Penalized-likelihood image reconstruction for digital holography.
01 May 2004-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 21, Iss: 5, pp 737-750
TL;DR: A new numerical reconstruction approach using a statistical technique that reconstructs the complex field of the object from the real-valued hologram intensity data and derives an optimization transfer algorithm that monotonically decreases the cost function at each iteration.
Abstract: Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.
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Dissertation•
01 Jan 2009
TL;DR: Fast and Motion Robust Dynamic R∗ 2 Reconstruction for Functional MRI and its Applications in Healthcare and Sports Medicine.
Abstract: Fast and Motion Robust Dynamic R∗ 2 Reconstruction for Functional MRI
1 citations
30 Mar 2022
TL;DR: In this paper , the Fourier transform of the Fresnel transform is modelled as a low-pass filtering process and Gibbs ringing is interpreted as an idealised low pass filtering process.
Abstract: Gibbs ringing is an artefact that occurs when a discontinuous signal is truncated in the Fourier domain. It is a phenomenon which occurs frequently in optics as apodization - the action of an aperture - and which can be interpreted as an idealised low pass filtering process. Diffraction can be approximately modelled using the Fresnel transform. The spectral method of calculating the Fresnel transform, a workhorse in digital holography and other fields, interprets the Fresnel transform as an all-pass filter. In this paper, we analyse the relationship between these phenomena and propose how to use this interpretation to improve image quality.
1 citations
TL;DR: In this paper, a survey of recent developments in various holographic applications powered by deep learning algorithms is presented, with case studies covering a wide range of problems and applications in order to highlight research achievements to date.
Abstract: Recent years have witnessed the unprecedented progress of deep learning applications in digital holography (DH). Nevertheless, there remain huge potentials in how deep learning can further improve performance and enable new functionalities for DH. Here, we survey recent developments in various DH applications powered by deep learning algorithms. This article starts with a brief introduction to digital holographic imaging, then summarizes the most relevant deep learning techniques for DH, with discussions on their benefits and challenges. We then present case studies covering a wide range of problems and applications in order to highlight research achievements to date. We provide an outlook of several promising directions to widen the use of deep learning in various DH applications.
1 citations
01 Jan 2015
TL;DR: A non-holographic microscope that uses off-axis illumination for resolution enhancement and the first experimental measurements of referenceless phase retrieval at multiple angles is developed and the reconstruction of images from a digital hologram is improved based on an iterative algorithm that alternatively updates amplitude and phase.
Abstract: Lee, Dennis Joseph Ph.D., Purdue University, May 2015. Computational Optical Imaging: Applications in Synthetic Aperture Imaging, Phase Retrieval, and Digital Holography. Major Professor: Andrew M. Weiner. Computational imaging has become an important field, as a merger of both algorithms and physical experiments. In the realm of microscopy and optical imaging, an important application is the problem of improving resolution, which is bounded by wavelength and numerical aperture according to the classic diffraction limit. We will investigate the resolution enhancement of phase objects such as transparent biological cells. One key challenge is how to measure phase experimentally. Standard interferometric techniques have the drawback of being sensitive to environmental vibrations and temperature fluctuations, and they use a reference arm which requires more space and cost. Non-holographic methods provide a way to overcome these disadvantages. Another challenge is how to reconstruct phase and amplitude from a digital hologram. The typical method of applying a filter in the frequency domain is limited by finite filter size. Optimization approaches offer a solution to this problem. The work presented here spans three main aspects of phase imaging microscopy including synthetic aperture imaging, phase retrieval, and digital holography. We develop a non-holographic microscope that uses off-axis illumination for resolution enhancement and demonstrate the first experimental measurements of referenceless phase retrieval at multiple angles. We implement a synthetic aperture microscope using an electrically tunable lens to defocus images, which avoids the need to mechanically move a camera on a translation stage. Finally, we improve the reconstruction of images from a digital hologram based on an iterative algorithm that alternatively updates amplitude and phase.
1 citations
09 Sep 2013
TL;DR: This work considers direct recognition of diffraction-patterns in in-line holograms and suggests the use of a dimensionality reduction technique to circumvent this limitation and show good detection and recognition performance both on simulated and experimental holograms.
Abstract: A digital hologram is a 2-D recording of the diffraction fringes created by 3-D objects under coherent lighting. These fringes encode the shape and 3-D location information of the objects. By simulating re-lighting of the hologram, the 3-D wave field can be reconstructed and a volumetric image of the objects recovered. Rather than performing object detection and identification in this reconstructed volume, we consider direct recognition of diffraction-patterns in in-line holograms and show that it leads to superior performance. The huge variability of diffraction patterns with object shape and 3-D location makes diffraction-pattern matching computationally expensive. We suggest the use of a dimensionality reduction technique to circumvent this limitation and show good detection and recognition performance both on simulated and experimental holograms.
1 citations
Cites background from "Penalized-likelihood image reconstr..."
...Direct matching of diffraction patterns on the in-line holograms dramatically improves the quality of reconstructed images [9, 10, 11] and the accuracy of particle hologram anal-...
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References
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TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.
12,159 citations
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...(18) Instead of using the condition above, we choose a surrogate function f(x; xn) that satisfies the following sufficient conditions:...
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TL;DR: An improvement of the resolution by one decimal wotild require a correction of the objective to four decimals, a practically hopeless task.
Abstract: IT is known that the spherical aberration of electron lenses sets a limit to the resolving power of electron microscopes at about 5 A. Suggestions for the correction of objectives have been made ; but these are difficult in themselves, and the prospects of improvement are further aggravated by the fact that the resolution limit is proportional to the fourth root of the spherical aberration. Tnus an improvement of the resolution by one decimal wotild require a correction of the objective to four decimals, a practically hopeless task.
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"Penalized-likelihood image reconstr..." refers background or methods in this paper
...Unlike the conventional filtering method, iterative techniques can use all of the information in the model (2) rather than discarding all but one of the four terms....
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...(2) and taking the Fourier transform, we convert the spatial-frequency spectrum of the recorded interference pattern into an angular spectrum of diffracted waves: I~n! 5 Io~n! 1 uUrefu(2)d ~n! 1 Uref Uo~n 2 a!...
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...(2) constitute the zero-order image; the third term, which is proportional to uo , leads to the formation of the primary image; and the fourth term, which is proportional to uo* , leads to the formation of the conjugate image....
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...5 uuo~r!u(2) 1 uuref~r!u(2) 1 uo~r!uref * ~r! 1 uo* ~r!uref~r!, (2)...
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