scispace - formally typeset
Search or ask a question

Showing papers on "Point spread function published in 2015"


Journal ArticleDOI
TL;DR: A fast, coherent US imaging tool for microbubble localization in 3-D using a pair of US transducers positioned at 90° to enable analysis of microvascular morphology, blood flow dynamics, and occlusions resulting from disease states is developed.
Abstract: Standard clinical ultrasound (US) imaging frequencies are unable to resolve microvascular structures due to the fundamental diffraction limit of US waves. Recent demonstrations of 2-D super-resolution both in vitro and in vivo have demonstrated that fine vascular structures can be visualized using acoustic single bubble localization. Visualization of more complex and disordered 3-D vasculature, such as that of a tumor, requires an acquisition strategy which can additionally localize bubbles in the elevational plane with high precision in order to generate super-resolution in all three dimensions. Furthermore, a particular challenge lies in the need to provide this level of visualization with minimal acquisition time. In this paper, we develop a fast, coherent US imaging tool for microbubble localization in 3-D using a pair of US transducers positioned at 90°. This allowed detection of point scatterer signals in 3-D with average precisions equal to $1.9~\mu \text{m}$ in axial and elevational planes, and $11~\mu \text{m}$ in the lateral plane, compared to the diffraction limited point spread function full-widths at half-maximum of 488, 1188, and $953~\mu \text{m}$ of the original imaging system with a single transducer. Visualization and velocity mapping of 3-D in vitro structures was demonstrated far beyond the diffraction limit. The capability to measure the complete flow pattern of blood vessels associated with disease at depth would ultimately enable analysis of in vivo microvascular morphology, blood flow dynamics, and occlusions resulting from disease states.

331 citations


Journal ArticleDOI
TL;DR: Super-resolution optical microscopy is an important tool in a number of scientific disciplines including chemical, (bio)physical and biomedical research, particularly with respect to the study of living cells and organisms.
Abstract: Far-field optical microscopy using focused light is an important tool in a number of scientific disciplines including chemical, (bio)physical and biomedical research, particularly with respect to the study of living cells and organisms. Unfortunately, the applicability of the optical microscope is limited, since the diffraction of light imposes limitations on the spatial resolution of the image. Consequently the details of, for example, cellular protein distributions, can be visualized only to a certain extent. Fortunately, recent years have witnessed the development of 'super-resolution' far-field optical microscopy (nanoscopy) techniques such as stimulated emission depletion (STED), ground state depletion (GSD), reversible saturated optical (fluorescence) transitions (RESOLFT), photoactivation localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM), structured illumination microscopy (SIM) or saturated structured illumination microscopy (SSIM), all in one way or another addressing the problem of the limited spatial resolution of far-field optical microscopy. While SIM achieves a two-fold improvement in spatial resolution compared to conventional optical microscopy, STED, RESOLFT, PALM/STORM, or SSIM have all gone beyond, pushing the limits of optical image resolution to the nanometer scale. Consequently, all super-resolution techniques open new avenues of biomedical research. Because the field is so young, the potential capabilities of different super-resolution microscopy approaches have yet to be fully explored, and uncertainties remain when considering the best choice of methodology. Thus, even for experts, the road to the future is sometimes shrouded in mist. The super-resolution optical microscopy roadmap of Journal of Physics D: Applied Physics addresses this need for clarity. It provides guidance to the outstanding questions through a collection of short review articles from experts in the field, giving a thorough discussion on the concepts underlying super-resolution optical microscopy, the potential of different approaches, the importance of label optimization (such as reversible photoswitchable proteins) and applications in which these methods will have a significant impact.

304 citations


Journal ArticleDOI
TL;DR: A non-line-of-sight imaging system that uses a single-pixel, single-photon avalanche diode (SPAD) to collect time- of-flight information that provides significant improvements in terms of power requirements, form factor, cost, and reconstruction time, while maintaining a comparable time resolution.
Abstract: By using time-of-flight information encoded in multiply scattered light, it is possible to reconstruct images of objects hidden from the camera’s direct line of sight. Here, we present a non-line-of-sight imaging system that uses a single-pixel, single-photon avalanche diode (SPAD) to collect time-of-flight information. Compared to earlier systems, this modification provides significant improvements in terms of power requirements, form factor, cost, and reconstruction time, while maintaining a comparable time resolution. The potential for further size and cost reduction of this technology make this system a good base for developing a practical system that can be used in real world applications.

236 citations


01 Jan 2015
TL;DR: A multichannel blind restoration technique for linearly degraded images without the explicit knowledge of either the Point Spread Function (PSF) or the original image is proposed.
Abstract: Images may be degraded for many reasons for example, out-of-focus optics produce blurred images, and variations in electronic imaging components introduce noise. Reducing blur or noise or both in images is known as image restoration. Multi-channel blind image restoration recovers an original image from several blurred versions without any knowledge of the blur function. In many applications the image to be processed has a multi-channel nature; i.e., there are several image planes available, called channels with redundant as well as complementary information. Here we propose a multichannel blind restoration technique for linearly degraded images without the explicit knowledge of either the Point Spread Function (PSF) or the original image. The blurred noisy image is compressed using 8 by 8 blocks DCT and filtered using zonal filter. The proposed restoration involves a DCT domain zonal filtering pre-processing followed by a post-processing step of time domain deconvolution. The technique applies to situations on which the scene consists of a finite support object against a uniformly black, gray or white and color backgrounds. Preliminary simulations in noise-free and noisy cases are conducted. The results are compared with standard Median filter for image denoising and the proposed blind restoration scheme is shown to exhibit improvement in SNR.

212 citations


Journal ArticleDOI
TL;DR: The recent GRavitational lEnsing Accuracy Testing (GREAT3) challenge as discussed by the authors was the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images.
Abstract: We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by similar to 1 per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S,rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.

171 citations


Journal ArticleDOI
20 Oct 2015
TL;DR: In this paper, the dispersive properties of a q=1/2 plate, specifically its group index difference Δng for ordinary and extraordinary polarization light, can be tuned for achieving single-aperture, alignment-tolerant stimulated emission depletion (STED) nanoscopy with versatile control over the color combinations as well as laser bandwidths.
Abstract: Spin to orbital angular momentum (OAM) conversion using a device known as a q-plate has gained recent attention as a convenient means of creating OAM beams. We show that the dispersive properties of a q=1/2 plate, specifically its group index difference Δng for ordinary and extraordinary polarization light, can be tuned for achieving single-aperture, alignment-tolerant stimulated emission depletion (STED) nanoscopy with versatile control over the color combinations as well as laser bandwidths. Point spread function measurements reveal the ability to achieve single-aperture STED illumination systems with high throughput (transmission >89%) and purity (donut beam extinction ratios as high as |−18.75| dB, i.e., ∼1% residual light in the dark center of the donut beam) for a variety of color combinations covering the entire visible spectrum, hence addressing several of the fluorescent dyes of interest in STED microscopy. In addition, we demonstrate dual-color STED illumination that would enable multiplexed imaging modalities as well as schemes that could use wide bandwidths up to 19 nm (and hence ultrashort pulses down to ∼50 fs). Switching between any of these color settings only involves changing the bias of the q-plate that does not alter the alignment of the system, hence potentially facilitating alignment-free, spectrally diverse multiplexed nanoscale imaging.

140 citations


Journal ArticleDOI
20 Dec 2015
TL;DR: In this paper, a camera-based ghost imaging system where the correlated photons have significantly different wavelengths is described. But the system is based on parametric down-conversion and the image data are recorded from the coincidently detected, position-correlated, visible photons at a wavelength of 460nm using a highly efficient, low-noise, photon counting camera.
Abstract: Conventional imaging systems rely upon illumination light that is scattered or transmitted by the object and subsequently imaged. Ghost-imaging systems based on parametric down-conversion use twin beams of position-correlated signal and idler photons. One beam illuminates an object while the image information is recovered from a second beam that has never interacted with the object. In this Letter, we report on a camera-based ghost imaging system where the correlated photons have significantly different wavelengths. Infrared photons at 1550 nm wavelength illuminate the object and are detected by an InGaAs/InP single-photon avalanche diode. The image data are recorded from the coincidently detected, position-correlated, visible photons at a wavelength of 460 nm using a highly efficient, low-noise, photon-counting camera. The efficient transfer of the image information from infrared illumination to visible detection wavelengths and the ability to count single photons allows the acquisition of an image while illuminating the object with an optical power density of only 100 pJ cm−2 s−1. This wavelength-transforming ghost-imaging technique has potential for the imaging of light-sensitive specimens or where covert operation is desired.

117 citations


Journal ArticleDOI
TL;DR: In this article, a frequency-diverse compressive metamaterial aperture imager is proposed, which consists of a parallel plate waveguide, in which an array of complementary, resonant metammaterial elements is patterned into one of the plates.
Abstract: The resolution of a frequency diverse compressive metamaterial aperture imager is investigated. The aperture consists of a parallel plate waveguide, in which an array of complementary, resonant metamaterial elements is patterned into one of the plates. Microwaves injected into the waveguide leak out through the resonant metamaterial elements, forming a spatially diverse waveform at the scene. As the frequency is scanned, the waveforms change, such that scene information can be encoded onto a set of frequency measurements. The compressive nature of the metamaterial imager enables image reconstruction from a significantly reduced number of measurements. We characterize the resolution of this complex aperture by studying the simulated point spread function (PSF) computed using different image reconstruction techniques. We compare the imaging performance of the system with that expected from synthetic aperture radar (SAR) limits.

99 citations


Patent
Scott McCloskey1
15 Jan 2015
TL;DR: In this article, a method that uses a point spread function to de-blur an original motion invariant image to create a modified motion invariants image is presented. But the method is not suitable for the detection of objects.
Abstract: A method that includes using a point spread function to de-blur an original motion invariant image to create a modified motion invariant image; using an edge detector to find edges in the modified motion invariant image; determining the distances between the edges and corresponding artifacts in the modified motion invariant image; using the distances between the edges and the corresponding artifacts to estimate a velocity of an object in the modified motion invariant image; generating a corrected point spread function corresponding to the estimated velocity of the object; and using the corrected point spread function to de-blur the original motion invariant image and create a resulting image.

97 citations


Journal ArticleDOI
TL;DR: In this article, a generic astronomical telescope configuration is analyzed by modeling a fast Cassegrain telescope followed by a single 90° deviation fold mirror, and the image plane irradiance distribution is the linear superposition of four PSF images.
Abstract: Detailed knowledge of the image of the point spread function (PSF) is necessary to optimize astronomical coronagraph masks and to understand potential sources of errors in astrometric measurements. The PSF for astronomical telescopes and instruments depends not only on geometric aberrations and scalar wave diffraction but also on those wavefront errors introduced by the physical optics and the polarization properties of reflecting and transmitting surfaces within the optical system. These vector wave aberrations, called polarization aberrations, result from two sources: (1) the mirror coatings necessary to make the highly reflecting mirror surfaces, and (2) the optical prescription with its inevitable non-normal incidence of rays on reflecting surfaces. The purpose of this article is to characterize the importance of polarization aberrations, to describe the analytical tools to calculate the PSF image, and to provide the background to understand how astronomical image data may be affected. To show the order of magnitude of the effects of polarization aberrations on astronomical images, a generic astronomical telescope configuration is analyzed here by modeling a fast Cassegrain telescope followed by a single 90° deviation fold mirror. All mirrors in this example use bare aluminum reflective coatings and the illumination wavelength is 800 nm. Our findings for this example telescope are: (1) The image plane irradiance distribution is the linear superposition of four PSF images: one for each of the two orthogonal polarizations and one for each of two cross-coupled polarization terms. (2) The PSF image is brighter by 9% for one polarization component compared to its orthogonal state. (3) The PSF images for two orthogonal linearly polarization components are shifted with respect to each other, causing the PSF image for unpolarized point sources to become slightly elongated (elliptical) with a centroid separation of about 0.6 mas. This is important for both astrometry and coronagraph applications. (4) Part of the aberration is a polarization-dependent astigmatism, with a magnitude of 22 milliwaves, which enlarges the PSF image. (5) The orthogonally polarized components of unpolarized sources contain different wavefront aberrations, which differ by approximately 32 milliwaves. This implies that a wavefront correction system cannot optimally correct the aberrations for all polarizations simultaneously. (6) The polarization aberrations couple small parts of each polarization component of the light (∼10^(-4)) into the orthogonal polarization where these components cause highly distorted secondary, or “ghost” PSF images. (7) The radius of the spatial extent of the 90% encircled energy of these two ghost PSF image is twice as large as the radius of the Airy diffraction pattern. Coronagraphs for terrestrial exoplanet science are expected to image objects 10^(-10), or 6 orders of magnitude less than the intensity of the instrument-induced “ghost” PSF image, which will interfere with exoplanet measurements. A polarization aberration expansion which approximates the Jones pupil of the example telescope in six polarization terms is presented in the appendix. Individual terms can be associated with particular polarization defects. The dependence of these terms on angles of incidence, numerical aperture, and the Taylor series representation of the Fresnel equations lead to algebraic relations between these parameters and the scaling of the polarization aberrations. These “design rules” applicable to the example telescope are collected in § 5. Currently, exoplanet coronagraph masks are designed and optimized for scalar diffraction in optical systems. Radiation from the “ghost” PSF image leaks around currently designed image plane masks. Here, we show a vector-wave or polarization optimization is recommended. These effects follow from a natural description of the optical system in terms of the Jones matrices associated with each ray path of interest. The importance of these effects varies by orders of magnitude between different optical systems, depending on the optical design and coatings selected. Some of these effects can be calibrated while others are more problematic. Polarization aberration mitigation methods and technologies to minimize these effects are discussed. These effects have important implications for high-contrast imaging, coronagraphy, and astrometry with their stringent PSF image symmetry and scattered light requirements.

88 citations


Journal ArticleDOI
20 Nov 2015
TL;DR: By using regularly spaced subdiffraction apertures filled with fluorescent dyes, this work reveals field-dependent aberrations as large as 50-100 nm and shows that they can be corrected to less than 25 nm over an extended 3D focal volume.
Abstract: The localization of single fluorescent molecules enables the imaging of molecular structure and dynamics with subdiffraction precision and can be extended to three dimensions using point spread function (PSF) engineering. However, the nanoscale accuracy of localization throughout a 3D single-molecule microscope's field of view has not yet been rigorously examined. By using regularly spaced subdiffraction apertures filled with fluorescent dyes, we reveal field-dependent aberrations as large as 50-100 nm and show that they can be corrected to less than 25 nm over an extended 3D focal volume. We demonstrate the applicability of this technique for two engineered PSFs, the double-helix PSF and the astigmatic PSF. We expect these results to be broadly applicable to 3D single-molecule tracking and superresolution methods demanding high accuracy.

Journal ArticleDOI
TL;DR: The Medium Resolution Spectrometer (MRS) for the JWST-MIRI instrument is described in this article, and the expected on-orbit optical performance is presented, based on testing of the MIRI Flight Model and including spectral and spatial coverage and resolution.
Abstract: We describe the design and performance of the Medium Resolution Spectrometer (MRS) for the JWST-MIRI instrument. The MRS incorporates four coaxial spectral channels in a compact opto-mechanical layout that generates spectral images over fields of view up to 7.7 X 7.7 arcseconds in extent and at spectral resolving powers ranging from 1,300 to 3,700. Each channel includes an all-reflective integral field unit (IFU): an 'image slicer' that reformats the input field for presentation to a grating spectrometer. Two 1024 X 1024 focal plane arrays record the output spectral images with an instantaneous spectral coverage of approximately one third of the full wavelength range of each channel. The full 5 to 28.5 micron spectrum is then obtained by making three exposures using gratings and pass-band-determining filters that are selected using just two three-position mechanisms. The expected on-orbit optical performance is presented, based on testing of the MIRI Flight Model and including spectral and spatial coverage and resolution. The point spread function of the reconstructed images is shown to be diffraction limited and the optical transmission is shown to be consistent with the design expectations.

Journal ArticleDOI
TL;DR: In this paper, the photonic dicer was used to reformat a telescope point spread function into a pseudo-slit which is highly multimode in one axis, but diffraction-limited in the other.
Abstract: The spectral resolution of a dispersive spectrograph is dependent on the width of the entrance slit. This means that astronomical spectrographs trade-off throughput with spectral resolving power. Recently, optical guided-wave transitions known as photonic lanterns have been proposed to circumvent this trade-off, by enabling the efficient reformatting of multimode light into a pseudo-slit which is highly multimode in one axis, but diffraction-limited in the other. Here, we demonstrate the successful reformatting of a telescope point spread function into such a slit using a three-dimensional integrated optical waveguide device, which we name the photonic dicer. Using the CANARY adaptive optics (AO) demonstrator on the William Herschel Telescope, and light centred at 1530 nm with a 160 nm full width at half-maximum, the device shows a transmission of between 10 and 20 per cent depending upon the type of AO correction applied. Most of the loss is due to the overfilling of the input aperture in poor and moderate seeing. Taking this into account, the photonic device itself has a transmission of 57 ± 4 per cent. We show how a fully-optimized device can be used with AO to provide efficient spectroscopy at high spectral resolution.

Journal ArticleDOI
TL;DR: The Medium Resolution Spectrometer (MRS) for the JWST-MIRI instrument is described in this paper, and the expected on-orbit optical performance is presented, based on testing of the MIRI Flight Model and including spectral and spatial coverage and resolution.
Abstract: We describe the design and performance of the Medium Resolution Spectrometer (MRS) for the JWST-MIRI instrument. The MRS incorporates four coaxial spectral channels in a compact opto-mechanical layout that generates spectral images over fields of view up to 7.7 × 7.7″ in extent and at spectral resolving powers ranging from 1300 to 3700. Each channel includes an all-reflective integral field unit (IFU): an “image slicer” that reformats the input field for presentation to a grating spectrometer. Two 1024 × 1024 focal plane detector arrays record the output spectral images with an instantaneous spectral coverage of approximately one third of the full wavelength range of each channel. The full 5–28.5 μm spectrum is then obtained by making three exposures using gratings and pass-band-determining filters that are selected using just two three-position mechanisms. The expected on-orbit optical performance is presented, based on testing of the MIRI Flight Model and including spectral and spatial coverage and resolution. The point spread function of the reconstructed images is shown to be diffraction limited and the optical transmission is shown to be consistent with the design expectations.

Journal ArticleDOI
TL;DR: 3D generalization of structure tensor analysis will further improve the utility of this method for validation of d-MRI by making it a more flexible experimental technique that closer resembles the inherently 3D nature ofd-MRI measurements.

Journal ArticleDOI
TL;DR: This work presents an approach that optimizes the wavefront during SML acquisition by combining an intensity independent merit function with a Genetic algorithm (GA) to optimize the PSF despite the fluctuating intensity.
Abstract: The resolution of Single Molecule Localization Microscopy (SML) is dependent on the width of the Point Spread Function (PSF) and the number of photons collected. However, biological samples tend to degrade the shape of the PSF due to the heterogeneity of the index of refraction. In addition, there are aberrations caused by imperfections in the optical components and alignment, and the refractive index mismatch between the coverslip and the sample, all of which directly reduce the accuracy of SML. Adaptive Optics (AO) can play a critical role in compensating for aberrations in order to increase the resolution. However the stochastic nature of single molecule emission presents a challenge for wavefront optimization because the large fluctuations in photon emission do not permit many traditional optimization techniques to be used. Here we present an approach that optimizes the wavefront during SML acquisition by combining an intensity independent merit function with a Genetic algorithm (GA) to optimize the PSF despite the fluctuating intensity. We demonstrate the use of AO with GA in tissue culture cells and through ~50µm of tissue in the Drosophila Central Nervous System (CNS) to achieve a 4-fold increase in the localization precision.

Journal ArticleDOI
TL;DR: A validated method for time-lapse SIM that focuses on cortical microtubules of different plant cell types by using one of the existing commercially available SIM platforms is described, which may be widely applied to the imaging of plant cells.
Abstract: This protocol describes a detailed method for superresolution imaging of plant tissues by structured illumination microscopy (SIM). Details include microscope calibration, tissue preparation, image acquisition and evaluation of SIM images. Although superresolution (SR) approaches have been routinely used for fixed or living material from other organisms, the use of time-lapse structured illumination microscopy (SIM) imaging in plant cells still remains under-developed. Here we describe a validated method for time-lapse SIM that focuses on cortical microtubules of different plant cell types. By using one of the existing commercially available SIM platforms, we provide a user-friendly and easy-to-follow protocol that may be widely applied to the imaging of plant cells. This protocol includes steps describing calibration of the microscope and channel alignment, generation of an experimental point spread function (PSF), preparation of appropriate observation chambers with available plant material, image acquisition, reconstruction and validation. This protocol can be carried out within two to three working days.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a method based on the Huygens-Fresnel principle for computing the diffracted intensity from measured or modeled profiles, which can be extended to optical systems with an arbitrary number of reflections.
Abstract: Context. The imaging sharpness of an X-ray telescope is chiefly determined by the optical quality of its focusing optics, which in turn mostly depends on the shape accuracy and the surface finishing of the grazing-incidence X-ray mirrors that compose the optical modules. To ensure the imaging performance during the mirror manufacturing, a fundamental step is predicting the mirror point spread function (PSF) from the metrology of its surface. Traditionally, the PSF computation in X-rays is assumed to be different depending on whether the surface defects are classified as figure errors or roughness. This classical approach, however, requires setting a boundary between these two asymptotic regimes, which is not known a priori.Aims. The aim of this work is to overcome this limit by providing analytical formulae that are valid at any light wavelength, for computing the PSF of an X-ray mirror shell from the measured longitudinal profiles and the roughness power spectral density, without distinguishing spectral ranges with different treatments.Methods. The method we adopted is based on the Huygens-Fresnel principle for computing the diffracted intensity from measured or modeled profiles. In particular, we have simplified the computation of the surface integral to only one dimension, owing to the grazing incidence that reduces the influence of the azimuthal errors by orders of magnitude. The method can be extended to optical systems with an arbitrary number of reflections – in particular the Wolter-I, which is frequently used in X-ray astronomy – and can be used in both near- and far-field approximation. Finally, it accounts simultaneously for profile, roughness, and aperture diffraction.Results. We describe the formalism with which one can self-consistently compute the PSF of grazing-incidence mirrors, and we show some PSF simulations including the UV band, where the aperture diffraction dominates the PSF, and hard X-rays where the X-ray scattering has a major impact on the PSF degradation. The results are validated with ray-tracing simulations, or by comparison with the analytical computation of the half-energy width based on the known scattering theory, where these approaches are applicable. Finally, we validate this by comparing the simulated PSF of a real Wolter-I mirror shell with the measured PSF in hard X-rays.

Journal ArticleDOI
TL;DR: The experimental results demonstrate that minimizing the blur-SURE yields highly accurate estimates of the PSF parameters, which also result in a restoration quality that is very similar to the one obtained with the exact PSF, when plugged into the recent multi-Wiener SURE-LET deconvolution algorithm.
Abstract: We propose an unbiased estimate of a filtered version of the mean squared error—the blur-SURE (Stein’s unbiased risk estimate)—as a novel criterion for estimating an unknown point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of Wiener processings. Based on this estimated blur kernel, we then perform nonblind deconvolution using our recently developed algorithm. The SURE-based framework is exemplified with a number of parametric PSF, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel. The experimental results demonstrate that minimizing the blur-SURE yields highly accurate estimates of the PSF parameters, which also result in a restoration quality that is very similar to the one obtained with the exact PSF, when plugged into our recent multi-Wiener SURE-LET deconvolution algorithm. The highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on SURE-like estimates.

Journal ArticleDOI
TL;DR: A new phase reconstruction method, called tomographic deconvolution phase microscopy (TDPM), is described which makes use of commercial microscopy hardware in realizing 3D QPI and is based on the 3D weak object transfer function theory, shown here to be capable of imaging "nonweak" phase objects with large phase excursions.
Abstract: The field of three-dimensional quantitative phase imaging (3D QPI) is expanding rapidly with applications in biological, medical, and industrial research, development, diagnostics, and metrology. Much of this research has centered on developing optical diffraction tomography (ODT) for biomedical applications. In addition to technical difficulties associated with coherent noise, ODT is not congruous with optical microscopy utilizing partially coherent light, which is used in most biomedical laboratories. Thus, ODT solutions have, for the most part, been limited to customized optomechanical systems which would be relatively expensive to implement on a wide scale. In the present work, a new phase reconstruction method, called tomographic deconvolution phase microscopy (TDPM), is described which makes use of commercial microscopy hardware in realizing 3D QPI. TDPM is analogous to methods used in deconvolution microscopy which improve spatial resolution and 3D-localization accuracy of fluorescence micrographs by combining multiple through-focal scans which are deconvolved by the system point spread function. TDPM is based on the 3D weak object transfer function theory which is shown here to be capable of imaging “nonweak” phase objects with large phase excursions. TDPM requires no phase unwrapping and recovers the entire object spectrum via object rotation, mitigating the need to fill in the “missing cone” of spatial frequencies algorithmically as in limited-angle ODT. In the present work, TDPM is demonstrated using optical fibers, including single-mode, polarization-maintaining, and photonic-crystal fibers as well as an azimuthally varying CO2-laser-induced long-period fiber grating period as test phase objects.

Journal ArticleDOI
TL;DR: This paper measured axial scaling factors as a function of refractive‐index mismatch for high‐aperture confocal microscopy imaging and found that their scaling factors are almost completely linearly dependent on refractive index and were in good agreement with theoretical predictions that take the full vectorial properties of light into account.
Abstract: Accurate distance measurement in 3D confocal microscopy is important for quantitative analysis, volume visualization and image restoration. However, axial distances can be distorted by both the point spread function (PSF) and by a refractive-index mismatch between the sample and immersion liquid, which are difficult to separate. Additionally, accurate calibration of the axial distances in confocal microscopy remains cumbersome, although several high-end methods exist. In this paper we present two methods to calibrate axial distances in 3D confocal microscopy that are both accurate and easily implemented. With these methods, we measured axial scaling factors as a function of refractive-index mismatch for high-aperture confocal microscopy imaging. We found that our scaling factors are almost completely linearly dependent on refractive index and that they were in good agreement with theoretical predictions that take the full vectorial properties of light into account. There was however a strong deviation with the theoretical predictions using (high-angle) geometrical optics, which predict much lower scaling factors. As an illustration, we measured the PSF of a correctly calibrated point-scanning confocal microscope and showed that a nearly index-matched, micron-sized spherical object is still significantly elongated due to this PSF, which signifies that care has to be taken when determining axial calibration or axial scaling using such particles.

Journal ArticleDOI
TL;DR: A complete and novel tomographic theory for a multi-directional tomography system consisting of a lens and CCD cameras is established and a 3D projection model based on the lens imaging theory is proposed and integrated into the multiplicative algebraic reconstruction technique (MART).
Abstract: Flame chemiluminescence tomography (FCT) has been widely used in flame diagnostics for three-dimensional (3D), spatially resolved measurements of instantaneous flame geometry and, to some extent, of species concentrations. However, in most studies, tomographic reconstructions are based on a traditional parallel projection model. Due to the light collection characteristics of a lens, a parallel projection model is not appropriate for the practical optical setups that are used for emission imaging, particularly at small F-numbers. Taking the light collection effect of the lens into account, this Letter establishes a complete and novel tomographic theory for a multi-directional tomography system consisting of a lens and CCD cameras. A modified camera calibration method is presented first. It determines the exact spatial locations and intrinsic parameters of the cameras. A 3D projection model based on the lens imaging theory is then proposed and integrated into the multiplicative algebraic reconstruction technique (MART). The new approach is demonstrated with a 12-camera system that is used to reconstruct the emission field of a propane flame, thereby resolving space and time.

Journal ArticleDOI
TL;DR: In this article, the authors presented a method for image coaddition in the limit of background-dominated noise which is optimal for any statistical test or measurement on the constant-in-time image (e.g., source detection, shape or flux measurement or star-galaxy separation).
Abstract: Stacks of digital astronomical images are combined in order to increase image depth. The variable seeing conditions, sky background and transparency of ground-based observations make the coaddition process non-trivial. We present image coaddition methods optimized for source detection and flux measurement, that maximize the signal-to-noise ratio (S/N). We show that for these purposes the best way to combine images is to apply a matched filter to each image using its own point spread function (PSF) and only then to sum the images with the appropriate weights. Methods that either match filter after coaddition, or perform PSF homogenization prior to coaddition will result in loss of sensitivity. We argue that our method provides an increase of between a few and 25 percent in the survey speed of deep ground-based imaging surveys compared with weighted coaddition techniques. We demonstrate this claim using simulated data as well as data from the Palomar Transient Factory data release 2. We present a variant of this coaddition method which is optimal for PSF or aperture photometry. We also provide an analytic formula for calculating the S/N for PSF photometry on single or multiple observations. In the next paper in this series we present a method for image coaddition in the limit of background-dominated noise which is optimal for any statistical test or measurement on the constant-in-time image (e.g., source detection, shape or flux measurement or star-galaxy separation), making the original data redundant. We provide an implementation of this algorithm in MATLAB.

Journal ArticleDOI
TL;DR: This experimental PSF allows the approach to take into account the laser beam shape, beam aberrations, and the laser-solid interaction, which in turn enhances the spatial resolution of the reconstructed volume.
Abstract: In this work, pre- and postacquisition procedures for enhancing the lateral resolution of laser ablation-inductively coupled plasma mass spectrometry (LA-ICPMS) in two- and three-dimensional (2D, 3D) nuclide distribution mapping beyond the laser beam waist are described. 2D images were constructed by projecting a rectangular grid of discrete LA positions, arranged at interspacings smaller than the dimensions of the laser beam waist, onto the sample surface, thus oversampling the region of interest and producing a 2D image convolved in the spatial domain. The pulse response peaks of a low-dispersion LA cell were isolated via signal deconvolution of the transient mass analyzer response. A 3D stack of 2D images was deconvolved by an iterative Richardson-Lucy algorithm with Total Variance regularization, enabling submicrometer image fidelity, demonstrated in the analysis of trace level features in corroded glass. A point spread function (PSF) could be derived from topography maps of single pulse craters from ...

Journal ArticleDOI
TL;DR: A localization scheme is proposed that can identify several overlapping molecule images while maintaining high localization precision and substantially increase the allowable labeling density and accelerate the data collection time of single-molecule localization microscopy by more than one order of magnitude.
Abstract: When a single molecule is detected in a wide-field microscope, the image approximates the point spread function of the system. However, as the distribution of molecules becomes denser and their images begin to overlap, existing solutions to determine the number of molecules present and their precise three-dimensional locations can tolerate little to no overlap. We propose a localization scheme that can identify several overlapping molecule images while maintaining high localization precision. A solution to this problem involving matched optical and digital techniques, as here proposed, can substantially increase the allowable labeling density and accelerate the data collection time of single-molecule localization microscopy by more than one order of magnitude.

Journal ArticleDOI
Siyuan Dong1, Pariksheet Nanda1, Kaikai Guo1, Jun Liao1, Guoan Zheng1 
TL;DR: An incoherent photographic imaging approach, termed Fourier ptychographic photography, that uses nonuniform structured light for super-resolution imaging that may find applications in photographic imaging settings, remote sensing, and imaging radar.
Abstract: Controlling photographic illumination in a structured fashion is a common practice in computational photography and image-based rendering Here we introduce an incoherent photographic imaging approach, termed Fourier ptychographic photography, that uses nonuniform structured light for super-resolution imaging In this approach, frequency mixing between the object and the structured light shifts the high-frequency object information to the passband of the photographic lens Therefore, the recorded intensity images contain object information that is beyond the cutoff frequency of the collection optics Based on multiple images acquired under different structured light patterns, we used the Fourier ptychographic algorithm to recover the super-resolution object image and the unknown illumination pattern We demonstrated the reported approach by imaging various objects, including a resolution target, a quick response code, a dollar bill, an insect, and a color leaf The reported approach may find applications in photographic imaging settings, remote sensing, and imaging radar It may also provide new insights for high-resolution imaging by shifting the focus from the collection optics to the generation of structured light

Journal ArticleDOI
TL;DR: The approximate invariance of the projector's IPSF is proved both numerically and experimentally and it is demonstrated that a structured light pattern projection technique using the proposed method can measure the shape of an object with large depth variances more accurately than normal projection techniques.
Abstract: A simple and cost-efficient method for extending a projector's depth-of-field (DOF) is proposed. By leveraging liquid lens technology, we can periodically modulate the focal length of a projector at a frequency that is higher than the critical flicker fusion (CFF) frequency. Fast periodic focal length modulation results in forward and backward sweeping of focusing distance. Fast focal sweep projection makes the point spread function (PSF) of each projected pixel integrated over a sweep period (IPSF; integrated PSF) nearly invariant to the distance from the projector to the projection surface as long as it is positioned within sweep range. This modulation is not perceivable by human observers. Once we compensate projection images for the IPSF, the projected results can be focused at any point within the range. Consequently, the proposed method requires only a single offline PSF measurement; thus, it is an open-loop process. We have proved the approximate invariance of the projector's IPSF both numerically and experimentally. Through experiments using a prototype system, we have confirmed that the image quality of the proposed method is superior to that of normal projection with fixed focal length. In addition, we demonstrate that a structured light pattern projection technique using the proposed method can measure the shape of an object with large depth variances more accurately than normal projection techniques.

Journal ArticleDOI
TL;DR: It is demonstrated that the assumptions of LST in combination with the formula for the PSF are a good model for the pulse-echo imaging process and can be replaced with a simple closed analytic term based on a far field approximation.
Abstract: This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

Journal ArticleDOI
TL;DR: An imaging strategy for the structured illumination technique is discussed and the use of a modified incoherent Fourier ptychographic procedure for reducing the number of acquisitions is demonstrated to shorten the acquisition time of super-resolution imaging and reduce phototoxicity of biological samples.
Abstract: Structured illumination technique enhances the lateral resolution by projecting non-uniform intensity patterns on a sample. In a typical implementation, three lateral phase shifts (0, 2π/3, 4π/3) are needed for each orientation of the sinusoidal pattern, and 3 different orientations are needed to double the bandwidth isotopically in the Fourier domain. To this end, 9 incoherent images are needed in the acquisition process. In this paper, we discuss an imaging strategy for the structured illumination technique and demonstrate the use of a modified incoherent Fourier ptychographic procedure for reducing the number of acquisitions. In the first implementation, we used complementary sinusoidal patterns for sample illumination. We show that, the number of lateral phase shifts can be reduced from 3 to 2 for each orientation of the sinusoidal pattern and the total number of image acquisitions can be reduced to 6 with 3 orientations. In the second implementation, we further reduce the number of image acquisitions to 4. We also show that, the resolution-doubled image can be recovered even with unknown phases of the sinusoidal patterns. We validate the proposed imaging procedure with non-fluorescence samples. The reported approach may shorten the acquisition time of super-resolution imaging and reduce phototoxicity of biological samples.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed an adjacency correction algorithm based on the use of the point spread function (PSF) which allows calculating the contribution of reflections from the nearby pixels to the apparent radiance of the target.