtering. The SBP enhanced holographic display is implemented, providing a more wide viewing angle. It is expected that this thesis will contribute to the development of the imaging and display fields, which share a common problem of small SBP. The author hopes that the proposed methods will inspire various researchers to approach the implementation of complex amplitude modulating systems, and various future industries, including 3-D inspection, holography, virtual reality, and augmented reality will be realized with high-performance.Abstract i Contents iii List of Tables vi List of Figures vii 1 Introduction 1 1.1 Complex Amplitude of Wave 1 1.2 Complex Amplitude Optical System 3 1.3 Motivation and Purpose of the Dissertation 5 1.4 Scope and Organization 8 2 Space-Bandwidth Product 10 2.1 Overview of Space-Bandwidth Product 10 2.2 Space-Bandwidth Product of Complex Amplitude Imaging Systems 11 2.3 Space-Bandwidth Product of Complex Amplitude Display Systems 13 3 Double Size Complex Amplitude Imaging via Digital Holography 15 3.1 Introduction 15 3.1.1 Digital Holography 16 3.1.2 Frequency Multiplexed Digital Holography 22 3.1.3 Adaptation of Diffractive Grating for Simple Interferometer 24 3.2 Principle 26 3.2.1 Single Diffraction Grating Off-Axis Digital Holography 26 3.2.2 Double Size Implementation with Multiplexed Illumination 29 3.3 Implementation 32 3.4 Experimental Results 34 3.4.1 Resolution Assessment 34 3.4.2 Imaging Result 36 3.4.3 Quantitative 3-D Measurement 38 3.5 Conclusion 42 4 High-Resolution Complex Amplitude Imaging via Fourier Ptychographic Microscopy 43 4.1 Introduction 43 4.1.1 Phase Retrieval 45 4.1.2 Fourier Ptychographic Microscopy 47 4.2 Principle 52 4.2.1 Imaging System for Single-Shot Fourier Ptychographic Microscopy 52 4.2.2 Multiplexed Illumination 55 4.2.3 Reconstruction Algorithm 58 4.3 Implementation 60 4.3.1 Numerical Simulation 60 4.3.2 System Design 64 4.4 Results and Assessment 65 4.4.1 Resolution 65 4.4.2 Phase Retrieval of Biological Specimen 68 4.5 Discussion 71 4.6 Conclusion 73 5 Viewing Angle Enhancement for Holographic Display 74 5.1 Introduction 74 5.1.1 Complex Amplitude Representation 76 5.1.2 DMD Holographic Displays 79 5.2 Principle 81 5.2.1 Structured Illumination 81 5.2.2 TM with Array System 83 5.2.3 Time Domain Design 84 5.3 Implementation 85 5.3.1 Hardware Design 85 5.3.2 Frequency Domain Design 85 5.3.3 Aberration Correction 87 5.4 Results 88 5.5 Discussion 92 5.5.1 Speckle 92 5.5.2 Applications for Near-eye Displays 94 5.6 Conclusion 99 6 Conclusion 100 Appendix 116 Abstract (In Korean) 117Docto

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and outlook on how to better use DL to improve the reliability and efficiency in PR. Furthermore, we present a live-updating resource (https://github.com/kqwang/phase-recovery) for readers to learn more about PR.Comment: 82 pages, 32 figure

Dual-plane coupled phase retrieval for non-prior holographic imaging

AbstractAccurate depiction of waves in temporal and spatial is essential to the investigation of interactions between physical objects and waves. Digital holography (DH) can perform quantitative analysis of wave–matter interactions. Full detector-bandwidth reconstruction can be realized based on in-line DH. But the overlapping of twin images strongly prevents quantitative analysis. For off-axis DH, the object wave and the detector bandwidth need to satisfy certain conditions to perform reconstruction accurately. Here, we present a reliable approach involving a coupled configuration for combining two in-line holograms and one off-axis hologram, using a rapidly converging iterative procedure based on two-plane coupled phase retrieval (TwPCPR) method. It realizes a fast-convergence holographic calculation method. High-resolution and full-field reconstruction by exploiting the full bandwidth are demonstrated for complex-amplitude reconstruction. Off-axis optimization phase provides an effective initial guess to avoid stagnation and minimize the required measurements of multi-plane phase retrieval. The proposed strategy works well for more extended samples without any prior assumptions of the objects including support, non-negative, sparse constraints, etc. It helps to enhance and empower applications in wavefront sensing, computational microscopy and biological tissue analysis

Non-iterative complex wave-field reconstruction based on Kramers-Kronig relations

A new computational imaging method to reconstruct the complex wave-field is reported. Due to the existence of zero frequency component, the measured signal by amplitude modulation of pupil has a spectrum similar to the one of off-axis hologram. The mathematical analogy between them is established in this paper. Based on this observation and analyticity of band-limited signal under any diffraction-limited system, an algorithm from Kramers-Kronig (KK) relations is utilized to recover the phase information only from the intensity patterns. From the sensing side, only two measurements are required at least. From the reconstruction algorithm side, our method is iteration-free and parameter-free, also without any assumption on sample characteristics. It owns several advantages over existing phase imaging methods and could provide a unique perspective to understand current computational imaging methods

Holographic fast gradient light interference microscopy (HF-GLIM)

Quantitative phase imaging has been an emerging technique in the field of biomedical imaging. As one type, gradient light interference microscopy (GLIM) is used to retrieve a quantitative gradient mapping of the phase delay that is produced by a biological sample. The method involves collecting four phase-shifted frames for a single field of view, which ultimately combines arithmetically into phase gradient information. The phase-shifting is done by a space light modulator (SLM) which intakes an appropriate voltage that converts into a corresponding phase retardation in the image field. Despite GLIM’s ability to generate a quantitative phase gradient of a sample, such module depends heavily on the operational speed of the SLM. The holographic fast gradient light interference microscopy (HF-GLIM) aims to retrieve a field of view with only a single image from the conventional differential interference contrast microscope (DIC), and is sent to a tilted Sagnac interferometer to create a holographic output at the camera. Through digital processing of the Hologram using Fourier filtering, the phase gradient that is given by the sample can be retrieved only through a single recording instance from the HF-GLIM. The publication aims to derive the functionality of HF-GLIM utilizing a mathematical derivation, geometrical analysis, and the simulation results.Ope

High-resolution transport-of-intensity quantitative phase microscopy with annular illumination

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.Comment: This manuscript was originally submitted on 20 Feb. 201