Learning Wavefront Coding for Extended Depth of Field Imaging

Depth of field is an important factor of imaging systems that highly affects the quality of the acquired spatial information. Extended depth of field (EDoF) imaging is a challenging ill-posed problem and has been extensively addressed in the literature. We propose a computational imaging approach for EDoF, where we employ wavefront coding via a diffractive optical element (DOE) and we achieve deblurring through a convolutional neural network. Thanks to the end-to-end differentiable modeling of optical image formation and computational post-processing, we jointly optimize the optical design, i.e., DOE, and the deblurring through standard gradient descent methods. Based on the properties of the underlying refractive lens and the desired EDoF range, we provide an analytical expression for the search space of the DOE, which is instrumental in the convergence of the end-to-end network. We achieve superior EDoF imaging performance compared to the state of the art, where we demonstrate results with minimal artifacts in various scenarios, including deep 3D scenes and broadband imaging

Extended depth-of-field imaging and ranging in a snapshot

Traditional approaches to imaging require that an increase in depth of field is associated with a reduction in numerical aperture, and hence with a reduction in resolution and optical throughput. In their seminal work, Dowski and Cathey reported how the asymmetric point-spread function generated by a cubic-phase aberration encodes the detected image such that digital recovery can yield images with an extended depth of field without sacrificing resolution [Appl. Opt. 34, 1859 (1995)]. Unfortunately recovered images are generally visibly degraded by artifacts arising from subtle variations in point-spread functions with defocus. We report a technique that involves determination of the spatially variant translation of image components that accompanies defocus to enable determination of spatially variant defocus. This in turn enables recovery of artifact-free, extended depth-of-field images together with a two-dimensional defocus and range map of the imaged scene. We demonstrate the technique for high-quality macroscopic and microscopic imaging of scenes presenting an extended defocus of up to two waves, and for generation of defocus maps with an uncertainty of 0.036 waves

Fourier optics approaches to enhanced depth-of-field applications in millimetre-wave imaging and microscopy

In the first part of this thesis millimetre-wave interferometric imagers are considered for short-range applications such as concealed weapons detection. Compared to real aperture systems, synthetic aperture imagers at these wavelengths can provide improvements in terms of size, cost, depth-of-field (DoF) and imaging flexibility via digitalrefocusing. Mechanical scanning between the scene and the array is investigated to reduce the number of antennas and correlators which drive the cost of such imagers. The tradeoffs associated with this hardware reduction are assessed before to jointly optimise the array configuration and scanning motion. To that end, a novel metric is proposed to quantify the uniformity of the Fourier domain coverage of the array and is maximised with a genetic algorithm. The resulting array demonstrates clear improvements in imaging performances compared to a conventional power-law Y-shaped array. The DoF of antenna arrays, analysed via the Strehl ratio, is shown to be limited even for infinitely small antennas, with the exception of circular arrays. In the second part of this thesis increased DoF in optical systems with Wavefront Coding (WC) is studied. Images obtained with WC are shown to exhibit artifacts that limit the benefits of this technique. An image restoration procedure employing a metric of defocus is proposed to remove these artifacts and therefore extend the DoF beyond the limit of conventional WC systems. A transmission optical microscope was designed and implemented to operate with WC. After suppression of partial coherence effects, the proposed image restoration method was successfully applied and extended DoF images are presented

Principles and applications of wavefront coding

Abstract unavailable please refer to PD

Topics in Three-Dimensional Imaging, Source Localization and Super-resolution

The realization that twisted light beams with helical phasefronts could carry orbital angular momentum (OAM) that is in excess of the photon\u27s spin angular momentum (SAM) has spawned various important applications. One example is the design of novel imaging systems that achieve three-dimensional (3D) imaging in a single snapshot via the rotation of point spread function (PSF). Based on a scalar-field analysis, a particular simple version of rotating PSF imagery, which was proposed by my advisor Dr. Prasad, furnishes a practical approach to perform 3D source localization using a spiral phase mask that generates a combination of Bessel vortex beams. For a special annular design of the mask, with the spiral-phase winding number in successive annuli changing by a fixed quantum number, this Bessel-beam combination can yield a shape and size invariant PSF that rotates as a function of the axial position of the source, and possesses a superior depth of field (DOF) when compared to other rotating PSFs. In the first part of this dissertation, we present a vector-field analysis of an improved rotating PSF design that encodes both the 3D location and polarization state of a monochromatic point dipole emitter for high numerical aperture (NA) microscopy, in which non-paraxial propagation of the imaging beam and the associated vector character of light fields are properly accounted for. By examining the angle of rotation and the spatial form of the PSF, one can simultaneously localize point sources and determine the polarization state of light emitted by them over a 3D field in a single snapshot. We also propose a more advanced approach for doing joint polarimetry and 3D localization using a SAM-OAM conversion device without the need for high NA is also proposed. A recent paradigm-shifting research proposal has focused on employing the toolbox of quantum parameter estimation for the problem of super-resolution of two incoherent point sources. Surprisingly, the quantum Fisher information (QFI) and associated quantum Cram\\u27er-Rao bound (QCRB) for estimating the one-dimensional transverse separation of the source pair are both finite constants that are achievable with purely classical measurements that utilize coherent projections of the optical wavefront. A second important contribution of this dissertation is the generalization of the previous quantum limited transverse super-resolution work to full 3D imaging with more general PSF. Under the assumption of known centroid, we first derive the general expression of $3\times 3$ QFI matrix with respect to (w.r.t.) the 3D pair separation vector, in terms of the correlation of the wavefront phase gradients in the imaging aperture. For a clear circular aperture, the QFI matrix turns out to be a separation-independent diagonal matrix. Coherent-projection bases that can attain the corresponding QCRB in special cases and small separation limits are also proposed with confirmation by numerical simulations. We next extend our 3D analysis to treat the more general 6-parameter problem of jointly estimating the 3D pair-centroid location and pair-separation vectors. We also present the results of computer simulation of an experimental protocol based on the use of Zernike-mode projections to attain these quantum estimation-limited bounds of performance

Design and implementation of a scene-dependent dynamically selfadaptable wavefront coding imaging system

A computational imaging system based on wavefront coding is presented. Wavefront coding provides an extension of the depth-of-field at the expense of a slight reduction of image quality. This trade-off results from the amount of coding used. By using spatial light modulators, a flexible coding is achieved which permits it to be increased or decreased as needed. In this paper a computational method is proposed for evaluating the output of a wavefront coding imaging system equipped with a spatial light modulator, with the aim of thus making it possible to implement the most suitable coding strength for a given scene. This is achieved in an unsupervised manner, thus the whole system acts as a dynamically selfadaptable imaging system. The program presented here controls the spatial light modulator and the camera, and also processes the images in a synchronised way in order to implement the dynamic system in real time. A prototype of the system was implemented in the laboratory and illustrative examples of the performance are reported in this paper

Wavefront sensing and conjugate adaptive optics in wide-field microscopy

The quality of microscopy imaging is often degraded by sample-induced aberrations. Adaptive optics (AO) is a standard approach to counter such aberrations. In common practice of AO, an active optical correction element, usually a deformable mirror (DM), is usually inserted in the pupil plane of the objective lens, namely pupil AO. However, as first proposed in the astronomy community and now gradually recognized by the optical microscopy community, the placement of the DM in a plane conjugate to a primary sample-induced aberration plane can be more advantageous, especially in situations where the aberration is spatially varying and arises mainly from a dominant layer. We refer to this technique as conjugate AO. In this thesis, we describe two novel implementations of sensor-based conjugate AO in wide-field microscopy, as well as the wavefront sensing techniques we developed for these implementations. Our first implementation is in trans-illumination configuration. The wavefront sensor is based on a technique called partitioned aperture wavefront (PAW) sensing, previously developed in our lab for quantitative phase contrast imaging. Our second conjugate AO is implemented with fluorescence microscopy. The wavefront sensing strategy is based on oblique back-illumination. In both implementations, we addressed the key challenges of developing wavefront sensors that are capable of operating with uncollimated light, which exhibits large diverging angles and may arbitrarily distribute as well. We show that both conjugate AO systems and their wavefront sensors are not only robust, well-suited for video-rate imaging, but also provide large corrected field of view, which is only limited by the microscope itself

Phase control and measurement in digital microscopy

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise