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

Genetically encoded calcium indicators (GECIs) are powerful tools for systems neuroscience. Recent efforts in protein engineering have significantly increased the performance of GECIs. The state-of-the art single-wavelength GECI, GCaMP3, has been deployed in a number of model organisms and can reliably detect three or more action potentials in short bursts in several systems in vivo. Through protein structure determination, targeted mutagenesis, high-throughput screening, and a battery of in vitro assays, we have increased the dynamic range of GCaMP3 by severalfold, creating a family of “GCaMP5” sensors. We tested GCaMP5s in several systems: cultured neurons and astrocytes, mouse retina, and in vivo in Caenorhabditis chemosensory neurons, Drosophila larval neuromuscular junction and adult antennal lobe, zebrafish retina and tectum, and mouse visual cortex. Signal-to-noise ratio was improved by at least 2- to 3-fold. In the visual cortex, two GCaMP5 variants detected twice as many visual stimulus-responsive cells as GCaMP3. By combining in vivo imaging with electrophysiology we show that GCaMP5 fluorescence provides a more reliable measure of neuronal activity than its predecessor GCaMP3. GCaMP5 allows more sensitive detection of neural activity in vivo and may find widespread applications for cellular imaging in general.

/pdf/optimization-of-a-gcamp-calcium-indicator-for-neural-3k5fuusflm.pdf

Optimization of a GCaMP calcium indicator for neural activity imaging.

http://xrm.phys.northwestern.edu/research/pdf_papers/2009/maiden_ultramic_2009.pdf

An improved ptychographical phase retrieval algorithm for diffractive imaging.

Specific labeling of biomolecules with bright fluorophores is the keystone of fluorescence microscopy. Genetically encoded self-labeling tag proteins can be coupled to synthetic dyes inside living cells, resulting in brighter reporters than fluorescent proteins. Intracellular labeling using these techniques requires cell-permeable fluorescent ligands, however, limiting utility to a small number of classic fluorophores. Here we describe a simple structural modification that improves the brightness and photostability of dyes while preserving spectral properties and cell permeability. Inspired by molecular modeling, we replaced the N,N-dimethylamino substituents in tetramethylrhodamine with four-membered azetidine rings. This addition of two carbon atoms doubles the quantum efficiency and improves the photon yield of the dye in applications ranging from in vitro single-molecule measurements to super-resolution imaging. The novel substitution is generalizable, yielding a palette of chemical dyes with improved quantum efficiencies that spans the UV and visible range.

/pdf/a-general-method-to-improve-fluorophores-for-live-cell-and-56mvzhhh2n.pdf

A general method to improve fluorophores for live-cell and single-molecule microscopy

Non-invasive optical imaging techniques, such as optical coherence tomography1, 2, 3, are essential diagnostic tools in many disciplines, from the life sciences to nanotechnology. However, present methods are not able to image through opaque layers that scatter all the incident light4, 5. Even a very thin layer of a scattering material can appear opaque and hide any objects behind it6. Although great progress has been made recently with methods such as ghost imaging7, 8 and wavefront shaping9, 10, 11, present procedures are still invasive because they require either a detector12 or a nonlinear material13 to be placed behind the scattering layer. Here we report an optical method that allows non-invasive imaging of a fluorescent object that is completely hidden behind an opaque scattering layer. We illuminate the object with laser light that has passed through the scattering layer. We scan the angle of incidence of the laser beam and detect the total fluorescence of the object from the front. From the detected signal, we obtain the image of the hidden object using an iterative algorithm14, 15. As a proof of concept, we retrieve a detailed image of a fluorescent object, comparable in size (50 micrometres) to a typical human cell, hidden 6 millimetres behind an opaque optical diffuser, and an image of a complex biological sample enclosed between two opaque screens. This approach to non-invasive imaging through strongly scattering media can be generalized to other contrast mechanisms and geometries

/pdf/non-invasive-imaging-through-opaque-scattering-layers-pgcpyzkk4c.pdf

Non-invasive imaging through opaque scattering layers

Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.

Efficient subpixel image registration algorithms

Techniques for controlling spectral width are used in conjunction with thin-film techniques in the design of guided-mode resonance (GMR) filters to provide simultaneous control over line-shape symmetry, sideband levels, and spectral width. Several factors that could limit the minimum spectral width are discussed. We used interference effects for passband shaping by stacking multiple GMR filters on top of one another. A design is presented for a 200-GHz telecommunications filter along with a tolerance analysis. Compared with a conventional thin-film filter, the GMR filter has fewer layers and looser thickness tolerances. Grating fabrication tolerances are also discussed.

Controlling the spectral response in guided-mode resonance filter design

The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than λ/50 root-mean-square (RMS) were obtained. Corrections better than λ/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.

Phase-error correction in digital holography

The effect of a uniform measurement bias, due to background light, stray light, detector dark current, or detector offset, on phase retrieval wavefront sensing algorithms is analyzed. Simulation results indicate that the root-mean-square error of the retrieved phase can be more sensitive to an unaccounted-for signal bias than to random noise in practical scenarios. Three methods for reducing the impact of signal bias are presented.

Phase retrieval with signal bias

This paper reports design, fabrication, and experimental demonstration of a silicon nitride photonic integrated circuit (PIC). The PIC is capable of conducting one-dimensional interferometric imaging with twelve baselines near λ = 1100-1600 nm. The PIC consists of twelve waveguide pairs, each leading to a multi-mode interferometer (MMI) that forms broadband interference fringes or each corresponding pair of the waveguides. Then an 18 channel arrayed waveguide grating (AWG) separates the combined signal into 18 signals of different wavelengths. A total of 103 sets of fringes are collected by the detector array at the output of the PIC. We keep the optical path difference (OPD) of each interferometer baseline to within 1 µm to maximize the visibility of the interference measurement. We also constructed a testbed to utilize the PIC for two-dimension complex visibility measurement with various targets. The experiment shows reconstructed images in good agreement with theoretical predictions.

Samuel T. Thurman

Papers

Efficient subpixel image registration algorithms

Controlling the spectral response in guided-mode resonance filter design

Phase-error correction in digital holography

Phase retrieval with signal bias

Interferometric imaging using Si 3 N 4 photonic integrated circuits for a SPIDER imager