Showing papers on "Point spread function published in 2016"
TL;DR: A systematic study of the imaging of water-immersed nanostructures by barium titanate glass microspheres of different size finds that the super-resolution imaging of a microsphere is dependent on the waist of its photonic nanojet, the best resolution being obtained with a 6 μm Ømicrosphere, which generates the nanojet with the minimum waist.
Abstract: Dielectric microspheres with appropriate refractive index can image objects with super-resolution, that is, with a precision well beyond the classical diffraction limit. A microsphere is also known to generate upon illumination a photonic nanojet, which is a scattered beam of light with a high-intensity main lobe and very narrow waist. Here, we report a systematic study of the imaging of water-immersed nanostructures by barium titanate glass microspheres of different size. A numerical study of the light propagation through a microsphere points out the light focusing capability of microspheres of different size and the waist of their photonic nanojet. The former correlates to the magnification factor of the virtual images obtained from linear test nanostructures, the biggest magnification being obtained with microspheres of ∼6-7 μm in size. Analyzing the light intensity distribution of microscopy images allows determining analytically the point spread function of the optical system and thereby quantifies its resolution. We find that the super-resolution imaging of a microsphere is dependent on the waist of its photonic nanojet, the best resolution being obtained with a 6 μm O microsphere, which generates the nanojet with the minimum waist. This comparison allows elucidating the super-resolution imaging mechanism.
182 citations
TL;DR: This work applies a digital microscanning approach to an infrared single-pixel camera that improves the SNR of reconstructed images by ∼ 50 % for the same acquisition time and provides access to a stream of low-resolution 'preview' images throughout each high-resolution acquisition.
Abstract: Single-pixel cameras provide a means to perform imaging at wavelengths where pixelated detector arrays are expensive or limited. The image is reconstructed from measurements of the correlation between the scene and a series of masks. Although there has been much research in the field in recent years, the fact that the signal-to-noise ratio (SNR) scales poorly with increasing resolution has been one of the main limitations prohibiting the uptake of such systems. Microscanning is a technique that provides a final higher resolution image by combining multiple images of a lower resolution. Each of these low resolution images is subject to a sub-pixel sized lateral displacement. In this work we apply a digital microscanning approach to an infrared single-pixel camera. Our approach requires no additional hardware, but is achieved simply by using a modified set of masks. Compared to the conventional Hadamard based single-pixel imaging scheme, our proposed framework improves the SNR of reconstructed images by ∼ 50 % for the same acquisition time. In addition, this strategy also provides access to a stream of low-resolution ‘preview’ images throughout each high-resolution acquisition.
141 citations
TL;DR: By exploiting chromatic dispersion, a new class of optical phase masks are designed that simultaneously yield controllably different PSFs for different wavelengths, enabling simultaneous multicolour tracking or super-resolution imaging in a single optical path.
Abstract: Super-resolution microscopy has revolutionized cellular imaging in recent years1-4. Methods relying on sequential localization of single point emitters enable spatial tracking at ~10-40 nm resolution. Moreover, tracking and imaging in three dimensions is made possible by various techniques, including point-spread-function (PSF) engineering5-9 -namely, encoding the axial (z) position of a point source in the shape that it creates in the image plane. However, a remaining challenge for localization-microscopy is efficient multicolour imaging - a task of the utmost importance for contextualizing biological data. Normally, multicolour imaging requires sequential imaging10, 11, multiple cameras12, or segmented dedicated fields of view13, 14. Here, we demonstrate an alternate strategy, the encoding of spectral information (colour), in addition to 3D position, directly in the image. By exploiting chromatic dispersion, we design a new class of optical phase masks that simultaneously yield controllably different PSFs for different wavelengths, enabling simultaneous multicolour tracking or super-resolution imaging in a single optical path.
139 citations
TL;DR: A convex optimization framework to simultaneously estimate the point spread function as well as the spike signal is proposed, by mildly constraining the pointspread function to lie in a known low-dimensional subspace and it is proved the proposed algorithm, dubbed as AtomicLift, is guaranteed to recover the Spike signal up to a scaling factor as soon as the number of samples is large enough.
Abstract: Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies of a band-limited or diffraction-limited point spread function, which is either determined by the nature or designed by the users; in other words, we observe the convolution between a point spread function and a sparse spike signal with unknown amplitudes and delays. While it is of great interest to accurately resolve the spike signal from as few samples as possible, however, when the point spread function is not known a priori, this problem is terribly ill-posed. This paper proposes a convex optimization framework to simultaneously estimate the point spread function as well as the spike signal, by mildly constraining the point spread function to lie in a known low-dimensional subspace. By applying the lifting trick, we obtain an underdetermined linear system of an ensemble of signals with joint spectral sparsity, to which atomic norm minimization is applied. Under mild randomness assumptions of the low-dimensional subspace as well as a separation condition of the spike signal, we prove the proposed algorithm, dubbed as AtomicLift, is guaranteed to recover the spike signal up to a scaling factor as soon as the number of samples is large enough. The extension of AtomicLift to handle noisy measurements is also discussed. Numerical examples are provided to validate the effectiveness of the proposed approaches.
139 citations
20 Oct 2016
TL;DR: In this paper, optical heterodyne detection in higher-order transverse electromagnetic modes (TEMs) can help in achieving sub-Rayleigh precision for a variety of microscopy-related tasks.
Abstract: The Rayleigh limit has so far applied to all microscopy techniques that rely on linear optical interaction and detection in the far field. Here we demonstrate that detecting the light emitted by an object in higher-order transverse electromagnetic modes (TEMs) can help in achieving sub-Rayleigh precision for a variety of microscopy-related tasks. Using optical heterodyne detection in TEM01, we measure the position of coherently and incoherently emitting objects to within 0.0015 and 0.012 of the Rayleigh limit, respectively, and determine the distance between two incoherently emitting objects positioned within 0.28 of the Rayleigh limit with a precision of 0.019 of the Rayleigh limit. Heterodyne detection in multiple higher-order TEMs enables full imaging with a resolution significantly below the Rayleigh limit in a way that is reminiscent of quantum tomography of optical states.
131 citations
TL;DR: This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramér-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy.
Abstract: Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based super-resolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramer-Rao lower bound. The Cramer-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramer-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation and, more generally, to demonstrate the flexibility of the mathematical framework.
122 citations
TL;DR: The image reconstruction of multiplane object using COACH was compared with that of other equivalent imaging systems, and has been found to possess a higher axial resolution compared to Fresnel incoherent correlation holography.
Abstract: We propose and demonstrate a new concept of incoherent digital holography termed coded aperture correlation holography (COACH). In COACH, the hologram of an object is formed by the interference of light diffracted from the object, with light diffracted from the same object, but that passes through a coded phase mask (CPM). Another hologram is recorded for a point object, under identical conditions and with the same CPM. This hologram is called the point spread function (PSF) hologram. The reconstructed image is obtained by correlating the object hologram with the PSF hologram. The image reconstruction of multiplane object using COACH was compared with that of other equivalent imaging systems, and has been found to possess a higher axial resolution compared to Fresnel incoherent correlation holography.
115 citations
TL;DR: A new adaptive digital fringe projection technique which avoids image saturation and has a high signal to noise ratio (SNR) in the three-dimensional (3-D) shape measurement of objects that has a large range of reflectivity variation across the surface.
Abstract: It is a challenge for any optical method to measure objects with a large range of reflectivity variation across the surface. Image saturation results in incorrect intensities in captured fringe pattern images, leading to phase and measurement errors. This paper presents a new adaptive digital fringe projection technique which avoids image saturation and has a high signal to noise ratio (SNR) in the three-dimensional (3-D) shape measurement of objects that has a large range of reflectivity variation across the surface. Compared to previous high dynamic range 3-D scan methods using many exposures and fringe pattern projections, which consumes a lot of time, the proposed technique uses only two preliminary steps of fringe pattern projection and image capture to generate the adapted fringe patterns, by adaptively adjusting the pixel-wise intensity of the projected fringe patterns based on the saturated pixels in the captured images of the surface being measured. For the bright regions due to high surface reflectivity and high illumination by the ambient light and surfaces interreflections, the projected intensity is reduced just to be low enough to avoid image saturation. Simultaneously, the maximum intensity of 255 is used for those dark regions with low surface reflectivity to maintain high SNR. Our experiments demonstrate that the proposed technique can achieve higher 3-D measurement accuracy across a surface with a large range of reflectivity variation.
108 citations
TL;DR: The realization of high speed color imaging through turbid media is successfully carried out by taking into account the media memory effect, the point spread function, the exit pupil of the optical system, and the optimized signal to noise ratio.
Abstract: Optical imaging through complex media has many important applications. Although research progresses have been made to recover optical image through various turbid media, the widespread application of the technology is hampered by the recovery speed, requirement on specific illumination, poor image quality and limited field of view. Here we demonstrate that above-mentioned drawbacks can be essentially overcome. The realization of high speed color imaging through turbid media is successfully carried out by taking into account the media memory effect, the point spread function, the exit pupil of the optical system, and the optimized signal to noise ratio. By retrieving selected speckles with enlarged field of view, high quality image is recovered with a responding speed only determined by the frame rates of the image capturing devices. The immediate application of the technique is expected to register static and dynamic imaging under human skin to recover information with a wearable device.
87 citations
TL;DR: The mirror-assisted excitation confinement enhanced the axial resolution six-fold and the lateral resolution two-fold for STED, which together achieved 19-nm resolution to resolve the inner rim of a nuclear pore complex and to discriminate the contents of 120 nm viral filaments.
Abstract: Axial excitation confinement beyond the diffraction limit is crucial to the development of next-generation, super-resolution microscopy. STimulated Emission Depletion (STED) nanoscopy offers lateral super-resolution using a donut-beam depletion, but its axial resolution is still over 500 nm. Total internal reflection fluorescence microscopy is widely used for single-molecule localization, but its ability to detect molecules is limited to within the evanescent field of ~ 100 nm from the cell attachment surface. We find here that the axial thickness of the point spread function (PSF) during confocal excitation can be easily improved to 110 nm by replacing the microscopy slide with a mirror. The interference of the local electromagnetic field confined the confocal PSF to a 110-nm spot axially, which enables axial super-resolution with all laser-scanning microscopes. Axial sectioning can be obtained with wavelength modulation or by controlling the spacer between the mirror and the specimen. With no additional complexity, the mirror-assisted excitation confinement enhanced the axial resolution six-fold and the lateral resolution two-fold for STED, which together achieved 19-nm resolution to resolve the inner rim of a nuclear pore complex and to discriminate the contents of 120 nm viral filaments. The ability to increase the lateral resolution and decrease the thickness of an axial section using mirror-enhanced STED without increasing the laser power is of great importance for imaging biological specimens, which cannot tolerate high laser power.
77 citations
TL;DR: In this article, a deconvolution method was proposed to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution.
Abstract: We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
TL;DR: In this article, a new algorithm for radio aperture synthesis imaging of extended and diffuse emission in total intensity is presented, which is derived using Bayesian statistical inference techniques, estimating the surface brightness in the sky assuming a priori log-normal statistics.
Abstract: We present resolve, a new algorithm for radio aperture synthesis imaging of extended and diffuse emission in total intensity. The algorithm is derived using Bayesian statistical inference techniques, estimating the surface brightness in the sky assuming a priori log-normal statistics. resolve estimates the measured sky brightness in total intensity, and the spatial correlation structure in the sky, which is used to guide the algorithm to an optimal reconstruction of extended and diffuse sources. During this process, the algorithm succeeds in deconvolving the effects of the radio interferometric point spread function. Additionally, resolve provides a map with an uncertainty estimate of the reconstructed surface brightness. Furthermore, with resolve we introduce a new, optimal visibility weighting scheme that can be viewed as an extension to robust weighting. In tests using simulated observations, the algorithm shows improved performance against two standard imaging approaches for extended sources, Multiscale-CLEAN and the Maximum Entropy Method.
TL;DR: The results indicate that self-calibration can improve even upon systems with presumably accurate geometric calibration and is applicable to situations where conventional calibration is not feasible, such as complex non-circular CBCT orbits and systems with irreproducible source-detector trajectory.
Abstract: Robotic C-arms are capable of complex orbits that can increase field of view, reduce artifacts, improve image quality, and/or reduce dose; however, it can be challenging to obtain accurate, reproducible geometric calibration required for image reconstruction for such complex orbits. This work presents a method for geometric calibration for an arbitrary source-detector orbit by registering 2D projection data to a previously acquired 3D image. It also yields a method by which calibration of simple circular orbits can be improved. The registration uses a normalized gradient information similarity metric and the covariance matrix adaptation-evolution strategy optimizer for robustness against local minima and changes in image content. The resulting transformation provides a 'self-calibration' of system geometry. The algorithm was tested in phantom studies using both a cone-beam CT (CBCT) test-bench and a robotic C-arm (Artis Zeego, Siemens Healthcare) for circular and non-circular orbits. Self-calibration performance was evaluated in terms of the full-width at half-maximum (FWHM) of the point spread function in CBCT reconstructions, the reprojection error (RPE) of steel ball bearings placed on each phantom, and the overall quality and presence of artifacts in CBCT images. In all cases, self-calibration improved the FWHM-e.g. on the CBCT bench, FWHM = 0.86 mm for conventional calibration compared to 0.65 mm for self-calibration (p < 0.001). Similar improvements were measured in RPE-e.g. on the robotic C-arm, RPE =��� 0.73 mm for conventional calibration compared to 0.55 mm for self-calibration (p < 0.001). Visible improvement was evident in CBCT reconstructions using self-calibration, particularly about high-contrast, high-frequency objects (e.g. temporal bone air cells and a surgical needle). The results indicate that self-calibration can improve even upon systems with presumably accurate geometric calibration and is applicable to situations where conventional calibration is not feasible, such as complex non-circular CBCT orbits and systems with irreproducible source-detector trajectory.
TL;DR: Two-dimensional imaging using illumination via a single-mode fiber with a multiply scattering tip and compressed sensing acquisition and the imaging device is mechanically scan-free and insensitive to bending of the fiber, making it suitable for micro-endoscopy.
Abstract: We demonstrate two-dimensional imaging using illumination via a single-mode fiber with a multiply scattering tip and compressed sensing acquisition. We illuminate objects with randomly structured, but deterministic, speckle patterns produced by a coherent light source propagating through a TiO2-coated fiber tip. The coating thickness is optimized to produce speckle patterns that are highly sensitive to laser wavelength, yet repeatable. Images of the object are reconstructed from the characterized wavelength dependence of the speckle patterns and the wavelength dependence of the total light collected from the object using a single photodetector. Our imaging device is mechanically scan-free and insensitive to bending of the fiber, making it suitable for micro-endoscopy.
26 May 2016
TL;DR: In this paper, a reconstruction approach for enhancing the resolution of the terahertz (THz) images is introduced, which can be used for analyzing, describing and modeling of these systems.
Abstract: This paper introduces a novel reconstruction approach for enhancing the resolution of the terahertz (THz) images. For this purpose the THz imaging equation is derived. According to our best knowledge we are reporting the first THz imaging equation by this paper. This imaging equation is universal for THz far-field imaging systems and can be used for analyzing, describing and modeling of these systems. The geometry and behavior of Gaussian beams in far-field region imply that the FWHM of the THz beams diverge as the frequencies of the beams decrease. Thus, the resolution of the measurement decreases in lower frequencies. On the other hand, the depth of penetration of THz beams decreases as frequency increases. Roughly speaking beams in sub 1.5 THz, are transmitted into integrated circuit (IC) packages and the similar packaged objects. Thus, it is not possible to use the THz pulse with higher frequencies in order to achieve higher resolution inspection of packaged items. In this paper, after developing the 3-D THz point spread function (PSF) of the scanning THz beam and then the THz imaging equation, THz images are enhanced through deconvolution of the THz PSF and THz images. As a result, the resolution has been improved several times beyond the physical limitations of the THz measurement setup in the far-field region and sub-Nyquist images have been achieved. Particularly, MSE and SSIM´ have been increased by 27% and 50% respectively. Details as small as 0.2 mm were made visible in the THz images which originally reveals no details smaller than 2.2 mm. In other words the resolution of the images has been increased by 10 times. The accuracy of the reconstructed images was proved by high resolution X-ray images.
TL;DR: This paper presents a blind deblurring pipeline able to restore real camera systems by slightly extending their DOF and recovering sharpness in regions slightly out of focus by relying first on the estimation of the spatially varying defocus blur.
Abstract: Real camera systems have a limited depth of field (DOF) which may cause an image to be degraded due to visible misfocus or too shallow DOF. In this paper, we present a blind deblurring pipeline able to restore such images by slightly extending their DOF and recovering sharpness in regions slightly out of focus. To address this severely ill-posed problem, our algorithm relies first on the estimation of the spatially varying defocus blur. Drawing on local frequency image features, a machine learning approach based on the recently introduced regression tree fields is used to train a model able to regress a coherent defocus blur map of the image, labeling each pixel by the scale of a defocus point spread function. A non-blind spatially varying deblurring algorithm is then used to properly extend the DOF of the image. The good performance of our algorithm is assessed both quantitatively, using realistic ground truth data obtained with a novel approach based on a plenoptic camera, and qualitatively with real images.
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TL;DR: The aim of this work is to achieve fast acoustic imaging with enhanced resolution by applying the tools used in SOFI to contrast-enhance ultrasound (CEUS) plane-wave scans, and may be used to obtain scans with enhanced spatial resolution and high temporal resolution, facilitating flow-dynamics monitoring.
Abstract: Ultrasound super-localization microscopy techniques presented in the last few years enable non-invasive imaging of vascular structures at the capillary level by tracking the flow of ultrasound contrast agents (gas microbubbles). However, these techniques are currently limited by low temporal resolution and long acquisition times. Super-resolution optical fluctuation imaging (SOFI) is a fluorescence microscopy technique enabling sub-diffraction limit imaging with high temporal resolution by calculating high order statistics of the fluctuating optical signal. The aim of this work is to achieve fast acoustic imaging with enhanced resolution by applying the tools used in SOFI to contrast-enhance ultrasound (CEUS) plane-wave scans. The proposed method was tested using numerical simulations and evaluated using two in-vivo rabbit models: scans of healthy kidneys and VX-2 tumor xenografts. Improved spatial resolution was observed with a reduction of up to 50% in the full width half max of the point spread function. In addition, substantial reduction in the background level was achieved compared to standard mean amplitude persistence images, revealing small vascular structures within tumors. The scan duration of the proposed method is less than a second while current superlocalization techniques require acquisition duration of several minutes. As a result, the proposed technique may be used to obtain scans with enhanced spatial resolution and high temporal resolution, facilitating flow-dynamics monitoring. Our method can also be applied during a breath-hold, reducing the sensitivity to motion artifacts.
TL;DR: A prototype device for performing swept synthetic aperture imaging using a conventional 1-D array transducer and ultrasound research scanner is presented and improvements in resolution, contrast and contrast-to-noise ratio are demonstrated in vivo and in a fetal phantom.
Abstract: Ultrasound image quality is often inherently limited by the physical dimensions of the imaging transducer. We hypothesize that, by collecting synthetic aperture data sets over a range of aperture positions while precisely tracking the position and orientation of the transducer, we can synthesize large effective apertures to produce images with improved resolution and target detectability. We analyze the two largest limiting factors for coherent signal summation: aberration and mechanical uncertainty. Using an excised canine abdominal wall as a model phase screen, we experimentally observed an effective arrival time error ranging from 18.3 ns to 58 ns (root-mean-square error) across the swept positions. Through this clutter-generating tissue, we observed a 72.9% improvement in resolution with only a 3.75 dB increase in side lobe amplitude compared to the control case. We present a simulation model to study the effect of calibration and mechanical jitter errors on the synthesized point spread function. The relative effects of these errors in each imaging dimension are explored, showing the importance of orientation relative to the point spread function. We present a prototype device for performing swept synthetic aperture imaging using a conventional 1-D array transducer and ultrasound research scanner. Point target reconstruction error for a 44.2 degree sweep shows a reconstruction precision of 82.8 μm and 17.8 μm in the lateral and axial dimensions respectively, within the acceptable performance bounds of the simulation model. Improvements in resolution, contrast and contrast-to-noise ratio are demonstrated in vivo and in a fetal phantom.
TL;DR: An efficient method to remove haze from single image based on dark channel prior and the multiple scattering described by atmosphere point spread function (APSF) is proposed in this paper and a superpixel method is employed for estimating the transmission on the sky and non-sky region, in order to mitigate the halo artifact around the sharp edges and reduce color distortion in the sky region.
TL;DR: In this article, a method based on keystone transform, fold factor phase term compensation and generalised dechirp process is proposed to remove the migrations (RM and DFM) and realize the coherent accumulation.
Abstract: Coherent integration for high-speed multi-targets detection is a challenging task in radar applications. First, range migration (RM) and Doppler frequency migration (DFM) induced by target's complex motions (i.e. high speed, acceleration, etc.) would result in serious integration performance loss. Second, if the scattering intensities of different targets differ significantly, the weak one would be shadowed by the strong target and makes it difficult to achieve the coherent accumulation for weak target. Existing methods either perform poorly or are too computationally expensive for coherent integration of high-speed manoeuvring targets. Two contributions are made towards addressing these limitations. First, a method based on keystone transform, fold factor phase term compensation and generalised dechirp process is proposed to remove the migrations (RM and DFM) and realise the coherent accumulation. Compared with the generalised Radon Fourier transform algorithm, the proposed method can avoid the blind speed sidelobe and has a much lower computational cost. Second, two CLEAN techniques based on sinc-like point spread function (PSF) and modified PSF are presented to eliminate the strong target's effect and highlight the weak ones. By this way, the coherent integration of strong target and weak ones can be achieved iteratively. Several simulations are provided to demonstrate the effectiveness.
TL;DR: A novel subtraction microscopy algorithm, exploiting fluorescence emission difference or switching laser mode and their derivatives for image enhancement, using the weighted subtraction coefficient, adjusted pixel-by-pixel with respect to the intensity distributions of initial images.
Abstract: We propose and demonstrate a novel subtraction microscopy algorithm, exploiting fluorescence emission difference or switching laser mode and their derivatives for image enhancement. The key novelty of the proposed approach lies in the weighted subtraction coefficient, adjusted pixel-by-pixel with respect to the intensity distributions of initial images. This method produces significant resolution enhancement and minimizes image distortions. Our theoretical and experimental studies demonstrate that this approach can be applied to any optical microscopy techniques, including label free and non-linear methods, where common super-resolution techniques cannot be used.
TL;DR: It is shown that with spatially incoherent illumination, the point spread function (PSF) width/spatial resolution of an imaging interferometer like that used in full-field optical coherence tomography (OCT) is almost insensitive to aberrations.
Abstract: We show that with spatially incoherent illumination, the point spread function (PSF) width/spatial resolution of an imaging interferometer like that used in full-field optical coherence tomography (OCT) is almost insensitive to aberrations. In these systems, aberrations mostly induce a reduction of the signal level that leads to a loss of the signal-to-noise ratio without broadening the system PSF. This is demonstrated by comparison with traditional scanning OCT and wide-field OCT with spatially coherent illuminations. Theoretical analysis and numerical calculation as well as experimental results are provided to show this specific merit of incoherent illumination in full-field OCT. To the best of our knowledge, this is the first time that such a result has been demonstrated.
TL;DR: It is shown that the position of single molecules in all three spatial dimensions can be estimated alongside its emission color by diffractive optics based design of the Point Spread Function (PSF).
Abstract: We show that the position of single molecules in all three spatial dimensions can be estimated alongside its emission color by diffractive optics based design of the Point Spread Function (PSF). The phase in a plane conjugate to the aperture stop of the objective lens is modified by a diffractive structure that splits the spot on the camera into closely spaced diffraction orders. The distance between and the size of these sub-spots are a measure of the emission color. Estimation of the axial position is enabled by imprinting aberrations such as astigmatism and defocus onto the orders. The overall spot shape is fitted with a fully vectorial PSF model. Proof-of-principle experiments on quantum dots indicate that a spectral precision of 10 to 20 nm, an axial localization precision of 25 to 50 nm, and a lateral localization precision of 10 to 30 nm can be achieved over a 1 μm range of axial positions for on average 800 signal photons and 17 background photons/pixel. The method appears to be rather sensitive to PSF model errors such as aberrations, giving in particular rise to biases in the fitted wavelength of up to 15 nm.
TL;DR: A dynamic imaging model based on a line segment spread function that reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius is established.
Abstract: Under dynamic conditions, star spots move across the image plane of a star tracker and form a smeared star image. This smearing effect increases errors in star position estimation and degrades attitude accuracy. First, an analytical energy distribution model of a smeared star spot is established based on a line segment spread function because the dynamic imaging process of a star tracker is equivalent to the static imaging process of linear light sources. The proposed model, which has a clear physical meaning, explicitly reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius. Furthermore, an analytical expression of the centroiding error of the smeared star spot is derived using the proposed model. An accurate and comprehensive evaluation of centroiding accuracy is obtained based on the expression. Moreover, analytical solutions of the optimal parameters are derived to achieve the best performance in centroid estimation. Finally, we perform numerical simulations and a night sky experiment to validate the correctness of the dynamic imaging model, the centroiding error expression, and the optimal parameters.
TL;DR: The effect of Airy illumination on the image quality and depth penetration of digitally scanned light-sheet microscopy in turbid neural tissue is investigated and it is found that the improvement when using an Airy light-sheets is greater in the presence of stronger sample-induced aberrations.
Abstract: We have investigated the effect of Airy illumination on the image quality and depth penetration of digitally scanned light-sheet microscopy in turbid neural tissue. We used Fourier analysis of images acquired using Gaussian and Airy light-sheets to assess their respective image quality versus penetration into the tissue. We observed a three-fold average improvement in image quality at 50 μm depth with the Airy light-sheet. We also used optical clearing to tune the scattering properties of the tissue and found that the improvement when using an Airy light-sheet is greater in the presence of stronger sample-induced aberrations. Finally, we used homogeneous resolution probes in these tissues to quantify absolute depth penetration in cleared samples with each beam type. The Airy light-sheet method extended depth penetration by 30% compared to a Gaussian light-sheet.
TL;DR: It is shown that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density.
Abstract: Fourier ptychographic microscopy (FPM) is implemented through aperture scanning by an LCOS spatial light modulator at the back focal plane of the objective lens. This FPM configuration enables the capturing of the complex scattered field for a 3D sample both in the transmissive mode and the reflective mode. We further show that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density. This implementation expands the scope of application for FPM and can be beneficial for areas such as tissue imaging and wafer inspection.
TL;DR: A compressive video microscope based on structured illumination with incoherent light source that allows the emission photons being collected by the full aperture of the microscope objective, and thus is suitable for the fluorescence readout mode is presented.
Abstract: We present a compressive video microscope based on structured illumination with incoherent light source. The source-side illumination coding scheme allows the emission photons being collected by the full aperture of the microscope objective, and thus is suitable for the fluorescence readout mode. A 2-step iterative reconstruction algorithm, termed BWISE, has been developed to address the mismatch between the illumination pattern size and the detector pixel size. Image sequences with a temporal compression ratio of 4:1 were demonstrated.
TL;DR: In this paper, a method for estimating the spatial resolution of real images from a logarithmic intensity plot in the Fourier domain is presented. But the method is not suitable for the detection limit of high-angle diffraction in reciprocal space.
Abstract: Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high-angle diffraction in reciprocal space. In electron microscopy, correlation in the Fourier domain is used for estimating the resolution. In this paper, we report a method for estimating the spatial resolution of real images from a logarithmic intensity plot in the Fourier domain. The logarithmic intensity plots of test images indicated that the full width at half maximum of a Gaussian point spread function can be estimated from the images. The spatial resolution of imaging X-ray microtomography using Fresnel zone-plate optics was also estimated with this method. A cross section of a test object visualized with the imaging microtomography indicated that square-wave patterns up to 120-nm pitch were resolved. The logarithmic intensity plot was calculated from a tomographic cross section of brain tissue. The full width at half maximum of the point spread function estimated from the plot coincided with the resolution determined from the test object. These results indicated that the logarithmic intensity plot in the Fourier domain provides an alternative measure of the spatial resolution without explicitly defining a noise criterion.
TL;DR: In this paper, the point spread function width of an imaging interferometer like that used in full-field optical coherence tomography (FFOCT) is almost insensitive to aberrations that mostly induce a reduction of the signal level without broadening.
Abstract: We show that with spatially incoherent illumination, the point spread function width of an imaging interferometer like that used in full-field optical coherence tomography (FFOCT) is almost insensitive to aberrations that mostly induce a reduction of the signal level without broadening. This is demonstrated by comparison with traditional scanning OCT and wide-field OCT with spatially coherent illuminations. Theoretical analysis, numerical calculation as well as experimental results are provided to show this specific merit of incoherent illumination in full-field OCT. To the best of our knowledge, this is the first time that such result has been demonstrated.
TL;DR: The extended fractional Fourier transform is introduced to address the single lens imaging with a fast algorithm for the transform by convolution combined with parallel iterative phase retrieval algorithm to reconstruct the complex amplitude of the object.
Abstract: A moveable lens is used for determining amplitude and phase on the object plane. The extended fractional Fourier transform is introduced to address the single lens imaging. We put forward a fast algorithm for the transform by convolution. Combined with parallel iterative phase retrieval algorithm, it is applied to reconstruct the complex amplitude of the object. Compared with inline holography, the implementation of our method is simple and easy. Without the oversampling operation, the computational load is less. Also the proposed method has a superiority of accuracy over the direct focusing measurement for the imaging of small size objects.