Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

A Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in RP Integration in RP.

The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)

Within the field of spectral imaging, the vast majority of instruments used are scanning devices. Recently, several snapshot spectral imaging systems have become commercially available, providing new functionality for users and opening up the field to a wide array of new applications. A comprehensive survey of the available snapshot technologies is provided, and an attempt has been made to show how the new capabilities of snapshot approaches can be fully utilized.

https://www.spiedigitallibrary.org/journals/optical-engineering/volume-52/issue-9/090901/Review-of-snapshot-spectral-imaging-technologies/10.1117/1.OE.52.9.090901.pdf

Review of snapshot spectral imaging technologies

Imaging spectroscopy involves the sensing of a large amount of spatial information across a multitude of wavelengths. Conventional approaches to hyperspectral sensing scan adjacent zones of the underlying spectral scene and merge the results to construct a spectral data cube. Push broom spectral imaging sensors, for instance, capture a spectral cube with one focal plane array (FPA) measurement per spatial line of the scene [1], [2]. Spectrometers based on optical bandpass filters sequentially scan the scene by tuning the bandpass filters in steps. The disadvantage of these techniques is that they require scanning a number of zones linearly in proportion to the desired spatial and spectral resolution. This article surveys compressive coded aperture spectral imagers, also known as coded aperture snapshot spectral imagers (CASSI) [1], [3], [4], which naturally embody the principles of compressive sensing (CS) [5], [6]. The remarkable advantage of CASSI is that the entire data cube is sensed with just a few FPA measurements and, in some cases, with as little as a single FPA shot.

Compressive Coded Aperture Spectral Imaging: An Introduction

In this perspective, the authors present the basic features of lens-free computational imaging tools and report performance comparisons with conventional microscopy methods. They also discuss the challenges that these computational on-chip microscopes face for their wide-scale biomedical application.

/pdf/imaging-without-lenses-achievements-and-remaining-challenges-1tjjxwd1cx.pdf

Imaging without lenses: achievements and remaining challenges of wide-field on-chip microscopy

A coded aperture snapshot spectral imager (CASSI) estimates the three-dimensional spatiospectral data cube from a snapshot two-dimensional coded projection, assuming that the scene is spatially and spectrally sparse. For less spectrally sparse scenes, we show that the use of multiple nondegenerate snapshots can make data cube recovery less ill-posed, yielding improved spatial and spectral reconstruction fidelity. Additionally, data acquisition can be easily scaled to meet the time/resolution requirements of the scene with little modification or extension of the original CASSI hardware. A multiframe reconstruction of a 640 × 480 × 53 voxel datacube with 450-650 nm white-light illumination of a scene reveals substantial improvement in the reconstruction fidelity, with limited increase in acquisition and reconstruction time.

Multiframe image estimation for coded aperture snapshot spectral imagers

Compressive holography enables 3D reconstruction from a single 2D holographic snapshot for objects that can be sparsely represented in some basis. The snapshot mode enables tomographic imaging of microscopic moving objects. We demonstrate video-rate tomographic image acquisition of two live water cyclopses with 5.2 μm spatial resolution and 60 μm axial resolution.

Video-rate compressive holographic microscopic tomography

We propose an estimation-theoretic approach to the inference of an incoherent 3D scattering density from 2D scattered speckle field measurements. The object density is derived from the covariance of the speckle field. The inference is performed by a constrained optimization technique inspired by compressive sensing theory. Experimental results demonstrate and verify the performance of our estimates.

/pdf/compressive-holography-of-diffuse-objects-5acxyf92nm.pdf

Compressive holography of diffuse objects

Diverse physical measurements can be modeled by X-ray transforms. While X-ray tomography is the canonical
example, reference structure tomography (RST) and coded aperture snapshot spectral imaging (CASSI)
are examples of physically unrelated but mathematically equivalent sensor systems. Historically, most x-ray
transform based systems sample continuous distributions and apply analytical inversion processes. On the other
hand, RST and CASSI generate discrete multiplexed measurements implemented with coded apertures. This
multiplexing of coded measurements allows for compression of measurements from a compressed sensing perspective.
Compressed sensing (CS) is a revelation that if the object has a sparse representation in some basis,
then a certain number, but typically much less than what is prescribed by Shannon's sampling rate, of random
projections captures enough information for a highly accurate reconstruction of the object. This paper investigates
the role of coded apertures in x-ray transform measurement systems (XTMs) in terms of data efficiency
and reconstruction fidelity from a CS perspective. To conduct this, we construct a unified analysis using RST
and CASSI measurement models. Also, we propose a novel compressive x-ray tomography measurement scheme
which also exploits coding and multiplexing, and hence shares the analysis of the other two XTMs. Using this
analysis, we perform a qualitative study on how coded apertures can be exploited to implement physical random
projections by "regularizing" the measurement systems. Numerical studies and simulation results demonstrate
several examples of the impact of coding.

Coded aperture computed tomography

We apply a coded aperture snapshot spectral imager (CASSI) to fluorescence microscopy. CASSI records a two-dimensional (2D) spectrally filtered projection of a three-dimensional (3D) spectral data cube. We minimize a convex quadratic function with total variation (TV) constraints for data cube estimation from the 2D snapshot. We adapt the TV minimization algorithm for direct fluorescent bead identification from CASSI measurements by combining a priori knowledge of the spectra associated with each bead type. Our proposed method creates a 2D bead identity image. Simulated fluorescence CASSI measurements are used to evaluate the behavior of the algorithm. We also record real CASSI measurements of a ten bead type fluorescence scene and create a 2D bead identity map. A baseline image from filtered-array imaging system verifies CASSI's 2D bead identity map.

/pdf/identification-of-fluorescent-beads-using-a-coded-aperture-k6lxdb62y8.pdf

Kerkil Choi

Papers

Multiframe image estimation for coded aperture snapshot spectral imagers

Video-rate compressive holographic microscopic tomography

Compressive holography of diffuse objects

Coded aperture computed tomography

Identification of fluorescent beads using a coded aperture snapshot spectral imager.