Michael Stefan Daniel Liebling

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In this thesis, we describe new approaches and methods for reconstructing complex-valued wave fields from digital holograms. We focus on Fresnel holograms recorded in an off-axis geometry, for which operational real-time acquisition setups readily exist. The three main research directions presented are the following. First, we derive the necessary tools to port methods and concepts of wavelet-based approaches to the field of digital holography. This is motivated by the flexibility, the robustness, and the u

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of

L _{ 2 }

to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by the special form that the dilation operator takes in the Fresnel domain. We derive a Heisenberg-like unc

Optical microscopy is an essential tool in biology and medicine. Imaging thin, yet non-flat objects in a single shot (without relying on more sophisticated sectioning setups) remains challenging as the shallow depth of field that comes with high-resolution ...

We present a new method for reconstructing digitally recorded off-axis Fresnel holograms. Currently-used reconstruction methods are based on the simulation and propagation of a reference wave that is diffracted by the hologram. This procedure introduces a twin-image and a zero-order term which are inherent to the diffraction phenomenon. These terms perturb the reconstruction and limit the field of view. Our new approach splits the reconstruction process into two parts. First, we recover the amplitude and th

We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the sinogram. The key idea is to combine the ramp filtering and the spline fitting process into a single filtering operation. We consider three different approaches. In the first, we simply adapt the standard FBP for spline interpolation. In the second approach

We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. We apply our results to derive spline-convolution-based algorithms for two closely related problems: the computation of the Radon transform and of its inverse. First, we present an efficient discrete implementation of the Radon transform that is optimal in the least-squares sense. We then consider the reverse problem and introduce a new spline-convo

Optical Projection Tomography (OPT) imaging provides isotropic resolution for samples up to a few millimeters. High resolution OPT is achieved by deconvolving Focal-Plane-Scanning (FPS-OPT) data but it requires to accurately know the system's Point Spread ...

Significance: Despite recent developments in microscopy, temporal aliasing can arise when imaging dynamic samples. Modern sampling frameworks, such as generalized sampling, mitigate aliasing but require measurement of temporally overlapping and potentially ...

We present a zero-order and twin image elimination algorithm for digital Fresnel holograms that were acquired in an off-axis geometry. These interference terms arise when the digital hologram is reconstructed and corrupt the result. Our algorithm is based on the Fresnelet transform, a wavelet-like transform that uses basis functions tailor-made for digital holography. We show that in the Fresnelet domain, the coefficients associated to the interference terms are separated both spatially and with respect to

We present a numerical two-step reconstruction procedure for digital off-axis Fresnel holograms. First, we retrieve the amplitude and phase of the object wave in the CCD plane. For each point we solve a weighted linear set of equations in the least-squares sense. The algorithm has O(N) complexity and gives great flexibility. Second, we numerically propagate the obtained wave to achieve proper focus. We apply the method to microscopy and demonstrate its suitability for the real time imaging of biological sam

The Bio Image and Signal Processing (BISP) Technical Committee (TC) of the IEEE Signal Processing Society (SPS) promotes activities within the broad technical field of biomedical image and signal processing. Areas of interest include medical and biological ...

We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data

We present a new class of wavelet bases—Fresnelets—which is obtained by applying the Fresnel transform operator to a wavelet basis of

L _{ 2 }

. The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and processing optically generated holograms recorded on CCD-arrays. We first investigate the multiresolution properties (translation, dilation) of the Fresnel transform that are needed to construct our new wavelet. We derive a Heisenberg-like uncertainty relation

Studying dynamic biological processes, such as heart development and function in zebrafish embryos, often relies on multi-channel fluorescence labeling to distinguish multiple anatomical features, yet also demands high frame rates to capture rapid cell mot ...

Three-dimensional information about an object, such as its depth, may be captured and stored digitally in a single, two-dimensional, real-valued hologram acquired in an off-axis geometry. Digital reconstruction of the hologram permits the quantitative retr ...

Many applications rely on thermal imagers to complement or replace visible light sensors in difficult imaging conditions. Recent advances in machine learning have opened the possibility of analyzing or enhancing images, yet these methods require large anno ...

We propose a robust autofocus method for reconstructing digital Fresnel holograms. The numerical reconstruction involves simulating the propagation of a complex wave front to the appropriate distance. Since the latter value is difficult to determine manually, it is desirable to rely on an automatic procedure for finding the optimal distance to achieve high-quality reconstructions. Our algorithm maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent waveletlike F

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a mono ...

Michael Stefan Daniel Liebling

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On Fresnelets, interference fringes, and digital holography

Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

Spatially-Variant CNN-Based Point Spread Function Estimation for Blind Deconvolution and Depth Estimation in Optical Microscopy

A Novel Non-Diffractive Reconstruction Method for Digital Holographic Microscopy

Filter Design for Filtered Back-Projection Guided by the Interpolation Model

Discretization of the radon transform and of its inverse by spline convolutions

Optics Versus Computation: Influence of Illumination and Reconstruction Model Accuracy in Focal-Plane-Scanning Optical Projection Tomography

Aliasing mitigation in optical microscopy of dynamic biological samples by use of temporally modulated color illumination and a standard RGB camera

Non-Linear Fresnelet Approximation for Interference Term Suppression in Digital Holography

Local Amplitude and Phase Retrieval Method for Digital Holography Applied to Microscopy

From Nano to Macro An overview of the IEEE Bio Image and Signal Processing Technical Committee

Complex-Wave Retrieval from a Single Off-Axis Hologram

Fresnelets—A New Wavelet Basis for Digital Holography

Temporal resolution doubling in fluorescence light-sheet microscopy via a hue-encoded shutter and regularization

Comparing Algorithms for Reconstructing Digital Off-Axis Fresnel Holograms

Perspectives and limitations of visible-thermal image pair synthesis via generative adversarial networks

Autofocus for Digital Fresnel Holograms by Use of a Fresnelet-Sparsity Criterion

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging