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.
Citations
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TL;DR: A new, high-speed algorithm is introduced that efficiently incorporates the data of an auxiliary off-axis hologram in the phase retrieval of the corresponding in-line hologram.
Abstract: Retrieving correct phase information from an in-line hologram is difficult as the object wave field and the diffractions of the zero order and the conjugate object term overlap. The existing iterative numerical phase retrieval methods are slow, especially in the case of high Fresnel number systems. Conversely, the reconstruction of the object wave field from an off-axis hologram is simple, but due to the applied spatial frequency filtering the achievable resolution is confined. Here, a new, high-speed algorithm is introduced that efficiently incorporates the data of an auxiliary off-axis hologram in the phase retrieval of the corresponding in-line hologram. The efficiency of the introduced combined phase retrieval method is demonstrated by simulated and measured holograms.
18 citations
TL;DR: It is illustrated that an accuracy comparable to that of state-of-the-art methods can be reached while accelerating parameter-space scanning while using a coarse-to-fine multiscale approach.
Abstract: In-line digital holography is an imaging technique that is being increasingly used for studying three-dimensional flows. It has been previously shown that very accurate reconstructions of objects could be achieved with the use of an inverse problem framework. Such approaches, however, suffer from higher computational times compared to less accurate conventional reconstructions based on hologram backpropagation. To overcome this computational issue, we propose a coarse-to-fine multiscale approach to strongly reduce the algorithm complexity. We illustrate that an accuracy comparable to that of state-of-the-art methods can be reached while accelerating parameter-space scanning.
16 citations
TL;DR: In this paper, a simple heuristic for determining the regularization parameter was proposed, and the use of density weighting and intensity correction as preconditioners and the role that coil sensitivity estimation has in regularization was discussed.
15 citations
TL;DR: The proposed hologram reconstruction algorithm is based on alternating a model fitting step and a regularized inversion step, and is applied in the context of fluid mechanics, where holograms of evaporating droplets are analyzed.
Abstract: In-line digital holography is a simple yet powerful tool to image absorbing and/or phase objects. Nevertheless, the loss of the phase of the complex wavefront on the sensor can be critical in the reconstruction process. The simplicity of the setup must thus be counterbalanced by dedicated reconstruction algorithms, such as inverse approaches, in order to retrieve the object from its hologram. In the case of simple objects for which the diffraction pattern produced in the hologram plane can be modeled using few parameters, a model fitting algorithm is very effective. However, such an approach fails to reconstruct objects with more complex shapes, and an image reconstruction technique is then needed. The improved flexibility of these methods comes at the cost of a possible loss of reconstruction accuracy. In this work, we combine the two approaches (model fitting and regularized reconstruction) to benefit from their respective advantages. The sample to be reconstructed is modeled as the sum of simple parameterized objects and a complex-valued pixelated transmittance plane. These two components jointly scatter the incident illumination, and the resulting interferences contribute to the intensity on the sensor. The proposed hologram reconstruction algorithm is based on alternating a model fitting step and a regularized inversion step. We apply this algorithm in the context of fluid mechanics, where holograms of evaporating droplets are analyzed. In these holograms, the high contrast fringes produced by each droplet tend to mask the diffraction pattern produced by the surrounding vapor wake. With our method, the droplet and the vapor wake can be jointly reconstructed.
15 citations
TL;DR: Improved axial accuracy and the capability to extend the reconstructed field beyond the physical limit of the sensor size (out-of-field reconstruction) are achieved at the cost of an increase of the computational load compared to (typically non iterative) classical approaches.
Abstract: Digital holography (DH) is being increasingly used for its time-resolved three-dimensional (3-D) imaging capabilities. A 3-D volume can be numerically reconstructed from a single 2-D hologram. Applications of DH range from experimental mechanics, biology, and fluid dynamics. Improvement and characterization of the 3-D reconstruction algorithms is a current issue. Over the past decade, numerous algorithms for the analysis of holograms have been proposed. They are mostly based on a common approach to hologram processing: digital reconstruction based on the simulation of hologram diffraction. They suffer from artifacts intrinsic to holography: twin-image contamination of the reconstructed images, image distortions for objects located close to the hologram borders. The analysis of the reconstructed planes is therefore limited by these defects. In contrast to this approach, the inverse problems perspective does not transform the hologram but performs object detection and location by matching a model of the hologram. Information is thus extracted from the hologram in an optimal way, leading to two essential results: an improvement of the axial accuracy and the capability to extend the reconstructed field beyond the physical limit of the sensor size (out-of-field reconstruction). These improvements come at the cost of an increase of the computational load compared to (typically non iterative) classical approaches.
14 citations
References
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TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
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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
5,674 citations
"Penalized-likelihood image reconstr..." refers methods in this paper
...(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: Detection, estimation, and modulation theory, Detection, estimation and modulation theorists, اطلاعات رسانی کشاورزی .
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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.
3,899 citations
"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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