Snapshot ptychography on array cameras.

We use convolutional neural networks to recover images optically down-sampled by 6.7 × using coherent aperture synthesis over a 16 camera array. Where conventional ptychography relies on scanning and oversampling, here we apply decompressive neural estimation to recover full resolution image from a single snapshot, although as shown in simulation multiple snapshots can be used to improve signal-to-noise ratio (SNR). In place training on experimental measurements eliminates the need to directly calibrate the measurement system. We also present simulations of diverse array camera sampling strategies to explore how snapshot compressive systems might be optimized.

Photon-limited bounds for phase retrieval.

We show that the optimal Cramér-Rao lower bound on the mean-square error for the estimation of a coherent signal from photon-limited intensity measurements is equal to the number of signal elements, or the number of signal elements minus one when we account for the unobservable reference phase. Whereas this bound is attained by phase-quadrature holography, we also show that it can be attained through a phase-retrieval system that does not require a coherent reference. We also present the bounds for classic phase-retrieval and ptychography, and show that practical coding strategies can approach optimal performance.

Piston alignment for a segmented-aperture imaging system by using piston-sweep phasing.

This Letter presents a novel method for aligning the piston settings for a segmented-aperture imaging system. By sweeping the piston setting for a reference segment, a stack of images can be acquired that encodes information about the relative piston alignment for all segments in the system. We also demonstrate how a matched-filter processing method can be used to estimate the relative piston settings to align the imaging system at its full resolution.

A role for oxysterol-binding protein-related protein 5 in endosomal cholesterol trafficking.

Oxysterol-binding protein (OSBP) and its related proteins (ORPs) constitute a large and evolutionarily conserved family of lipid-binding proteins that target organelle membranes to mediate sterol signaling and/or transport. Here we characterize ORP5, a tail-anchored ORP protein that localizes to the endoplasmic reticulum. Knocking down ORP5 causes cholesterol accumulation in late endosomes and lysosomes, which is reminiscent of the cholesterol trafficking defect in Niemann Pick C (NPC) fibroblasts. Cholesterol appears to accumulate in the limiting membranes of endosomal compartments in ORP5-depleted cells, whereas depletion of NPC1 or both ORP5 and NPC1 results in luminal accumulation of cholesterol. Moreover, trans-Golgi resident proteins mislocalize to endosomal compartments upon ORP5 depletion, which depends on a functional NPC1. Our results establish the first link between NPC1 and a cytoplasmic sterol carrier, and suggest that ORP5 may cooperate with NPC1 to mediate the exit of cholesterol from endosomes/lysosomes.

Compressive holography of diffuse objects.

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.

Performance bounds for the estimation of the degree of polarization from various sensing modalities.

Performance bounds (Cramer-Rao bounds on root-mean-square errors) are computed for the estimation of the degree of polarization for reflected fields with active laser illumination [Proc. SPIE 5888, 58880N (2005)]. The bounds are computed from various sensing modalities, which involves the measurement and processing of (1) the four intensities outputs of a four-channel polarimeter, (2) the intensities of two orthogonal field components, and (3) the total intensity of the field. Each modality includes detector noise models and utilizes realistic data-collection models.

Lipid-regulated sterol transfer between closely apposed membranes by oxysterol-binding protein homologues.

Sterols are transferred between cellular membranes by vesicular and poorly understood nonvesicular pathways. Oxysterol-binding protein-related proteins (ORPs) have been implicated in sterol sensing and nonvesicular transport. In this study, we show that yeast ORPs use a novel mechanism that allows regulated sterol transfer between closely apposed membranes, such as organelle contact sites. We find that the core lipid-binding domain found in all ORPs can simultaneously bind two membranes. Using Osh4p/Kes1p as a representative ORP, we show that ORPs have at least two membrane-binding surfaces; one near the mouth of the sterol-binding pocket and a distal site that can bind a second membrane. The distal site is required for the protein to function in cells and, remarkably, regulates the rate at which Osh4p extracts and delivers sterols in a phosphoinositide-dependent manner. Together, these findings suggest a new model of how ORPs could sense and regulate the lipid composition of adjacent membranes.

Thin infrared imaging systems through multichannel sampling.

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.

Signal-processing approaches for image-resolution restoration for TOMBO imagery.

Thin observation module by bounded optics (TOMBO) is an optical system that achieves compactness and thinness by replacing a conventional large full aperture by a lenslet array with several smaller apertures. This array allows us to collect diverse low-resolution measurements. Finding an efficient way of combining these diverse measurements to make a high-resolution image is an important research problem. We focus on finding a computational method for performing the resolution restoration and evaluating the method via simulations. Our approach is based on advanced signal-processing concepts: we construct a computational data model based on Fourier optics and propose restoration algorithms based on minimization of an information-theoretic measure, called Csiszár's I divergence between two nonnegative quantities: the measured data and the hypothetical images that are induced by our algorithms through the use of our computational data model. We also incorporate Poisson and Gaussian noise processes to model the physical measurements. To solve the optimization problem, we adapt the popular expectation-maximization method. These iterative algorithms, in a multiplicative form, preserve powerful nonnegativity constraints. We further incorporate a regularization based on minimization of total variation to suppress incurring artifacts such as roughness on the surfaces of the estimates. Two sets of simulation examples show that the algorithms can produce very high-quality estimates from noiseless measurements and reasonably good estimates from noisy measurements, even when the measurements are incomplete. Several interesting and useful avenues for future work such as the effects of measurement selection are suggested in our conclusional remarks.

The High Mobility Group Box Transcription Factor Nhp6Ap enters the nucleus by a calmodulin-dependent, Ran-independent pathway.

A gradient of Ran.GTP typically regulates traffic through the nuclear pore by modulating association of receptors with cargo. However, here we demonstrate that the yeast high mobility group box transcription factor Nhp6Ap enters the nucleus via a novel nuclear localization signal recognized by calcium calmodulin in a process that does not require Ran. Calmodulin is strictly required for the nondiffusional nuclear entry of Nhp6Ap. Calmodulin and DNA exhibit mutually exclusive binding to NHP6A, indicating that the directionality of Nhp6Ap nuclear accumulation may be driven by DNA-dependent dissociation of calmodulin. Our findings demonstrate that calmodulin can serve as a molecular switch triggering nuclear entry with subsequent dissociation of calmodulin binding upon interaction of cargo with chromatin. This pathway appears to be evolutionarily conserved; mammalian high mobility group box transcription factors often have two nuclear localization signals: one a classical Ran-dependent signal and a second that binds calmodulin. The finding that Nhp6Ap nuclear entry requires calmodulin but not Ran indicates that Nhp6Ap is a good model for studying this poorly understood but evolutionarily conserved calmodulin-dependent nuclear import pathway.

Approach for reconstructing anisoplanatic adaptive optics images.

Atmospheric turbulence corrupts astronomical images formed by ground-based telescopes. Adaptive optics systems allow the effects of turbulence-induced aberrations to be reduced for a narrow field of view corresponding approximately to the isoplanatic angle theta(0). For field angles larger than theta(0), the point spread function (PSF) gradually degrades as the field angle increases. We present a technique to estimate the PSF of an adaptive optics telescope as function of the field angle, and use this information in a space-varying image reconstruction technique. Simulated anisoplanatic intensity images of a star field are reconstructed by means of a block-processing method using the predicted local PSF. Two methods for image recovery are used: matrix inversion with Tikhonov regularization, and the Lucy-Richardson algorithm. Image reconstruction results obtained using the space-varying predicted PSF are compared to space invariant deconvolution results obtained using the on-axis PSF. The anisoplanatic reconstruction technique using the predicted PSF provides a significant improvement of the mean squared error between the reconstructed image and the object compared to the deconvolution performed using the on-axis PSF.

Sterol transport in yeast and the oxysterol binding protein homologue (OSH) family.

Sterols such as cholesterol are a significant component of eukaryotic cellular membranes, and their unique physical properties influence a wide variety of membrane processes. It is known that the concentration of sterol within the membrane varies widely between organelles, and that the cell actively maintains this distribution through various transport processes. Vesicular pathways such as secretion or endocytosis may account for this traffic, but increasing evidence highlights the importance of nonvesicular routes as well. The structure of an oxysterol-binding protein homologue (OSH) in yeast (Osh4p/Kes1p) has recently been solved, identifying it as a sterol binding protein, and there is evidence consistent with the role of a cytoplasmic, nonvesicular sterol transporter. Yeast have seven such proteins, which appear to have distinct but overlapping functions with regard to maintaining intracellular sterol distribution and homeostasis. Control of sterol distribution can have far-reaching effects on membrane-related functions, and Osh proteins have been implicated in a variety of processes such as secretory vesicle budding from the Golgi and establishment of cell polarity. This review summarizes the current body of knowledge regarding this family and its potential functions, placing it in the context of known and hypothesized pathways of sterol transport in yeast.

Optimal beams for propagation through random media.

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Green's function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Green's function.

Signal recovery from autocorrelation and cross-correlation data.

A signal recovery technique is motivated and derived for the recovery of several nonnegative signals from measurements of their autocorrelation and cross-correlation functions. The iterative technique is shown to preserve nonnegativity of the signal estimates and to produce a sequence of estimates whose correlations better approximate the measured correlations as the iterations proceed. The method is demonstrated on simulated data for active imaging with dual-frequency or dual-polarization illumination.

Iterative transform algorithm for the computation of optimal beams.

The problem of maximizing the integrated-weighted intensity of a transmitted beam in a receiver plane is equivalent to the problem of finding the largest eigenvalue's eigenfunction for a particular Hermitian operator. Application of the power method for the determination of this eigenfunction, along with its associated eigen-value, results in an iterative transform algorithm that can be applied to arbitrary apertures, nonnegative windows, and propagation media. The computational complexity of each iteration of this algorithm is equivalent to the numerical propagation of an arbitrary beam through the transmission medium.

The tricalbin C2 domains: lipid-binding properties of a novel, synaptotagmin-like yeast protein family.

The tricalbins are a recently discovered family of Saccharomyces cerevisae proteins containing a predicted N-terminal transmembrane domain and at least three C2 domains. They are thought to be yeast homologues of synaptotagmin, a hypothesis supported by structural similarities and past studies that implicated tricalbins in processes of membrane trafficking and sorting. We expressed and purified constructs consisting of single tricalbin C2 domains, and assayed their ability to bind lipids in response to calcium. Protein-lipid overlay assays indicated that the C-terminal C2 domains (C2C) of tricalbins 1 and 3 bind numerous species of acidic phospholipid, including phosphatidylserine and several phosphoinositides, and the amount of protein bound was greatly enhanced in the presence of 1 mM calcium. Sedimentation assays using mixed phosphatidylserine/phosphatidylcholine (PS/PC) vesicles confirmed that the C2C domains of tricalbin 1 and 3 bind membranes in a calcium-responsive manner and showed that they are more sensitive to calcium than the C2A domain of synaptotagmin I. Both assays revealed that all of the C2 domains of tricalbin 2 are insensitive to calcium. Fluorimetric assays exploiting the position of naturally occurring tryptophans in tricalbin 1 C2C and tricalbin 3 C2C confirmed that these domains are capable of binding calcium and that this is coupled to the binding of acidic phospholipid. Combining this with past protein-protein interaction data, we theorize that the calcium-insensitive tricalbin 2 mediates the creation of hetero-oligomeric tricalbin complexes in which tricalbin 1 or 3 or both supply a calcium-dependent membrane binding activity.

Experimental estimation of the spatial statistics of turbulence-induced index of refraction fluctuations in the upper atmosphere.

We present results from an experiment to estimate the parameters of homogeneous, isotropic optical turbulence in the upper atmosphere. The balloon-borne experiment made high-resolution temperature measurements at seven points on a hexagonal grid for altitudes from 12,000 to 18,000 m. From the temperature data, we obtained index of refraction fluctuations that can be used to compute a sample-based estimate for a parameterized description of the spatial autocorrelation of the turbulence. The three parameters of interest were a proportionality constant Pc, the power-law parameter alpha, and the outer scale L0. The results obtained for Pc are within the expected range and agree well with independent measurements made from a standard rising thermosonde measurement made approximately simultaneously with the data collection. Values for a were in the range 1.52 < or = alpha < or = 1.73 were observed, which are significantly less than the power law used in the Kolmogorov and von Karman models, alpha = 1.833. Values observed for L0 were in the range 5 < or = L0 < or = 19 m. Evidence that alpha may be consistently less than that used in the Kolmogorov and von Karman models likely has the most significant implications for systems that must work in or through the tropopause.

Measurement and data processing approach for detecting anisotropic spatial statistics of the turbulence-induced index of refraction fluctuations in the upper atmosphere.

We discuss a method of data reduction and analysis that has been developed for a novel experiment to detect anisotropic turbulence in the tropopause and to measure the spatial statistics of these flows. The experimental concept is to make measurements of temperature at 15 points on a hexagonal grid for altitudes from 12,000 to 18,000 m while suspended from a balloon performing a controlled descent. From the temperature data, we estimate the index of refraction and study the spatial statistics of the turbulence-induced index of refraction fluctuations. We present and evaluate the performance of a processing approach to estimate the parameters of an anisotropic model for the spatial power spectrum of the turbulence-induced index of refraction fluctuations. A Gaussian correlation model and a least-squares optimization routine are used to estimate the parameters of the model from the measurements. In addition, we implemented a quick-look algorithm to have a computationally nonintensive way of viewing the autocorrelation function of the index fluctuations. The autocorrelation of the index of refraction fluctuations is binned and interpolated onto a uniform grid from the sparse points that exist in our experiment. This allows the autocorrelation to be viewed with a three-dimensional plot to determine whether anisotropy exists in a specific data slab. Simulation results presented here show that, in the presence of the anticipated levels of measurement noise, the least-squares estimation technique allows turbulence parameters to be estimated with low rms error.